Smartphone Selection with HF-MEREC-COBRA and HF-MEREC-TOPSIS

Abstract

In the rapidly changing world of e-commerce logistics, selecting the best custom-designed smartphone is crucial for operational efficiency. Motivated by this need, in this study, a hybrid multi-criteria decision-making (MCDM) approach is presented for assessing custom-designed smartphones for a crowdsourced e-commerce logistics firm in Turkey, HepsiJET. This approach addresses various possibly contradictory qualitative and quantitative criteria, requiring a hybrid MCDM method like the proposed HF-MEREC-COBRA (hesitant fuzzy - Method based on the Removal Effects of Criteria - Comprehensive Distance Based Ranking) for decision-making. The HF-MEREC-COBRA method uses the hesitant fuzzy Method based on the Removal Effects of Criteria (HF-MEREC) to compute criteria weights, followed by the use of hesitant fuzzy Comprehensive Distance Based Ranking (HF-COBRA) to evaluate and rank smartphone options. Integration of MEREC and COBRA methods with the use of Hesitant Fuzzy Linguistic Term Sets (HFLTS) and the concept of hesitant fuzzy sets (HFS), namely HF-MEREC-COBRA, has never been studied in the literature. For comparative analysis, the HF-MEREC-TOPSIS (HF-MEREC-Technique for Order Preference by Similarity to Ideal Solution) method is also applied to the same problem. A case study is conducted where five smartphone alternatives are evaluated by five expert decision-makers (DMs) using twenty-seven evaluation criteria. Both HF-MEREC-COBRA and HF-MEREC-TOPSIS methods yielded the same ranking, which resulted in Xiaomi Redmi Note 11 Pro 128 GB 8 GB Ram (A2) being the best alternative. A sensitivity analysis is performed, revealing that HF-MEREC-COBRA maintains strong robustness against moderate variations, up to ±40%, in criterion weights.

Introduction

Mobile gadgets are becoming more and more essential to human life as they develop. It is no longer enough to call them phones; they have evolved beyond this conventional role to become the main tool for a variety of tasks, such as internet shopping, financial transactions, and email correspondence. As such, they are aptly referred to as smartphones, a phrase that appropriately captures their multipurpose nature. Global smartphone usage data show how common smartphones are becoming, with an estimated 7.4 billion smartphone users by 2024. This number is expected to rise to almost 7.9 billion by 2028, highlighting the continued growth and importance of these gadgets in the digital age (Ericsson, 2024). Due to the influence of social media and the development of internet-based communication channels, smartphone usage has increased significantly in Turkey. Over 68 million people in the nation owned smartphones by 2022, demonstrating a high level of digital penetration. At the same time, since 2010, sales of mobile phones have significantly increased worldwide. In 2010, 297 million smartphones were sold globally; by 2021, that number had risen to 1.43 billion. This exponential increase demonstrates the smartphone market's dynamic character and rising demand. International businesses are increasingly competing for market share in the fiercely competitive smartphone sales scene. With new businesses struggling for market share, competition is getting fiercer every day. Brands like Xiaomi and Huawei have significantly increased their market share in Turkey; during the last four years, each has seen a growth of more than 10%. Well-known companies like Samsung, Apple, Huawei, and Xiaomi enhance this competitive climate even more and together create a lively and dynamic market.

Besides the extensive adoption of smartphones, Turkey's logistics industry has been undergoing a major shift, largely driven by the rapid growth of e-commerce and the increasing use of crowdsourced delivery models. Companies like HepsiJET have become noticeable players in this changing environment, using digital platforms and freelance couriers to meet increasing customer expectations. The logistics sector in Turkey, now worth over $100 billion, continues to grow due to urban development, digital innovation, and ongoing investments in infrastructure. In such a rapidly growing and competitive environment, smartphones have become essential tools for couriers, helping them navigate routes, stay connected, and manage tasks efficiently. Choosing the right smartphone is not an easy task, involving multiple potentially conflicting criteria; therefore, it is really critical to have a structured, reliable method for evaluating and selecting the most suitable smartphones.

The fact that smartphones greatly improve people's lives is the reason for the increasing prevalence of phone use. With just their smartphones, people may travel from one place to another. Smartphones are quite convenient for people who need to change directions while driving, even if they are not used for conversation. According to reports, 46% of smartphone users regularly used navigation apps between July 2021 and June 2022 (Ericsson, 2024). In the logistics industry, drivers and couriers greatly benefit from navigation software. As a result, mobile phone use has become essential to logistics. Numerous smartphone applications, especially those for fleet management, benefit logistics firms; the increased popularity and dependability of navigation apps worldwide have also improved logistics firms’ efficiency. Navigation apps have helped almost every courier and driver in logistics companies.

Logistics firms use Industry 4.0 to improve their operational efficiency by implementing new technologies. Logistics organizations may now stand out in a highly competitive market thanks to innovations like route optimization, machine learning applications, and company-specific mobile applications (Bayram et al., 2023; Kup et al., 2023; Türkmen et al., 2023). Logistics businesses are moving closer to operational excellence in their last-mile operations by including capabilities like barcode readers, point-to-point navigation, and route optimization into their smartphone applications. The phones used by couriers must automatically overcome specific hardware and software restrictions to take full advantage of these benefits. Using smartphones that meet certain hardware and software requirements will make operational transactions more convenient for couriers. It has become difficult for couriers to choose the best phone in the current situation, when there are many smartphone options and many competing criteria to take into consideration. A support system, more specifically a comprehensive MCDM method, is required to help logistics firms and crowdsourced couriers make phone selections, where various conflicting criteria are crucial. Hence, this study focuses on the development of a novel MCDM method, the HF-MEREC-COBRA method, to rank smartphone alternatives. In this research, for validation purposes, another MCDM method, HF-MEREC-TOPSIS, is utilized. In both methods, HF-MEREC is initially used to compute the importance criteria weights, and then HF-COBRA or HF-TOPSIS is utilized to rank the alternatives from best to worst.

In this study, HF-MEREC and HF-COBRA are integrated, and a method called HF-MEREC-COBRA is proposed to have both methods’ advantages. In MEREC, the change in criteria weights determines the weight of a criterion (Ecer & Aycin, 2023; Ecer & Pamucar, 2022; Kaya et al., 2023). This characteristic separates MEREC from other methods utilized for the determination of weights, such as “Shannon's entropy”, “AHP (Analytic Hierarchy Process)”, “CRITIC (CRiteria Importance Through Inter-criteria Correlation)”, etc. (Ecer & Aycin, 2023). The benefits of MEREC over conventional methods include straightforward computation, easy comprehension, and a strong mathematical foundation (Ecer & Aycin, 2023; Ecer and Hashemkhani Zolfani, 2022). Subjective methods such as AHP, ANP (Analytic Network Process), BWM, and SMART (Simple Multi-Attribute Rating Technique) are not efficient when there are many criteria, since the accuracy of decision-makers’ preferences decreases due to mental tasks. However, in an objective weighing method such as MEREC, decision-makers have no role in determining the weights (Alfares & Duffuaa, 2015). Since MEREC uses the removal effects of each criterion on the performance of alternatives for computing the weights, this perspective might also help decision-makers to exclude some criteria from consideration (Keshavarz-Ghorabaee et al., 2021). COBRA (Krstić et al., 2022a) on the other hand, is a distance-based method that evaluates options by combining two distance measurements (Euclidean and taxicab) from three distinct solution types: average, nadir, and ideal. The primary advantage of this method is its thoroughness. By truly separating the distances of alternatives using Euclidean and Taxicab distances, COBRA increases the dependability of the results (Krstić et al., 2022a). In this research, HF-MEREC-TOPSIS is used for validation since TOPSIS is user-friendly and returns precise results. Through the use of “Hesitant Fuzzy Linguistic Term Sets (HFLTS)” and the concept of “hesitant fuzzy sets (HFS)” (Torra, 2010; Torra & Narukawa, 2009), HF-MEREC-COBRA and HF-MEREC-TOPSIS address the ambiguity, uncertainty, and hesitations inherent in human judgment, which is beneficial in complicated decision-making scenarios. In both methods, the “fuzzy envelope approach” (Liu & Rodríguez, 2014) is used for converting HFLTS evaluations to related “Triangular fuzzy numbers (TFNs)”. The motivation of this study is that the integration of HFLTS and HFS concepts with the MEREC and COBRA methods (HF-MEREC-COBRA) to solve a MCDM problem has not yet been explored in the literature. The research question of this study can be stated as “How can HF-MEREC-COBRA improve the robustness and effectiveness of smartphone selection for crowdsourced e-commerce logistics operations?” In the next sections, to answer this question, details of HF-MEREC-COBRA and HF-MEREC-TOPSIS are presented along with a case study about evaluating custom-designed smartphones for a crowdsourced e-commerce logistics firm in Turkey and a sensitivity analysis to reveal the effects of criterion weight changes.

2. Literature Review

In the literature, assessment of smartphones with MCDM methods has been pursued in several studies. Işıklar and Büyüközkan (2007) and Gangurde and Akarte (2013) first applied the Analytic Hierarchy Process (AHP) to determine the weights of the criteria, and then TOPSIS, to rank mobile phone options. Rezaei (2015) implemented the best-worst method (BWM) for phone selection. Yildiz and Ergul (2015) first employed the Analytic Network Process (ANP) and then the generalised Choquet integral (GCI) method for evaluation and selection of smartphones. Büyüközkan and Güleryüz (2016) explored the Intuitionistic Fuzzy sets with TOPSIS (IF-TOPSIS) to evaluate smartphone alternatives concerning various criteria. Deb et al. (2018) employed AHP to evaluate criteria and then rank mobile phones. Perçin and Pancarooğlu (2019) explored the integrated Structural Equation Model (SEM) – AHP to rank smartphone alternatives. Saqlain et al. (2020) developed the neutrosophic fuzzy TOPSIS and applied the method to rank smartphone options. Singh et al. (2020) implemented Kano model to identify Kano categories of all features with a customer survey, fuzzy AHP to calculate criteria weights, and then TOPSIS to determine the ranking of alternatives. Dahooie et al. (2021) explored “Integrated Determination of Objective Criteria Weights (IDOCRIW)” method with intuitionistic fuzzy sets (IFS) to determine criteria weights, and then the “Intuitionistic Fuzzy Multiple Objective Optimization based on a ratio analysis plus a full multiplicative form (IF-MULTIMOORA)” method to rank the mobile phones. To the best of the authors’ knowledge, HF-MEREC-COBRA has never been utilized for phone selection or any other MCDM problem.

