Restricted accessResearch articleFirst published online 2026-2
A reliability allocation method based on 2-tuple Pythagorean fuzzy linguistic-Pythagorean fuzzy induced ordered weighted averaging weighted average operator
Reliability allocation is a critical aspect of product reliability design, as the reasonableness of the allocation results directly affects the attainment of the desired reliability design index. However, traditional reliability allocation methods exhibit limited capability in expressing and handling fuzzy information, and they fail to consider the weight relationship among allocation factors. To address these drawbacks, this study proposes a novel reliability allocation method based on 2-tuple Pythagorean fuzzy linguistic-Pythagorean fuzzy induced ordered weighted averaging weighted average (2TPFL-PFIOWAWA) operators. In this method, different experts have the autonomy to select the appropriate 2-tuple Pythagorean fuzzy linguistic variable to conduct diverse evaluations of the target. Subsequently, the 2TPFL-PFIOWAWA is employed to aggregate these fuzzy assessments. This operator accounts for weight relationships among allocation factors, effectively minimizing subjective biases and enhancing the robustness of decision outcomes. The feasibility of the proposed method is validated through comparative analysis of case studies.
WangYYamRCMZuoMJ, et al. A comprehensive reliability allocation method for design of CNC lathes. Reliab Eng Syst Safety2001; 72: 247–252.
2.
YangJEHwangM-JSungT-Y, et al. Application of genetic algorithm for reliability allocation in nuclear power plants. Reliab Eng Syst Safety1999; 65: 229–238.
3.
UmmaBMaaCOaA, et al. Optimization and estimation in system reliability allocation problem. Reliab Eng Syst Safety2021; 212: 107620.
4.
YueXZhangH.Modified hybrid bat algorithm with genetic crossover operation and smart inertia weight for multilevel image segmentation. Appl Soft Comput2020; 90: 106157.
5.
JingXLPanQKGaoL.Local search-based metaheuristics for the robust distributed permutation flowshop problem. Appl Soft Comput2021; 105: 107247.
6.
AndersonRT.Reliability design handbook. New York, NY: IIT Research Institute, 1976.
7.
ZadehLA.Fuzzy sets. Inf Control1965; 8: 338–353.
8.
LiuJCZhuYFZhaoWJ.Quadratic programming method for cooperative games with coalition values expressed by triangular fuzzy numbers and its application in the profit distribution of logistics coalition. Math Probl Eng2019; 2019: 1–10.
9.
HuBLiuBZhouJ, et al. Health risk assessment on heavy metals in urban street dust of Tianjin based on trapezoidal fuzzy numbers. Hum Ecol Risk Assess2016; 22: 678–692.
10.
GargamaHChaturvediSK.Criticality assessment models for failure mode effects and criticality analysis using fuzzy logic. IEEE Trans Reliab2011; 60: 102–110.
11.
LiuHCLiuLBianQH, et al. Failure mode and effects analysis using fuzzy evidential reasoning approach and grey theory. Expert Syst Appl2011; 38: 4403–4415.
12.
ChangK-H.A novel reliability allocation approach using the OWA tree and soft set. Ann Oper Res2016; 244: 3–22.
13.
ChenTZhengSLiaoH, et al. A multi-attribute reliability allocation method considering uncertain preferences. Qual Reliab Eng Int2016; 32: 2233–2244.
14.
FengYHongZChengJ, et al. Environmental-friendly reliability allocation for product platform based on expert measurement and ICN. Comput Electr Eng2017; 64: 132–144.
SuoMQLiYPHuangGH.Multicriteria decision making under uncertainty: an advanced ordered weighted averaging operator for planning electric power systems. Eng Appl Artif Intell2012; 25: 72–81.
17.
AlhichriHBaziYAlajlanN, et al. A novel fusion approach based on induced ordered weighted averaging operators for chemometric data analysis. J Chemom2013; 27: 447–456.
18.
ZengSWangQMerigoJMPT. Induced intuitionistic fuzzy ordered weighted averaging: weighted average operator and its application to business decision-making. Comput Sci Inf Syst2014; 11: 839–857.
19.
ChangKHChangYCWenTC, et al. An innovative approach integrating 2-tuple and lowga operators in process failure mode and effects analysis. Int J Innov Comput Inf Control2012; 8: 747–761.
20.
ChangKH.Evaluate the orderings of risk for failure problems using a more general RPN methodology. Microelectron Reliab2009; 49: 1586–1596.
21.
RodgerJAPankajPGonzalezSP.Decision making using a fuzzy induced linguistic ordered weighted averaging approach for evaluating risk in a supply chain. Int J Adv Manuf Technol2014; 70: 711–723.
22.
YagerRRFilevDP.Induced ordered weighted averaging operators. IEEE Trans Syst Man Cybern B1999; 29: 141–150.
23.
MerigóJ.A unified model between the weighted average and the induced OWA operator. Expert Syst Appl2011; 38: 11560–11572.
24.
ZhangX.A novel approach based on similarity measure for pythagorean fuzzy multiple criteria group decision making. Int J Intell Syst2016; 31: 593–611.
25.
GargH.Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision-making process. Int J Intell Syst2018; 33: 1234–1263.
26.
ZengSMMuZBalezentisT.A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making. Int J Intell Syst2018; 33: 573–585.
27.
ZadehLA.The concept of a linguistic variable and its application to approximate reasoning—I. Inf Sci1975; 8: 199–249.
28.
HerreraFHerrera-ViedmaEMartinezL.A fusion approach for managing multi-granularity linguistic term sets in decision making. Fuzzy Sets Syst2000; 114: 43–58.
29.
HerreraFMartinezL.A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst2000; 8: 746–752.
30.
LiWYuSPeiH, et al. A hybrid approach based on fuzzy AHP and 2-tuple fuzzy linguistic method for evaluation in-flight service quality. J Air Transp Manag2017; 60: 49–64.
31.
SantosLOsiroLLimaR.A model based on 2-tuple fuzzy linguistic representation and Analytic Hierarchy Process for supplier segmentation using qualitative and quantitative criteria. Expert Syst Appl2017; 79: 53–64.
32.
DengXWeiGHuiG, et al. Models for safety assessment of construction project with some 2-tuple linguistic Pythagorean fuzzy Bonferroni mean operators. IEEE Access2018; 6: 52105–52137.
33.
ZhangQLiuSTuQ.A 2-tuple fuzzy linguistic model for criteria evaluation on technological innovation of marine enterprises. J Coast Res2019; 94: 634.
34.
ZhangXLXuZS.Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst2014; 29: 1061–1078.
35.
YagerRR.Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst2014; 22: 958–965.
