Site selection for food distribution using rough set approach and TOPSIS method

Abstract

Suitable site selection for a specific purpose is a crucial activity, and of the greatest importance to a project manager. Several methods have been proposed by the research community for effective site selection, but all proposed methods incur high costs. This study explores the combination of a rough set theory approach (RSTA) with Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for suitable site selection for food distribution. This method provides a set of rules to determine different sites, which ultimately can help management develop strategies for suitable site selection. A set of rules for suitable site selection are derived from information related to a practical case, Pakistan Red Crescent Society (PRCS), to demonstrate the prediction ability of RSTA. The results clearly demonstrate that the RSTA model can be a valuable tool for site identification. Rough set theory also assists management in making appropriate decisions based on their objectives while avoiding unnecessary costs. However, while RSTA provides rules to determine the best sites for food distribution, it does not pinpoint the best sites for food distribution. To be more precise and accurate, this work is extended to another multi-criteria decision-making technique solution: the TOPSIS method. By using this method, this study provides the best top priority site for food distribution of PRCS.

1 Introduction

With the rapid changes in the contemporary world environment, it has now become mandatory to focus on new areas of emerging needs for people worldwide. World citizens are running out of food due to wars, natural disasters, economic crises, etc. All these factors have created a situation in which people from all over the world, through international organizations, attempt to help disadvantaged people so that they can fight hunger effectively. One such organization, the Pakistan Red Crescent Society (PRCS), has been helping deserving people in most parts of the country. Most of the organizational activities are performed by PRCS in rural areas and at various sites around the country. The primary challenge to PRCS is the selection of appropriate sites for food distribution to Internally Displaced Persons (IDPs) in rural areas of Pakistan.

Site selection is a multi-criteria decision making problem for which PRCS takes into account a number of factors, such as security of the area, community involvement, technical aspects, locations, authorities, and environmental considerations.

Considering these factors, this study explores the use of a novel approach by combining the Rough Set Theory Approach (RSTA) with the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to select the most suitable sites for food distribution based on the above-mentioned factors. It has been assumed that the combination of these tools will help management make appropriate decisions based on a multi-criteria decision environment to achieve their objectives, and to avoid unnecessary costs.

The remainder of the paper is organized as follows. Section 2 presents a literature review, while Section 3 discusses preliminary studies. The development methodology is presented in Section 4, which is followed by the evaluation of methods in Section 5. Section 6 presents results and discussion, while Section 7 describes the strengths and weaknesses of the proposed research method. A summary of this paper is presented in Section 8, with experimental conclusions.

2 Literature review

The literature review indicates that many studies have been previously conducted on the subject of site selection and multi-criteria decision making. Arabani et al. [16] suggested an effective way to determine the best location for dams. Neshaei, et al. [19] investigated site locations of buried concrete water reservoirs. Cruz et al. [3] suggested a method of shipment scheduling. Sun, et al. [20] conducted research on site selection of passenger stations in the valley-city (China). Jing [27] conducted research regarding site selection for a logistics park. Important research on site selection of an aviation spare distribution center for military aircraft has been conducted by Chen, et al. [5]. Furthermore, Jingfeng, et al. [2] performed site selection decision making for a distribution logistics park. Moreover, site selection criteria for coastal tourism facilities have been proposed by Lo [6]. Alternatively, Lindgren [4] evaluated the selection of sites for development caused by the improper sitting of residential complexes and industrial facilities. In another study, Lawson [24] suggested the selection of a suitable site for an aquaculture venture. Another interesting research on site selection was also contributed by Yasser, et al. [17]. Moreover, a new addition to the field of site selection has been made by Elhadary, et al. [21], by introducing the rough set classification and attribute reduction method to landfill site selection. Srafaraz, et al. [23] developed a new hybrid MCDM technique to choose the locations of shopping malls in Tehran. In continuation, Majid, et al. [16] proposed an integrated MCDM SWARA–WASPAS method to select one city out of 25 in which to implement future solar power plants.

3 Preliminaries

3.1 Rough set theory

Rough set theory was originally proposed by Z. Pawlak in the early 1980s. Rough set theory deals with the classification analysis of data tables. The primary goal of rough set analysis is to synthesize the approximation of concepts from acquired data [30].

More details about rough set theory can be found in work done by Walczak, et al., Komorowaski, et al., Yao, et al., K. Kaneiwa, Dey, et al., Rissino, et al., Zhang, et al., Yiyu, et al. and Pawlak [1, 28, 29].