In the literature, various versions of the fuzzy MEREC method were utilized to determine (fuzzy) criteria weights in combination with some other ranking methods. Hezam et al. (2022) worked on a combined intuitionistic fuzzy MEREC and Ranking Sum method to evaluate weights objectively and subjectively, and then implemented the intuitionistic fuzzy “double normalization-based multi-aggregation (DNMA)” method to rank alternative fuel vehicles. Wan et al. (2023) utilized spherical fuzzy MEREC to compute weights of criteria and then spherical fuzzy CoCoSo (COmbined COmpromise SOlution) to rank solar power station locations. Makki and Abdulaal (2023) applied fuzzy MEREC using the geometric mean (fuzzy MEREC-G) to compute fuzzy weights and then fuzzy RATMI (ranking the alternatives based on the trace to median index) to rank forklift alternatives to purchase for a warehouse. Zhang et al. (2023) combined spherical fuzzy sets, prospect theory, and EDAS (extending evaluation based on distance from average solution) and ranked stock investments after calculating weights with MEREC. Liu et al. (2023) implemented generalized hesitant fuzzy (GHF) entropy and GHF-MEREC to determine the criteria weights and then GHF-EDAS to select energy projects. Chaurasiya and Jain (2023) studied the intuitionistic fuzzy-MEREC-SWARA (Stepwise Weight Assessment Ratio Analysis)-CoCoSo method for assessing plastic waste disposal technologies. In their study, objective weights were found with MEREC, subjective weights were evaluated with SWARA, and then alternatives were ranked with CoCoSo utilizing intuitionistic fuzzy sets. Afterwards, Chaurasiya and Jain (2024) employed Pythagorean fuzzy MEREC-SWARA to determine objective and subjective weights, and then Pythagorean fuzzy ARAS (Additive Ratio Assessment approach) to select internet of things adaptation for smart city waste management. Abdelaal et al. (2024) employed fuzzy MEREC-G for the computation of criteria weights and then fuzzy TOPSIS to assess strategic objectives and projects in Saudi Arabian universities. Liu et al. (2024) developed MEREC-TODIM (an acronym in Portuguese for Interactive MCDM) with probabilistic HFS and applied it to examples related to “Carbon Capture Utilization Storage and PhD Admission Interviews”. Nedeljković et al. (2024) employed fuzzy MEREC to determine criteria weights and then the fuzzy RAWEC (Ranking of Alternatives with Weights of Criterion) method to rank different cabbage sales channels in the Semberija region. Mao et al. (2024) applied MEREC and ANP with HFLTS and TFN to assess risk criteria related to “deep-sea floating offshore wind power projects”. Mondal et al. (2024) implemented the Pythagorean fuzzy MEREC to compute fuzzy criteria weights and then the Pythagorean fuzzy MARCOS (measurement alternatives and ranking according to compromise solution) to rank sustainable forest management models. Olteanu (Burcă) et al. (2024) employed fuzzy MEREC to calculate weights of criteria and then the fuzzy AROMAN (Alternative Ranking Order Method Accounting for two-step Normalization) method to rank European investment sectors.

The fuzzy version of the COBRA method (fuzzy COBRA) has been the focus of research for only a few research papers in the literature. Krstic et al. (2022b) employed fuzzy Delphi-ANP to compute criteria weights and then fuzzy COBRA to rank smart reverse logistics development scenarios. Tadic et al. (2023) implemented fuzzy AHP to compute criteria weights and then fuzzy COBRA to rank smart material handling solutions in logistics centers. Tadic et al. (2024) applied “fuzzy Delphi-based fuzzy factor relationship (Fuzzy D-FARE)” and fuzzy COBRA methods to evaluate tactics to defeat obstacles for drone use in “Last-Mile Logistics”. Zorlu et al. (2024) implemented SWARA -COBRA with Spherical Fuzzy Sets to assess geosites of Aksaray, Turkey. To the best of the authors’ knowledge, HF-COBRA has never been studied in the literature. Kang et al. (2024) integrated logarithmic percentage change-driven objective weighting (LOPCOW) and COBRA methods with Probabilistic Picture Fermatean (PPF) Fuzzy Sets and evaluated hydrokinetic energy harnessing technologies for various marine and river-based applications.

Integration of MEREC and COBRA has been applied in a few research papers. Taşçi (2024) applied SWARA-MEREC-COBRA to evaluate the sustainability performance of Anadolu Insurance company, where SWARA was used to compute criteria weights subjectively and MEREC, objectively, and then COBRA was utilized to determine the performance rankings. Asker (2024) employed MEREC-COBRA to analyze the Covid-19 pandemic's effect on the financial performance of airlines. MEREC was utilized to weigh the financial ratios of airlines, and then COBRA was applied to rank the financial performances. In Table 1, as a summary, at first, MCDM methods utilized for phone evaluation are presented, and then applications of various versions of the MEREC and COBRA methods are given. To the best of the authors’ knowledge, in the literature, HF-MEREC-COBRA has never been studied. Therefore, the novelty of this study is the presentation of HF-MEREC-COBRA method, applied to a MCDM problem.

Table 1.

MCDM Methods Utilized for Phone Evaluation and Applications various Versions of MEREC and COBRA Methods.

Study	Method(s) Used	Application	Study	Method(s) Used	Application
Işıklar and Büyüközkan (2007)	AHP + TOPSIS	Mobile phone selection	Deb et al. (2018)	AHP	Mobile phone ranking
Gangurde and Akarte (2013)	AHP + Modified TOPSIS	Mobile phone selection	Perçin and Pancarooğlu (2019)	SEM + AHP	Smartphone selection
Rezaei (2015)	BWM	Phone selection	Saqlain et al. (2020)	Neutrosophic Fuzzy TOPSIS	Smartphone ranking
Yildiz and Ergul (2015)	ANP + GCI	Smartphone selection	Singh et al. (2020)	Kano + Fuzzy AHP + TOPSIS	Mobile phone selection
Büyüközkan and Güleryüz (2016)	Intuitionistic fuzzy TOPSIS	Smartphone evaluation	Dahooie et al. (2021)	Intuitionistic fuzzy IDOCRIW  + MULTIMOORA	Mobile phone selection
Study	Method(s) Used	Application	Study	Method(s) Used	Application
Hezam et al. (2022)	Intuitionistic fuzzy MEREC + ranking sum + DNMA	Alternative fuel vehicles	Mao et al. (2024)	MEREC + ANP + HFLTS	Offshore wind risk assessment
Wan et al. (2023)	Spherical fuzzy MEREC + CoCoSo	Solar power site selection	Mondal et al. (2024)	Pythagorean fuzzy -MEREC + MARCOS	Forest management
Makki and Abdulaal (2023)	Fuzzy MEREC-G + RATMI	Forklift selection	Olteanu (Burcă) et al. (2024)	fuzzy MEREC + AROMAN	Investment sector ranking
Zhang et al. (2023)	Spherical fuzzy + prospect theory + EDAS	Stock investment	Krstic et al. (2022b)	Fuzzy Delphi-ANP + COBRA	Reverse logistics
Liu et al. (2023)	GHF Entropy + GHF-MEREC + EDAS	Energy project selection	Tadic et al. ( 2023)	Fuzzy AHP + COBRA	Material handling in logistics
Chaurasiya and Jain (2023)	Intuitionistic fuzzy MEREC + SWARA  + CoCoSo	Plastic waste disposal	Tadic et al. (2024)	Fuzzy D-FARE + COBRA	Drone logistics
Chaurasiya and Jain (C2024)	Pythagorean fuzzy MEREC + SWARA  + ARAS	IoT for smart cities	Zorlu et al. (2024)	Spherical Fuzzy SWARA + COBRA	Geosite assessment
Abdelaal et al. (2024)	Fuzzy MEREC-G + TOPSIS	University project evaluation	Kang et al. (2024)	LOPCOW + COBRA  + PPF Sets	Hydrokinetic energy
Liu et al. (2024)	Probabilistic HFS + MEREC + TODIM	Carbon capture, PhD interviews	Taşçi (2024)	SWARA + MEREC  + COBRA	Insurance sustainability
Nedeljkovic et al. ( 2024)	Fuzzy MEREC + RAWEC	Agricultural sales channels	Asker (2024)	MEREC + COBRA	Airline financial performance, impact of COVID-19

3. Methodology

3.1. Hesitant Fuzzy Sets (HFS) Theory and “Fuzzy Envelope Approach”

In HF-MEREC-COBRA and HF-MEREC-TOPSIS, “fuzzy envelope approach” (Liu & Rodríguez, 2014) is utilized for hesitant evaluations, and matching TFNs are defined. With this method, based on the HFLTS, and the concept of HFS. (Torra, 2010; Torra & Narukawa, 2009), verbal representations can be represented by a TFN. Here, more specifically, “Triangular Hesitant Fuzzy Sets (THFS)” are employed to describe the doubtful data, and hesitation and ambiguity of preferences of DMs. “Fuzzy set theory contains classes with soft boundaries” (Klir & Yuan, 1995; Lootsma, 1997) and using “fuzzy set theories, crisp ones can be fuzzified” (Zadeh, 1994). A “fuzzy number” is a fuzzy set $F=\{(x,{\mu }_F(x)),x\in R\}$ where x is $R:-\mathrm{\infty }<x<+\mathrm{\infty }\text{; }$ and ${\mu }_F(x)$ is from R to [0, 1]. TFNs are simple to employ hence it is commonly employed. A TFN, $\tilde{M}=(l,m,u)\text{; }l\le m\le u$ , has “triangular type membership function”;

$$\begin{array}{r}{\mu }_F(x)=\{\begin{array}{c}0x<l\\ x-l/m-ll\le x\le m\\ u-x/u-mm\le x\le u\\ 0x>u\end{array}\end{array}$$

(1)

Arithmetic operations with two positive TFNs $\tilde{P}=(l_1,m_1,u_{1\text{; }}),\tilde{R}=(l_2,m_2,u_2)l_1\le m_1\le u_1,l_2\le m_2\le u_{2\text{; }}$ and a “crisp number” C are given as (Anojkumar et al., 2014; Samanlioglu & Ayağ, 2021; Wu et al., 2016):

$$\begin{array}{rl}\tilde{P}+\tilde{R}& =(l_1+l_2,m_1+m_2,u_1+u_2)\end{array}$$

(2)

$$\begin{array}{rl}\tilde{P}+C& =(l_1+C,m_1+C,u_1+C)\end{array}$$

(3)

$$\begin{array}{rl}\tilde{P}-\tilde{R}& =(l_1-u_2,m_1-m_2,u_1-l_2)\end{array}$$

(4)

$$\begin{array}{rl}\tilde{P}-C& =(l_1-C,m_1-C,u_1-C)\end{array}$$

(5)

$$\begin{array}{rl}\tilde{P}*\tilde{R}& =(l_1*l_2,m_1*m_2,u_1*u_2)\end{array}$$

(6)

$$\begin{array}{rl}\tilde{P}*C& =(l_1*C,m_1*C,u_1*C)forC\ge 0\text{; }\end{array}$$

(7)

$$\begin{array}{rl}\frac{\tilde{P}}{\tilde{R}}& =\left(\frac{l_1}{u_2},\frac{m_1}{m_2},\frac{u_1}{l_2}\right)\end{array}$$

$$\begin{array}{rl}\frac{\tilde{P}}{\tilde{R}}& =\left(min\left(\frac{l_1}{l_2},\frac{l_1}{u_2},\frac{u_1}{l_2},\frac{u_1}{u_2}\right),\frac{m_1}{m_2},max\left(\frac{l_1}{l_2},\frac{l_1}{u_2},\frac{u_1}{l_2},\frac{u_1}{u_2}\right)\right)\text{if}\tilde{P}\text{and}\tilde{R}\text{are}\text{two}\text{TFNs}.\end{array}$$

(8)

$$\begin{array}{rl}\frac{\tilde{P}}{C}& =\left(\frac{l_1}{C},\frac{m_1}{C},\frac{u_1}{C}\right)\text{; }for\text{; }C>0\end{array}$$

(9)

$$\begin{array}{rl}{\tilde{P}}^{-1}& =\left(\frac{1}{\text{; }{u}_1},\frac{1}{\text{; }{m}_1},\frac{1}{\text{; }{l}_1}\right)\end{array}$$

(10)

$$\begin{array}{rl}& \begin{array}{ll}MAX(\tilde{P}+\tilde{R})& =(max(l_1,l_2),max(\text{; }{m}_1,m_2),\text{max}(\text{; }{u}_1,u_2))\text{and}\\ MIN(\tilde{P}+\tilde{R})& =(min(l_1,l_2),min(\text{; }{m}_1,m_2),\text{min}(\text{; }{u}_1,u_2))\end{array}\end{array}$$

(11)

$$\begin{array}{rl}Crisp(\tilde{P})& =\frac{(4m_1+l_1+u_1)}{6}(‘‘\text{to}\text{defuzzify},\text{the}\text{graded}\text{mean}\text{integration}\text{approach}")(\text{Yong},2006)\end{array}$$

(12)

In THFS, the membership degree of an element is expressed with TFNs. If Y is a fixed set, the HFS on Y gives back a subset of $[0,1]$ by:

$$\begin{array}{r}K=\left\{⟨y,h_N(y)⟩|y\in Y\right\}\end{array}$$

(13)

where $h_N(y)$ is the “possible membership degree” of element $y\in Y$ to set N with values in $[0,1]$ . The lower and upper bounds are:

$$\begin{array}{r}{h}_{(y)}^{-}=minh(y),\text{; }{h}_{(y)}^{+}=maxh(y).\text{; }\end{array}$$

(14)

Several operations for 2 HFS h₁, h₂ are:

$$\begin{array}{rl}{h_1}^{\gimel }& ={\cup }_{\gamma \in h_1}\{{\gamma }^{\gimel }\}\text{; }\end{array}$$

(15)

$$\begin{array}{rl}\gimel h_1& ={\cup }_{\gamma \in h_1}\{1-{(1-\gamma )}^{\gimel }\}\end{array}$$

(16)

$$\begin{array}{rl}{h}_1\pm h_2& ={\cup }_{\gamma 1\in h1,\gamma 2\in h2}\{{\gamma }^1+{\gamma }^2-{\gamma }^1{\gamma }^2\}\end{array}$$

(17)

$$\begin{array}{rl}{h}_1\cap h_2& ={\cup }_{\gamma 1\in h1,\gamma 2\in h2}min\{{\gamma }^1,{\gamma }^2\}\text{and}{h}_1\cup h_2={\cup }_{\gamma 1\in h1,\gamma 2\in h2}max\{{\gamma }^1,{\gamma }^2\}\end{array}$$

(18)

$$\begin{array}{rl}{h}_1\otimes h_2& ={\cup }_{\gamma 1\in h1,\gamma 2\in h2}\{{\gamma }^1{\gamma }^2\}.\end{array}$$

(19)

An “Ordered Weighting Averaging (OWA)” operator is given as:

$$\begin{array}{r}OWA(a_1,a_2,\dots ,a_n)=\sum _{j=1}^n{w}_j{b}_j\end{array}$$

(20)

where, $b_j$ is the j^th largest of $a_1,a_2,\dots ,a_n$ , $w_j\in [0,1]\text{; ; }\mathrm{\forall }j\text{; }and\text{; }\sum _{j=1}^n{w}_j=1.\text{; }$ (Ayağ & Samanlioglu, 2021; Başar, 2017; Samanlioglu & Ayağ, 2020, 2021)

Here, “fuzzy envelope approach” (Liu & Rodríguez, 2014) is used to associate DM's hesitant evaluations. DM's assessment scales are sorted so that the lowest is $s_l$ and the highest is $s_h$ . If the DM's assessments are between $s_i$ and $s_j$ , then $s_l\le s_i\le s_j\le s_h$ .

With the HFLTS, “linguistic terms” can be expressed by a TFN $\tilde{A}=(d,e,f)$ , and a, b and c are:

$$\begin{array}{rl}d& =min\{d_L^i,d_M^i,d_M^{i+1},\dots ,d_M^j,d_R^j\}=d_L^i\text{; }\end{array}$$

(21)

$$\begin{array}{rl}e& =\{\begin{array}{l}{d}_M^{i}ifi+1=j\\ OW{A}_W\{d_M^i,d_M^{i+1},\dots ,d_M^j\}otherwise\end{array}\text{; }\end{array}$$

(22)

$$\begin{array}{rl}f& =max\{d_L^i,d_M^i,d_M^{i+1},\dots ,d_M^j,d_R^j\}=d_R^j\text{; }\end{array}$$

(23)

“Weight vector in OWA operator” (Filev & Yager, 1998) is given as:

$$\begin{array}{r}{w}_1={\beta }^{n-1},w_2=(1-\beta ){\beta }^{n-2},\dots ,w_n=(1-\beta ),\text{where}\beta =\frac{l-j+i}{l-1}\end{array}$$

(24)

Here, l is “the number of terms” in scale in Table 2, “j is the rank of the highest, and i is the rank of the lowest assessment value. i and j can be ranks from 0 to l, and n = j-i.” (Başar, 2017; Samanlioglu & Ayağ, 2020, 2021)

Table 2.

Utilized Scale in HF-MEREC-COBRA and HF-MEREC- TOPSIS.

“Linguistic terms”	“TFN”
“Very poor (VP)”	“(0,0,1)”
“Poor (P)”	“(0,1,3)”
“Medium poor (MP)”	“(1,3,5)”
“Fair (F)”	“(3,5,7)”
“Medium good (MG)”	“(5,7,9)”
“Good (G)”	“(7,9,10)”
“Very good (VG)”	“(9,10,10)”

In HF-MEREC-COBRA and HF-MEREC-TOPSIS, first, the weights of criteria are defined with HF-MEREC, and then, utilizing HF-COBRA and HF-TOPSIS, smartphone alternatives are ranked from best to worst. The scale utilized in HF-MEREC-COBRA and HF-MEREC-TOPSIS is given in Table 2 (Samanlioglu & Ayağ, 2021; Samanlioglu et al., 2018). In HF-MEREC-COBRA and HF-MEREC-TOPSIS, DMs evaluate alternatives with respect to each criterion with the linguistic terms in Table 2. Then, “fuzzy envelope approach” is utilized with Eqs. (20)-(24), and from these linguistic assessments of DMs’, corresponding TFNs are obtained. Afterwards, ${\tilde{z}}_{ij}=\frac{1}{K}({\tilde{z}}_{ij}^1(+){\tilde{z}}_{ij}^2(+)\dots (+)z_{ij}^K)$ is calculated, where ${\tilde{z}}_{ij}^K=(a_{ij}^K,b_{ij}^K,c_{ij}^K)\mathrm{\forall }i,j,k$ is the corresponding TFN of the K^th DM. With m alternatives and n criteria, mxn fuzzy decision matrix $\begin{array}{ccccc}\widetilde{z_{11}}& \widetilde{z_{12}}& ..& ..& \widetilde{z_{1n}}\\ \widetilde{z_{21}}& \widetilde{z_{22}}& ..& ..& \widetilde{z_{2n}}\\ ..& ..& ..& ..& ..\\ ..& ..& ..& ..& ..\\ \widetilde{z_{n1}}& \widetilde{z_{n2}}& ..& ..& \widetilde{z_{mn}}\end{array}$ , with positive TFNs ${\tilde{z}}_{ij}=(a_{ij},b_{ij},c_{ij})\mathrm{\forall }i,j$ is determined.

3.2 HF-MEREC Weight Calculation

The MEREC (Keshavarz-Ghorabaee et al., 2021; Saidin et al., 2023) is a recent MCDM method that gives straightforward and accurate results. This method employs each criterion's removal effect on estimating alternatives to obtain the criteria weights. Evaluating an option based on removing the criterion and considering the deviations is a new concept in determining the criterion weights compared to the most common methods, like AHP and CRITIC. MEREC utilizes the exclusion perspective and elimination-induced effects to obtain the weights of the criteria set rather than the inclusion standpoint, which is the basis of other weighting approaches. Here, the steps are as follows:

Step 1: - $\tilde{Z}=({\tilde{z}}_{ij}{)}_{mxn}$ is normalized with the following Eq. (25) and Eq. (26) and $\tilde{X}=({\tilde{x}}_{ij}{)}_{mxn}$ is obtained.

$$\begin{array}{rl}{\tilde{x}}_{ij}& =\left(\frac{a_{ij}}{c_j^{max}},\frac{b_{ij}}{c_j^{max}},\frac{c_{ij}}{c_j^{max}}\right)\mathrm{\forall }i\text{and}\mathrm{\forall }\text{j}\in \text{B}(\text{benefit}\text{criteria})\end{array}$$

(25)

$$\begin{array}{rl}{\tilde{x}}_{ij}& =\left(\frac{f_j^{min}}{c_{ij}},\frac{f_j^{min}}{b_{ij}},\frac{f_j^{min}}{a_{ij}}\right)\mathrm{\forall }i\text{and}\mathrm{\forall }\text{j}\in \text{C}(\text{cost}\text{criteria})\end{array}$$

(26)

Step 2: $\tilde{X}$ is defuzzified with Eq. (12), $X=(\text{; }{x}_{ij}{)}_{mxn}$ with crisp $x_{ij}$ elements is obtained.

Step 3: Determine the overall performance of each alternative with Eq. (27) (Saidin et al., 2023):

$$\begin{array}{r}{S}_i=\frac{1}{n}\sum _{j=1}^n\ln (1-x_{ij})\mathrm{\forall }i\end{array}$$

(27)

Step 4: Determine the alternatives’ performance by eliminating each criterion with Eq. (28). Here, $S_{ij}^{\mathrm{\prime }}$ is the overall performance of the ith alternative to the elimination of the jth criterion (Saidin et al., 2023).

$$\begin{array}{r}{S}_{ij}^{\mathrm{\prime }}=\frac{1}{n}\sum _{k=1,k\ne j}^n\ln (1-x_{ij})\mathrm{\forall }i,j\end{array}$$

(28)

Step 5: Obtain the aggregate of absolute deviations $d_j$ that represents the result of eliminating the jth criterion.

$$\begin{array}{r}{d}_j=\sum _{i=1}^m|{S^{\mathrm{\prime }}}_{ij}-S_i|\end{array}$$

(29)

Step 6: Calculate the final criterion weights $(w_j)$ for each criterion j.

$$\begin{array}{r}{w}_j=\frac{d_j}{{\sum }_{k=1}^n{d}_k}\end{array}$$

(30)

3.3 HF-COBRA Ranking Method

COBRA (Krstić et al., 2022a) is a MCDM method that ranks alternatives based on comprehensive distances, taking into consideration Euclidean and Taxicab distances from ideal, negative ideal, and average solutions. The steps of the method are as follows:

Step 1: Determine the weighted normalized decision matrix $\tilde{Y}=({\tilde{y}}_{ij}{)}_{mxn}$ with Eq. (31) where ${\tilde{y}}_{ij}=({\alpha }_{ij},{\beta }_{ij},{\gamma }_{ij})$ :

$$\begin{array}{r}{\tilde{y}}_{ij}={\tilde{x}}_{ij}.w_j\end{array}$$

(31)

Step 2: Determine the fuzzy positive ideal $({\widetilde{PIS}}_j)$ , fuzzy negative ideal $({\widetilde{NIS}}_j)$ , and fuzzy average solution $({\widetilde{AS}}_j)$ regarding each criterion j:

$$\begin{array}{rl}{\widetilde{PIS}}_j& =({\alpha }_{kj}^{PIS},{\beta }_{kj}^{PIS},{\gamma }_{kj}^{PIS})=\left(\underset{i}{max}({\alpha }_{ij},\underset{i}{max}({\beta }_{ij})\underset{i}{max}({\gamma }_{ij})\right)\mathrm{\forall }j\in B\end{array}$$

(32)

$$\begin{array}{rl}{\widetilde{PIS}}_j& =({\alpha }_{kj}^{PIS},{\beta }_{kj}^{PIS},{\gamma }_{kj}^{PIS})=\left(\underset{i}{min}({\alpha }_{ij},\underset{i}{min}({\beta }_{ij})\underset{i}{min}({\gamma }_{ij})\right)\mathrm{\forall }j\in C\end{array}$$

(33)

$$\begin{array}{rl}{\widetilde{NIS}}_j& =({\alpha }_{kj}^{NIS},{\beta }_{kj}^{NIS},{\gamma }_{kj}^{NIS})=\left(\underset{i}{min}({\alpha }_{ij},\underset{i}{min}({\beta }_{ij})\underset{i}{min}({\gamma }_{ij})\right)\mathrm{\forall }j\in B\end{array}$$

(34)

$$\begin{array}{rl}{\widetilde{NIS}}_j& =({\alpha }_{kj}^{NIS},{\beta }_{kj}^{NIS},{\gamma }_{kj}^{NIS})=\left(\underset{i}{max}({\alpha }_{ij},\underset{i}{max}({\beta }_{ij})\underset{i}{max}({\gamma }_{ij})\right)\mathrm{\forall }j\in C\end{array}$$

(35)

$$\begin{array}{rl}{\widetilde{AS}}_j& =({\alpha }_{kj}^{AS},{\beta }_{kj}^{AS},{\gamma }_{kj}^{AS})=\left(\underset{i}{\text{mean}}({\alpha }_{ij},\underset{i}{\text{mean}}({\beta }_{ij})\underset{i}{\text{mean}}({\gamma }_{ij})\right)\mathrm{\forall }j\in B,C\end{array}$$

(36)

Step 3: For each alternative i, determine the distance from the positive ideal solution $d{\widetilde{(PIS)}}_i$ , negative ideal solution $d{\widetilde{(NIS)}}_i$ , and positive $d{{\widetilde{(AS)}}_i}^{+}$ and negative $d{{\widetilde{(AS)}}_i}^{-}$ distances from the average solution.

$$\begin{array}{rl}d(\tilde{R}{)}_i& =dE(\tilde{R}{)}_i+{\sigma }_{\tilde{R}}\times dT(\tilde{R}{)}_i\mathrm{\forall }i\end{array}$$

(37)

$$\begin{array}{rl}{\sigma }_{\tilde{R}}& =\underset{i}{max}dE(\tilde{R}{)}_i-\underset{i}{min}dE(\tilde{R}{)}_i\end{array}$$

(38)

where $\tilde{R}$ represents $\widetilde{NIS},\widetilde{PIS},\widetilde{AS}$ and ${\sigma }_{\tilde{R}}$ is the correction coefficient. $dE(\tilde{R})$ is the Euclidean distance and $dT(\tilde{R})$ is the Taxicab distance.

$$\begin{array}{rl}dE{\widetilde{(PIS)}}_i& =\sum _{j=1}^n\sqrt{\frac{({({\alpha }_{kj}^{PIS}-{\alpha }_{ij})}^2+4\times {({\beta }_{kj}^{PIS}-{\beta }_{ij})}^2+{({\gamma }_{kj}^{PIS}-{\gamma }_{ij})}^2)}{6}}\mathrm{\forall }i\end{array}$$

(39)

$$\begin{array}{rl}dT{\widetilde{(PIS)}}_i& =\sum _{j=1}^n\frac{(|{\alpha }_{kj}^{PIS}-{\alpha }_{ij}|+4\times |{\beta }_{kj}^{PIS}-{\beta }_{ij}|+|{\gamma }_{kj}^{PIS}-{\gamma }_{ij}|)}{6}\mathrm{\forall }i\end{array}$$

(40)

$$\begin{array}{rl}dE{\widetilde{(NIS)}}_i& =\sum _{j=1}^n\sqrt{\frac{({({\alpha }_{kj}^{NIS}-{\alpha }_{ij})}^2+4\times {({\beta }_{kj}^{NIS}-{\beta }_{ij})}^2+{({\gamma }_{kj}^{,NIS}-{\gamma }_{ij})}^2)}{6}}\mathrm{\forall }i\end{array}$$

(41)

$$\begin{array}{rl}dT{\widetilde{(NIS)}}_i& =\sum _{j=1}^n\frac{(|{\alpha }_{kj}^{NIS}-{\alpha }_{ij}|+4\times |{\beta }_{kj}^{NIS}-{\beta }_{ij}|+|{\gamma }_{kj}^{NIS}-{\gamma }_{ij}|)}{6}\mathrm{\forall }i\end{array}$$

(42)

$$\begin{array}{rl}dE{{\widetilde{(AS)}}_i}^{+}& =\sum _{j=1}^n\sqrt{\frac{({\rho }_{ij}^{+}{({\alpha }_{kj}^{AS}-{\alpha }_{ij})}^2+4\times {\rho }_{ij}^{+}{({\beta }_{kj}^{AS}-{\beta }_{ij})}^2+{\rho }_{ij}^{+}{({\gamma }_{kj}^{AS}-{\gamma }_{ij})}^2)}{6}}\mathrm{\forall }i\end{array}$$

(43)

$$\begin{array}{rl}dT{{\widetilde{(AS)}}_i}^{+}& =\sum _{j=1}^n\frac{({\rho }_{ij}^{+}|{\alpha }_{kj}^{AS}-{\alpha }_{ij}|+4\times {\rho }_{ij}^{+}|{\beta }_{kj}^{AS}-{\beta }_{ij}|+{\rho }_{ij}^{+}|{\gamma }_{kj}^{AS}-{\gamma }_{ij}|)}{6}\mathrm{\forall }i\end{array}$$

(44)

where,

$$\begin{array}{rl}{\rho }_{ij}^{+}& =\{\begin{array}{c}\begin{array}{c}1ifcrisp({\widetilde{AS}}_j)<y_{ij}\mathrm{\forall }i\\ \end{array}\\ 0ifcrisp({\widetilde{AS}}_j)>y_{ij}\mathrm{\forall }i\end{array}\end{array}$$

(45)

$$\begin{array}{rl}dE{{\widetilde{(AS)}}_i}^{-}& =\sum _{j=1}^n\sqrt{\frac{({\rho }_{ij}^{-}{({\alpha }_{kj}^{AS}-{\alpha }_{ij})}^2+4\times {\rho }_{ij}^{-}{({\beta }_{kj}^{AS}-{\beta }_{ij})}^2+{\rho }_{ij}^{-}{({\gamma }_{kj}^{AS}-{\gamma }_{ij})}^2)}{6}}\mathrm{\forall }i\end{array}$$

(46)

$$\begin{array}{r}dT{{\widetilde{(AS)}}_i}^{-}=\sum _{j=1}^n\frac{({\rho }_{ij}^{-}|{\alpha }_{kj}^{AS}-{\alpha }_{ij}|+4\times {\rho }_{ij}^{-}|{\beta }_{kj}^{AS}-{\beta }_{ij}|+{\rho }_{ij}^{-}|{\gamma }_{kj}^{AS}-{\gamma }_{ij}|)}{6}\mathrm{\forall }i\end{array}$$

(47)

where,

$$\begin{array}{r}{\rho }_{ij}^{-}=\{\begin{array}{c}\begin{array}{c}1ifcrisp({\widetilde{AS}}_j)>y_{ij}\mathrm{\forall }i\\ \end{array}\\ 0ifcrisp({\widetilde{AS}}_j)<y_{ij}\mathrm{\forall }i\end{array}\end{array}$$

(48)

Step 4: Rank the alternatives based on increasing values of the comprehensive distance of each alternative $i(d{C}_i)$ . The best alternative has the smallest $d{C}_i.$

$$\begin{array}{r}d{C}_i=(d{\widetilde{(PIS)}}_i-d{\widetilde{(NIS)}}_i-d{{\widetilde{(AS)}}_i}^{+}+d{{\widetilde{(AS)}}_i}^{-})/4\end{array}$$

(49)

An illustrative figure that summarizes the steps of HF-MEREC-COBRA is given in Figure 1.

Figure 1.

Steps of HF-MEREC-COBRA.

3.4 HF-TOPSIS Validation Method

Steps of HF-TOPSIS (Burak et al., 2022) are given below as:

Step 1: After calculation of the fuzzy positive ideal $({\widetilde{PIS}}_j)$ , fuzzy negative ideal $({\widetilde{NIS}}_j)$ regarding each criteria j with the same methodology as HF-COBRA, calculate for each alternative i, the distance from the positive ideal solution $dV{\widetilde{(PIS)}}_i$ and negative ideal solution $dV{\widetilde{(NIS)}}_i$ , with the vertex method as:

$$\begin{array}{r}dV{\widetilde{(PIS)}}_i=\sum _{j=1}^n\sqrt{\frac{({({\alpha }_{kj}^{PIS}-{\alpha }_{ij})}^2+{({\beta }_{kj}^{PIS}-{\beta }_{ij})}^2+{({\gamma }_{kj}^{PIS}-{\gamma }_{ij})}^2)}{3}}\mathrm{\forall }i\end{array}$$

(50)

$$\begin{array}{r}dV{\widetilde{(NIS)}}_i=\sum _{j=1}^n\sqrt{\frac{({({\alpha }_{kj}^{NIS}-{\alpha }_{ij})}^2+{({\beta }_{kj}^{NIS}-{\beta }_{ij})}^2+{({\gamma }_{kj}^{,NIS}-{\gamma }_{ij})}^2)}{3}}\mathrm{\forall }i\end{array}$$

(51)

Step 2: Determine the closeness coefficient of each alternative i and rank the alternatives in decreasing order (closest to 1 is the best alternative).

$$\begin{array}{r}C{C}_i=dV{\widetilde{(NIS)}}_i/(dV{\widetilde{(NIS)}}_i+dV{\widetilde{(PIS)}}_i)\mathrm{\forall }i\end{array}$$

(52)

4 Case Study and Results

27 maximization (benefit, higher is better) criteria (C1, C2, …, C27) are determined as given in Table 3 with the help of DMs. There are 5 DMs (DM1, DM2, …, DM5) that are working at HepsiJET and these are a mobile software developer (DM1), a procurement department member (DM2), an experienced courier (DM3), an experienced courier (DM4), and a process development manager (DM5). Having decision-makers with different domains and perspectives is crucial in selecting specifically designed smartphones for a crowdsourced e-commerce logistics company. Smartphone alternatives that are going to be assessed are Reeder P13 Blue Max 2022 128 GB (A1), Xiaomi Redmi Note 11 Pro 128 GB 8 GB Ram (A2), Xiaomi Redmi 9c 64 GB (A3), Samsung Galaxy A23 128 GB (A4), and Oppo Reno 5 Lite 128 GB (A5).

Table 3.

Benefit Criteria for Smartphone Alternatives.

C1	Processor Speed	C15	Display Brightness
C2	Number of Cores	C16	Rear Camera Quality
C3	Ram Capacity	C17	Front Camera Quality
C4	Graphics Performance	C18	Low-Light Performance
C5	Multitasking and Performance Options	C19	Optical Image Stabilization
C6	Battery Capacity	C20	4G/5G Support
C7	Fast-Charging Support	C21	Wifi and Bluetooth Capability
C8	Standby Time	C22	GPS Accuracy and Navigation
C9	IP Rating	C23	NFC Capability
C10	Drop Resistance	C24	Software UI Design
C11	Shock Resistance	C25	Brand Reputation & Support
C12	Scratch Resistance	C26	Eco-Friendliness & Sustainability
C13	Screen Size	C27	Cost Effectiveness
C14	Screen Resolution

Table 4.

Evaluation of Alternatives with Respect to Each Criterion by 5 DMs.

		C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12	C13	C14	C15	C16	C17	C18	C19	C20	C21	C22	C23	C24	C25	C26	C27
A1	DM1	MG-G	F	MG-G	MG-G	MG-G	F	P-MP	F	P-MP	MP	F	P	F	MP	MG-G	P-MP	P-MP	MP	F	P	F	P	VP	MG-G	F	MG-G	G
	DM2	MG	MG	MG-G	MG	MG-G	F	P-MP	MP	P-MP	MP	F	P	F	F	MG-G	MP	MP	P-MP	MG	P	F	P	VP	MG	MP	MG-G	MG
	DM3	MG-G	F	MG-G	MG	G	MP	P-MP	MP	MP	MP	MP	P-MP	MP	F	MG	P	P	MP	F	P	MP	P	VP	MG-G	MP	G	MG-G
	DM4	MG-G	F	F	MG	MG-G	MP	MP	MP	P-MP	MP	P-MP	P	F	MP	MG-G	MP	MP	MP	MP	P	MP	P	VP	MG	F	MG-G	G
	DM5	G	F	F	MG-G	MG-G	P-MP	MP	F	P-MP	MP	F	P	MP	F	MG-G	P	P	MP	MG	P	F	P	VP	MG-G	MP	MG-G	MG
A2	DM1	G-VG	G-VG	VG	VG	G	G	F	F	F	MG	MG	F	G	G	G	G	VG	G-VG	VG	G	G	G	VG	G	G	G	MG-G
	DM2	G	G	G-VG	G-VG	G	G	F	MG	F	G	MG-G	MG-G	G-VG	MG-G	G	G-VG	VG	G	VG	G	G	G	VG	G	G	G	MG
	DM3	G-VG	G	VG	VG	G	G-VG	F	MG	MG	MG-G	MG-G	MG-G	VG	G-VG	G-VG	G	G-VG	G-VG	G-VG	G-VG	G-VG	G-VG	VG	G	G	G	MG-G
	DM4	G-VG	VG	G-VG	G-VG	G	G-VG	MP	F	MG	MG-G	MG	MG	G	G-VG	VG	G-VG	VG	G	G	G-VG	G-VG	G-VG	VG	G	G	G	MG-G
	DM5	G	VG	VG	VG	G	G-VG	MP	MG-G	F	G	MG	G	G-VG	G-VG	G-VG	G	G-VG	G	G-VG	G-VG	G-VG	G-VG	VG	G-VG	G-VG	G	MG
A3	DM1	MG-G	G	MG-G	MG-G	MG	G	F	MP	F	MP	F	MG-G	MG	MG-G	MG	P-MP	P-MP	MP	F	P	F	P	VP	G	G	MG	G
	DM2	MG-G	MG-G	MG-G	MG-G	MG-G	G	F	F	MP	MP	MP	MP	MG-G	MG	MP	MP	MP	P	MG	P	MG	P	VP	G	G	MG-G	MG-G
	DM3	MG	G	MG	MG	MG-G	G-VG	MP	F	P-MP	P-MP	P-MP	P-MP	G	MG-G	MP	P	P	MP	MG	P	MG	P	VP	G	G	MG-G	G
	DM4	MG	G	MG-G	MG-G	MG	G-VG	MP	MP	P-MP	P-MP	P-MP	P-MP	G	MG-G	F	MP	MP	P	F	P	MG	P	VP	G	G	MG	MG-G
	DM5	MG	MG-G	MG	MG-G	MG-G	G-VG	F	MP	F	F	F	F	MG-G	MG	MG	P	P	P-MP	MG	P	MG-G	P	VP	G-VG	G-VG	MG-G	MG-G
A4	DM1	G	G-VG	G	G	G-VG	G	F	MG-G	MG-G	MG-G	MG-G	MG-G	G-VG	G	G	G	G-VG	G	G-VG	VG	VG	VG	VG	G-VG	G-VG	G-VG	F
	DM2	G	G-VG	MG-G	G	G-VG	G	MP	MG	MG-G	MG-G	G	G	G	MG-G	G	G	G	MG-G	G-VG	VG	VG	VG	VG	G-VG	G-VG	G-VG	MG
	DM3	MG-G	G	MG-G	G-VG	G-VG	G-VG	MP	MG	G	G	MG-G	G	G-VG	G-VG	G	MG-G	G-VG	G	G	VG	VG	VG	VG	G-VG	G-VG	G-VG	F
	DM4	G	G-VG	G	G	VG	G-VG	F	MG	G	MG-G	G	MG-G	G-VG	G	G-VG	MG-G	G	G	G	G-VG	G-VG	G-VG	VG	G	G-VG	VG	MG-G
	DM5	G	G	MG-G	G	G	G-VG	MP	MG-G	MG	MG-G	MG-G	MG	G	G	G	MG	G	MG	G	G-VG	G-VG	G-VG	VG	G-VG	G-VG	G	G
A5	DM1	G	G	MG-G	G	G	MG-G	MG	MG-G	MG	MG-G	MG	MG	MG-G	MG	MG-G	VG	G	MG-G	G-VG	G	G	G	VG	G	MG-G	G	F
	DM2	MG-G	MG-G	MG-G	G	G	MG-G	MG	MG	F	G	MG	G	MG-G	G	MG-G	G-VG	G-VG	G	G-VG	G	G	G	VG	G	MG-G	G	MG
	DM3	MG-G	G	MG-G	MG-G	G	G	MG-G	MG-G	G	G	MG-G	G	MG	MG	MG	G-VG	G	MG-G	G	G-VG	G-VG	G-VG	VG	MG-G	G	G	MG-G
	DM4	G	MG-G	G	G	G	G	MG	MG	G	MG-G	G	MG-G	MG-G	MG	MG	VG	G-VG	MG-G	G	G-VG	G-VG	G-VG	VG	G	MG-G	G	MG-G
	DM5	MG	G	MG-G	G	MG-G	MG-G	MG	MG-G	MG-G	G	MG-G	G	MG-G	G	MG-G	G-VG	G	G	G	G-VG	G-VG	G-VG	VG	G	G	MG-G	G

Table 5.

Fuzzy Decision Matrix $\tilde{Z}$ _.

	A1	A2	A3	A4	A5
C1	(5.4,8.6,9.8)	(7,9.75,10)	(5,7.8,9.4	(6.6,9,10)	(5.8,8.6,9.8)
C2	(3.4,6.2,7.4)	(7.5,9.5,10)	(6.2,9,10)	(7,9.6,10)	(6.2,9,10)
C3	(4.2,7.8,8.8)	(8,10,10)	(5,8.2,9.6)	(5.8,9,10)	(5.4,9,10)
C4	(5,7.8,9.4)	(8,10,10)	(5,8.6,9.8)	(7,9.2,10)	(6.6,9,10)
C5	(5.4,9,10)	(7,9,10)	(5,8.2,9.6)	(7.4,9.8,10)	(6.6,9,10)
C6	(1.6,4.2,5.8)	(7,9.5,10)	(7,9.6,10)	(7,9.6,10)	(5.8,9,10)
C7	(0.4,3,5)	(2.5,5.25,6.5)	(2.2,4.8,6.2)	(1.8,4.2,5.8)	(5,7.4,9.2)
C8	(1.8,4.2,5.8)	(4,6.5,8)	(1.8,4.2,5.8)	(5,7.8,9.4)	(5,8.2,9.6)
C9	(0.2,3,5)	(4,6.5,8)	(1.4,4.2,5.8)	(5.8,8.6,9.8)	(5.4,8,9.2)
C10	(1,3,5)	(5.5,8.5,9.75)	(1,3.6,5.4)	(5.4,9,10)	(6.2,9,10)
C11	(2,4.8,6.2)	(5,8,9.5)	(1.4,4.2,5.8)	(5.8,9,10)	(5.4,8.2,9.6)
C12	(0,1.4,3.4)	(4.5,7.75,9)	(1.8,4.8,6.4)	(5.8,8.6,9.8)	(6.2,8.6,9.8)
C13	(2.2,4.8,6.2)	(7.5,9.5,10)	(5.8,8.6,9.8)	(7,9.6,10)	(5,8.6,9.8)
C14	(2.2,4.8,6.2)	(6.5,9.5,10)	(5,8.2,9.6)	(6.6,9.2,10)	(5.8,7.8,9.4)
C15	(5,8.6,9.8)	(7.5,9.5,10)	(3,5.2,7)	(7,9.2,10)	(5,8.2,9.6)
C16	(0.4,2.2,4.2)	(7,9.5,10)	(0.4,2.2,4.2)	(5.8,8.6,9.8)	(7.8,10,10)
C17	(0.4,2.2,4.2)	(8.5,10,10)	(0.4,2.2,4.2)	(7,9.4,10)	(7,9.4,10)
C18	(0.8,3,5)	(7,9.5,10)	(0.4,2.2,4.2)	(6.2,8.6,9.8)	(5.8,9,10)
C19	(3.4,5.8,7.4)	(8,9.75,10)	(4.2,6.6,8.2)	(7,9.4,10)	(7,9.4,10)
C20	(0,1,3)	(7,9.5,10)	(0,1,3)	(8.2,10,10)	(7,9.6,10)
C21	(2.2,4.8,6.2)	(7,9.5,10)	(4.6,7.2,8.8)	(8.2,10,10)	(7,9.6,10)
C22	(0,1,3)	(7,9.5,10)	(0,1,3)	(8.2,10,10)	(7,9.6,10)
C23	(0,0,1)	(9,10,10)	(0,0,1)	(9,10,10)	(9,10,10)
C24	(5,8.2,9.6)	(7,9,10)	(7,9.2,10)	(7,9.8,10)	(6.6,9,10)
C25	(1.8,4.2,5.8)	(7,9,10)	(7,9.2,10)	(7,10,10)	(5.8,9,10)
C26	(5.4,9,10)	(7,9,10)	(5,8.2,9.6)	(7.4,9.8,10)	(6.6,9,10)
C27	(5.8,8.2,9.6)	(5,8.5,9.75)	(5.8,9,10)	(4.6,7.4,8.6)	(5,8,9.2)

Table 6.

Overall Performance of Each Alternative $S_i$ .

Alternative	$S_i$
A1	−0.795
A2	−2.339
A3	−1.098
A4	−2.378
A5	−2.101

Table 7.

The Overall Performance of ith Alternative to the Elimination of the jth Criterion $S_{ij}^{\mathrm{\prime }}$ , the aggregate of Absolute Deviations $d_j$ , and Obtained Criterion Weights w with HF-MEREC.

	A1	A2	A3	A4	A5	$d_j$	w
C1	−0.730	−2.239	−1.045	−2.301	−2.035	0.362	0.042
C2	−0.761	−2.243	−1.022	−2.283	−2.025	0.376	0.043
C3	−0.745	−2.213	−1.040	−2.305	−2.029	0.379	0.043
C4	−0.742	−2.213	−1.034	−2.294	−2.023	0.404	0.046
C5	−0.723	−2.259	−1.040	−2.272	−2.023	0.393	0.045
C6	−0.775	−2.247	−1.003	−2.283	−2.027	0.375	0.043
C7	−0.781	−2.310	−1.072	−2.357	−2.043	0.149	0.017
C8	−0.774	−2.299	−1.078	−2.320	−2.037	0.203	0.023
C9	−0.782	−2.301	−1.079	−2.308	−2.043	0.199	0.023
C10	−0.781	−2.275	−1.082	−2.307	−2.025	0.240	0.028
C11	−0.772	−2.284	−1.079	−2.305	−2.042	0.229	0.026
C12	−0.788	−2.287	−1.075	−2.308	−2.029	0.224	0.026
C13	−0.772	−2.243	−1.032	−2.283	−2.037	0.344	0.039
C14	−0.772	−2.251	−1.040	−2.297	−2.046	0.306	0.035
C15	−0.731	−2.243	−1.071	−2.294	−2.043	0.328	0.038
C16	−0.785	−2.247	−1.089	−2.312	−1.979	0.300	0.034
C17	−0.785	−2.202	−1.089	−2.289	−2.012	0.334	0.038
C18	−0.782	−2.247	−1.089	−2.311	−2.027	0.256	0.029
C19	−0.764	−2.228	−1.059	−2.289	−2.012	0.359	0.041
C20	−0.790	−2.247	−1.093	−2.249	−2.006	0.326	0.037
C21	−0.772	−2.247	−1.053	−2.249	−2.006	0.385	0.044
C22	−0.790	−2.247	−1.093	−2.249	−2.006	0.326	0.037
C23	−0.794	−2.187	−1.097	−2.227	−1.949	0.456	0.052
C24	−0.737	−2.259	−1.014	−2.276	−2.023	0.401	0.046
C25	−0.775	−2.259	−1.014	−2.268	−2.027	0.368	0.042
C26	−0.723	−2.259	−1.040	−2.272	−2.023	0.393	0.045
C27	−0.734	−2.277	−1.024	−2.332	−2.047	0.297	0.034

At first, HF-MEREC is utilized to compute $w=(w_1,w_2,\dots ,w_n)$ . DMs evaluate alternatives with respect to each criterion with the “linguistic terms” in Table 2, as seen in Table 4. These linguistic terms are converted to matching TFNs based on the scale presented in Table 2. Also, based on the “fuzzy envelop approach”, HFLTS are converted to matching TFNs, utilizing Eqs. (20)-(24). For example, a HFLT such as “MG-G” corresponds to TFN (5,9,10) and “G-VG” corresponds to (7,10,10). Afterwards, by taking the average of 5 DMs’ corresponding TFNs, fuzzy decision matrix $\tilde{Z}$ in Table 5 is obtained. Since all the criteria are benefit criteria, fuzzy decision matrix $\tilde{Z}$ is normalized based on Eq. (25) and the elements of the matrix are defuzzified with Eq. (12), resulting in $X=(\text{; }{x}_{ij}{)}_{mxn}$ matrix. The overall performance of each alternative, $S_i$ , is computed with Eq. (27) as presented in Table 6. In Table 7, the overall performance of ith alternative to the elimination of the jth criterion $S_{ij}^{\mathrm{\prime }}$ determined with Eq. (28), the aggregate of absolute deviations $d_j$ calculated with Eq. (29), and resulting criterion weights determined with Eq. (30) are presented. These weights $w=(w_1,w_2,\dots ,w_n)$ , obtained with HF-MEREC, become an input to HF-COBRA and HF-TOPSIS.

Afterwards, HF-COBRA is employed to rank the alternatives. In HF-COBRA, after determining the weighted normalized decision matrix $\tilde{Y}$ , the fuzzy positive ideal $({\widetilde{PIS}}_j)$ , fuzzy negative ideal $({\widetilde{NIS}}_j)$ , and fuzzy average solution $({\widetilde{AS}}_j)$ regarding each criterion j are obtained with Eq. (32), Eq. (34) and Eq. (36) as seen in Table 8, respectively. Then, for each alternative i, the distance from the positive ideal solution $d{\widetilde{(PIS)}}_i$ , negative ideal solution $d{\widetilde{(NIS)}}_i$ , and positive $d{{\widetilde{(AS)}}_i}^{+}$ and negative $d{{\widetilde{(AS)}}_i}^{-}$ distances from the average solution are computed with Eqs. (37)-(48) as presented in Table 9. Here, ${\sigma }_{\widetilde{PIS}}=0.091,{\sigma }_{\widetilde{NIS}}=0.087,{\sigma }_{\widetilde{As+}}=0.035,\text{; and}{\sigma }_{\widetilde{As-}}=\mathrm{0.062.}$ Finally, with Eq. (49) comprehensive distance of each alternative $i(d{C}_i)$ is calculated, and alternatives are ranked from the best to the worst based on these values. $d{C}_i$ values and the ranking are also given in Table 9. As seen in Table 9, the final ranking is: Xiaomi Redmi Note 11 Pro 128 GB 8 GB Ram (A2), Samsung Galaxy A23 128 GB (A4), Oppo Reno 5 Lite 128 GB (A5), Xiaomi Redmi 9c 64 GB (A3) and Reeder P13 Blue Max 2022 128 GB (A1), with Xiaomi Redmi Note 11 Pro 128 GB 8 GB Ram (A2) being the best since the alternative with the smallest $d{C}_i$ value is the best.

Table 8.

The Fuzzy Positive Ideal $({\widetilde{PIS}}_j)$ , Fuzzy Negative Ideal $({\widetilde{NIS}}_j)$ , and Fuzzy Average Solution $({\widetilde{AS}}_j)$ Regarding Each Criterion j.

	${\widetilde{PIS}}_j$	${\widetilde{NIS}}_j$	${\widetilde{AS}}_j$
C1	(0.029,0.041,0.042)	(0.021,0.032,0.039)	(0.025,0.036,0.041)
C2	(0.032,0.041,0.043)	(0.015,0.027,0.032)	(0.026,0.037,0.041)
C3	(0.035,0.043,0.043)	(0.018,0.034,0.038)	(0.025,0.038,0.042)
C4	(0.037,0.046,0.046)	(0.023,0.036,0.044)	(0.029,0.041,0.046)
C5	(0.033,0.044,0.045)	(0.023,0.037,0.043)	(0.028,0.041,0.045)
C6	(0.030,0.041,0.043)	(0.007,0.018,0.025)	(0.024,0.036,0.039)
C7	(0.009,0.014,0.017)	(0.001,0.006,0.009)	(0.004,0.009,0.012)
C8	(0.012,0.020,0.023)	(0.004,0.010,0.014)	(0.009,0.015,0.019)
C9	(0.014,0.020,0.023)	(0.000,0.007,0.012)	(0.008,0.014,0.018)
C10	(0.017,0.025,0.028)	(0.003,0.008,0.014)	(0.011,0.018,0.022)
C11	(0.015,0.024,0.026)	(0.004,0.011,0.015)	(0.010,0.018,0.022)
C12	(0.016,0.023,0.026)	(0.000,0.004,0.009)	(0.010,0.016,0.020)
C13	(0.030,0.038,0.039)	(0.009,0.019,0.024)	(0.022,0.032,0.036)
C14	(0.023,0.033,0.035)	(0.008,0.017,0.022)	(0.018,0.028,0.032)
C15	(0.028,0.036,0.038)	(0.011,0.020,0.026)	(0.021,0.031,0.035)
C16	(0.027,0.034,0.034)	(0.001,0.008,0.014)	(0.015,0.022,0.026)
C17	(0.033,0.038,0.038)	(0.002,0.008,0.016)	(0.018,0.025,0.029)
C18	(0.021,0.028,0.029)	(0.001,0.006,0.012)	(0.012,0.019,0.023)
C19	(0.033,0.040,0.041)	(0.014,0.024,0.030)	(0.024,0.034,0.038)
C20	(0.031,0.037,0.037)	(0.000,0.004,0.011)	(0.017,0.023,0.027)
C21	(0.036,0.044,0.044)	(0.010,0.021,0.027)	(0.026,0.036,0.040)
C22	(0.031,0.037,0.037)	(0.000,0.004,0.011)	(0.017,0.023,0.027)
C23	(0.047,0.052,0.052)	(0.000,0.000,0.005)	(0.028,0.031,0.034)
C24	(0.032,0.045,0.046)	(0.023,0.038,0.044)	(0.030,0.042,0.046)
C25	(0.030,0.042,0.042)	(0.008,0.018,0.024)	(0.024,0.035,0.039)
C26	(0.033,0.044,0.045)	(0.023,0.037,0.043)	(0.028,0.041,0.045)
C27	(0.020,0.031,0.034)	(0.016,0.025,0.029)	(0.018,0.028,0.032)

Table 9.

$dE{\widetilde{(PIS)}}_i,dE{\widetilde{(NIS)}}_i,dE{{\widetilde{(AS)}}_i}^{+},dE{{\widetilde{(AS)}}_i}^{-},dT{\widetilde{(PIS)}}_i,dT{\widetilde{(NIS)}}_i,dT{{\widetilde{(AS)}}_i}^{+},dT{{\widetilde{(AS)}}_i}^{-},d{\widetilde{(PIS)}}_i,d{\widetilde{(NIS)}}_i,d{{\widetilde{(AS)}}_i}^{+},d{{\widetilde{(AS)}}_i}^{-}$ and $d{C}_i$ Values of Each Alternative in HF-COBRA and the Final Ranking of Alternatives Based on HF-MEREC-COBRA.

	A1	A2	A3	A4	A5
$dE{\widetilde{(PIS)}}_i$	0.102	0.012	0.090	0.013	0.017
$dE{\widetilde{(NIS)}}_i$	0.013	0.099	0.041	0.100	0.035
$dE{{\widetilde{(AS)}}_i}^{+}$	0.002	0.037	0.008	0.037	0.035
$dE{{\widetilde{(AS)}}_i}^{-}$	0.062	0.000	0.051	0.003	0.001
$dT{\widetilde{(PIS)}}_i$	0.439	0.040	0.340	0.036	0.063
$dT{\widetilde{(NIS)}}_i$	0.027	0.426	0.126	0.430	0.403
$dT{{\widetilde{(AS)}}_i}^{+}$	0.002	0.144	0.017	0.152	0.124
$dT{{\widetilde{(AS)}}_i}^{-}$	0.257	0.000	0.173	0.004	0.001
$d{\widetilde{(PIS)}}_i$	0.106	0.012	0.093	0.013	0.017
$d{\widetilde{(NIS)}}_i$	0.014	0.103	0.042	0.104	0.036
$d{{\widetilde{(AS)}}_i}^{+}$	0.002	0.037	0.008	0.038	0.035
$d{{\widetilde{(AS)}}_i}^{-}$	0.063	0.000	0.052	0.003	0.001
$d{C}_i$	0.039	−0.032	0.024	−0.031	−0.013
Ranking	5	1	4	2	3

Subsequently, for validation purposes, HF-MEREC-TOPSIS is implemented. Utilizing the fuzzy positive ideal $({\widetilde{PIS}}_j)$ and fuzzy negative ideal $({\widetilde{NIS}}_j)$ regarding each criterion j in Table 8, the distance from the positive ideal solution $dV{\widetilde{(PIS)}}_i$ and negative ideal solution $dV{\widetilde{(NIS)}}_i$ with the vertex method (Eq. (50) and Eq.(51)) are calculated. Then, closeness coefficient of each alternative, $C{C}_i$ is computed and alternatives are ranked from best to worst based on these values. The best alternative has the highest $C{C}_i$ value (closest to 1). In Table 10, $dV{\widetilde{(PIS)}}_i,dV{\widetilde{(NIS)}}_i$ and $C{C}_i$ values of each alternative are presented, along with the ranking of alternatives based on HF-MEREC-TOPSIS. As seen from Table 9 and Table 10, HF-MEREC-COBRA and HF-MEREC-TOPSIS ranking of alternatives are exactly the same, with Xiaomi Redmi Note 11 Pro 128 GB 8 GB Ram (A2) being the best alternative.

Table 10.

$dV{\widetilde{(PIS)}}_i,dV{\widetilde{(NIS)}}_i$ and $C{C}_i$ Values of Each Alternative in HF-TOPSIS and the Final Ranking of Alternatives Based on HF-MEREC-TOPSIS.

	A1	A2	A3	A4	A5
$dV{\widetilde{(PIS)}}_i$	0.099	0.011	0.087	0.013	0.017
$dV{\widetilde{(NIS)}}_i$	0.012	0.096	0.040	0.096	0.092
$C{C}_i$	0.110	0.895	0.318	0.882	0.841
Ranking	5	1	4	2	3

For sensitivity analysis, the ranking effect of weight changes for each criterion is analyzed. Let $w_i$ be the original criterion weight obtained from HF-MEREC that is going to be changed in the sensitivity analysis. Let $\mathrm{\Delta }$ be the change (if it is positive, the weight is increasing, and if it is negative, the weight is decreasing). Update the criterion weight so that new weight is $w_i^{\mathrm{\prime }}=w_i(1+\mathrm{\Delta })$ and scale all the other weights proportionally so that the total sum of weights remains as 1. For all other weights, the scaling is done this way: Let $A=1-w_i$ and $B=1-w_i{}^{\mathrm{\prime }}$ , so then for each criterion $w_j$ (where $j\ne i$ ), $w_j^{\mathrm{\prime }}=w_j\left(\frac{B}{A}\right)$ .

Here, each criterion weight is increased and decreased by %10, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% and 100% and the effect on the ranking of HF-MEREC-COBRA is analyzed. When, the weight of each criterion is increased and decreased by %10, %20, %30 and %40 ( $\mathrm{\Delta }=$ 0.1, −0.1,0.2, −0.2, 0.3,-0.3, 0.4, −0.4), the ranking of alternatives with HF-MEREC-COBRA stayed the same as with the original weights so the ranking was still A2 (best), A4, A5, A3, A1. When the weight of criterion 9 $(w_9)$ is increased by %50 ( $(\mathrm{\Delta }=0.5)$ , only the best and second-best alternatives switched places, so the ranking became A4 (best), A2, A5, A3, A1. Based on this, one can say that criterion 9 is the most sensitive to changes. The same ranking change happened (A4 (best), A2, A5, A3, A1), when $w_9,\text{; }{w}_{20},w_{22},w_{25}\text{; }$ and $\mathrm{\Delta }=$ 0.6, 0.7, 0.8, 0.9, 1.0; $w_{27}\text{; }$ and $\mathrm{\Delta }=$ −0.6, −0.7, −0.8, −0.9, −1.0; $w_{21}\text{; }$ and $\mathrm{\Delta }=$ 0.7, 0.8, 0.9, 1.0; $w_8,w_{12}\text{; }$ and $\mathrm{\Delta }=$ 0.8, 0.9, 1.0; $w_{16}\text{; }$ and $\mathrm{\Delta }=-$ 0.8, −0.9, −1.0; $w_3\text{; }$ and $\mathrm{\Delta }=$ −1.0; $w_{11}\text{; }$ and $\mathrm{\Delta }=$ 1.0.

The results of the sensitivity analysis display that the HF-MEREC-COBRA shows a high degree of robustness to moderate changes in criterion weights. Particularly, when the weights of individual criteria were altered by up to ±40%, the ranking of alternatives remained unchanged, consistently identifying A2 as the best alternative. This stability shows that the decision-making process with HF-MEREC-COBRA is not excessively sensitive to small changes in criteria weights. However, as the weight of criterion 9 is increased by 50%, a swap between the top two alternatives, A2 and A4, happens. Same ranking swap also occurred with larger positive changes in weights of criteria 9, 20, 22, 25, 21, 8, 12, and 11, and with larger negative changes in weights of criteria 27, 16, and 3. These outcomes suggest that while the model is mostly stable, some criteria, especially criterion 9, are more sensitive to changes and have a greater impact on the ranking.

5 Discussion

The results obtained with HF-MEREC-COBRA and HF-MEREC-TOPSIS, taking into consideration 27 criteria, accurately reflected the needs of HepsiJET's logistics personnel. The best alternative Xiaomi Redmi Note 11 Pro 128 GB 8 GB Ram (A2), aligned well with the operational needs of the personnel, especially considering the high weights assigned to critical criteria such as GPS accuracy and navigation (0.037), battery capacity (0.043), 4G/5G support (0.037), and drop resistance (0.028). Accurate, reliable, and fast GPS and navigation are critical for timely deliveries and route optimization. Battery capacity is crucial since teams often work long shifts without access to charging stations. Durability is also a key concern since phones might be dropped, bumped, and exposed to various elements. The weights assigned to drop resistance (0.028), IP rating (0.023), and shock resistance (0.026) show this fact. Alternatives Xiaomi Redmi Note 11 Pro 128 GB 8 GB Ram (A2) and Samsung Galaxy A23 128 GB (A4), that scored well in these categories, are likely to last longer and reduce the need for repairs and replacements. Connectivity features such as WiFi/Bluetooth (0.044), NFC (0.037) were also emphasized by the logistics team as important for continuous package scanning, device syncing, and communication with dispatch systems. These capabilities are significant for workflow efficiency. The worst alternative, Reeder P13 Blue Max 2022 128 GB (A1), underperformed in several of those high-weight (important) criteria. Therefore, it is expected to cause more inefficiencies in the logistics operations.

Overall, the proposed decision-making process with HF-MEREC-COBRA and HF-MEREC-TOPSIS seems to capture the practical needs of the logistics personnel effectively. However, as suggested by the team and managers, field testing of the top two models, especially Xiaomi Redmi Note 11 Pro 128 GB 8 GB Ram (A2), is necessary to confirm the real-world performance of these alternatives to ensure that the selected device not only excels on paper but also in real life and day-to-day logistics operations.

6 Conclusions

In conclusion, a novel, systematic MCDM method is developed in this research, namely HF-MEREC-COBRA, to assess specifically designed smartphones for a crowdsourced e-commerce logistics company in Turkey, HepsiJET. To the best of the authors’ knowledge, HF-COBRA has never been studied in the literature, and consequently, there is no research that applies HF-MEREC-COBRA to a MCDM problem. The HF-MERE-COBRA method allows DMs to benefit from both MEREC and COBRA methods’ advantages, and the utilization of HFLTS allows DMs to reflect their hesitancies and uncertainties in the decision-making process. Having the same ranking of smartphones also with HF-MEREC-TOPSIS reinforces the stability of the HF-MEREC-COBRA. Moreover, HF-MEREC-COBRA shows high robustness and strong anti-interference capability, maintaining stable results, even under moderate changes in criterion weights (up to ±40%). For large-scale MCDM problems, involving large number of criteria and/or alternatives such as the presented case study, HF-MEREC-COBRA is more computationally efficient and less burdensome than (hybrid fuzzy) methods with AHP, since in HF-MEREC-COBRA, unlike (hybrid fuzzy) methods with AHP, subjective weight assignments and pairwise comparisons of criteria are avoided in the HF-MEREC step. On the other hand, the HF-COBRA step of HF-MEREC-COBRA ranks alternatives based on comprehensive distance measures that are computationally straightforward and suitable for problems with large numbers of alternatives. The practical use of HF-MEREC-COBRA and for validation, HF-MEREC-TOPSIS, in this research marks a notable advancement in the intricate task of choosing smartphones, particularly in the realm of e-commerce logistics. These methods enhance decision-making by effectively handling both qualitative and quantitative criteria, including uncertainty and hesitation in expert evaluations. This research goes beyond simply assisting in device selection; it serves as a guide for acquiring a dependable digital ally that boosts the efficiency and reliability of logistics personnel in an increasingly demanding, technology-driven market. A limitation of this study is that the evaluated alternatives might become outdated quickly due to the rapid evolution of smartphone technologies. However, the proposed HF-MEREC-COBRA framework remains applicable for future evaluations with updated alternatives.

For future research, since AI and machine learning algorithms can handle large volumes of data, from existing smartphone users in the company, feedback data related to the evaluation criteria can be collected, and by identifying patterns and extracting relevant features, the importance weights of criteria that are computed with HF-MEREC can be re-adjusted and then HF-COBRA or other methods such as HF-CoCoSo, HF-MULTIMOORA, etc. can be utilized to rank smartphone alternatives. Moreover, HF-MEREC-COBRA can be applied to different MCDM problems in the logistics and supply chain management sector, such as fleet vehicle selection, warehouse technology procurement, and courier route optimization.