3.2 TOPSIS method

TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) was developed by Yoonet al. in 1980 [13, 14]. This method deals with multi-criteria decision making. The basic concept of the TOPSIS method asserts that the chosen alternative should demonstrate the shortest distance from the ideal solution and the farthest distance from the negative-ideal solution. The TOPSIS method is consists of the following steps:

Step 1: Construct the normalized decision matrix to transform the various attribute dimensions into non-dimensional attributes, which allows comparison across attributes. $r_{\mathit{ij}}=\frac{x_{\mathit{ij}}}{\sqrt{{\sum }_{i=1}^m{x}_{\mathit{ij}}^2}}$(1)

Step 2: Construct the weighted normalized decision matrix. $\mathit{v}=\left[\begin{array}{c}\hfill {\mathit{v}}_{11}{\mathit{v}}_{12}...{\mathit{v}}_{1j}...{\mathit{v}}_{ln}\hfill \\ \hfill ....\hfill \\ \hfill ....\hfill \\ \hfill ....\hfill \\ \hfill {\mathit{v}}_{i1}{\mathit{v}}_{i2}...{\mathit{v}}_{\mathit{ij}}...{\mathit{v}}_{\mathit{in}}\hfill \\ \hfill ....\hfill \\ \hfill ....\hfill \\ \hfill ....\hfill \\ \hfill {\mathit{v}}_{m1}{\mathit{v}}_{m2}...{\mathit{v}}_{\mathit{mj}}...{\mathit{v}}_{\mathit{mn}}\hfill \\ \hfill \hfill \end{array}\right]$(2)$=\left[\begin{array}{c}\hfill {\mathit{w}}_1{\mathit{v}}_{11}{\mathit{w}}_2{\mathit{v}}_{12}...{\mathit{w}}_j{\mathit{v}}_{1j}...{\mathit{w}}_n{\mathit{v}}_{ln}\hfill \\ \hfill ....\hfill \\ \hfill ....\hfill \\ \hfill ....\hfill \\ \hfill {\mathit{w}}_1{\mathit{v}}_{i1}{\mathit{w}}_2{\mathit{v}}_{i2}...{\mathit{w}}_j{\mathit{v}}_{\mathit{ij}}...{\mathit{w}}_n{\mathit{v}}_{\mathit{in}}\hfill \\ \hfill ....\hfill \\ \hfill ....\hfill \\ \hfill ....\hfill \\ \hfill {\mathit{w}}_1{\mathit{v}}_{m1}{\mathit{w}}_2{\mathit{v}}_{m2}...{\mathit{w}}_j{\mathit{v}}_{\mathit{mj}}...{\mathit{w}}_n{\mathit{v}}_{\mathit{mn}}\hfill \\ \hfill \hfill \end{array}\right]$

Step 3: Determine the ideal and negative-idealsolutions.

$\begin{array}{ccc}\hfill A^{+}& \hfill =\hfill & \left\{\right(\underset{i}{max}{\mathit{v}}_{\mathit{ij}}/j\in J),\underset{i}{(min{\mathit{v}}_{\mathit{ij}}/j\in J)}/\hfill \\ \hfill & \hfill \hfill & i=1,2,\dots m\}=\{{\mathit{v}}_1^{+},{\mathit{v}}_2^{+},\dots ,{\mathit{v}}_n^{+}\}\hfill \\ \hfill A^{-}& \hfill =\hfill & \left\{\right(\underset{i}{min}{\mathit{v}}_{\mathit{ij}}/j\in J),\underset{i}{(max{\mathit{v}}_{\mathit{ij}}/j\in J)}/\hfill \\ \hfill & \hfill \hfill & i=1,2,\dots m\}=\{{\mathit{v}}_1^{-},{\mathit{v}}_2^{-},\dots ,{\mathit{v}}_n^{-}\}\hfill \end{array}$(3) $\begin{array}{ccc}\hfill \mathit{where}J& \hfill =\hfill & \{j=1,2,\dots ,n|\hfill \\ \hfill & \hfill \hfill & j\mathit{associated}\mathit{with}\mathit{benefit}\mathit{criteria}\}\hfill \\ \hfill J& \hfill =\hfill & \{j=1,2,\dots ,n|\hfill \\ \hfill & \hfill \hfill & j\mathit{associated}\mathit{with}\mathit{benefit}\mathit{criteria}\}\hfill \end{array}$

Step 4: Calculate the separation measure.

–Ideal separation $S_i^{+}=\sqrt{\sum _{j=1}^n({\mathit{v}}_{\mathit{ij}}-{\mathit{v}}_j^{-}{)}^2}i=1,2,\dots \dots ,m$(4)

–Negative ideal separation $S_i^{-}=\sqrt{\sum _{j=1}^n({\mathit{v}}_{\mathit{ij}}-{\mathit{v}}_j^{-}{)}^2}i=1,2,\dots \dots ,m$(5)

Step 5: Calculate the relative closeness to the ideal solution. $\begin{array}{c}\hfill C_i^{*}=\frac{S_i^{-}}{(S_i^{+}+S_i^{-})},0<C_i^{+}<1,i=1,2,\dots ,m\hfill \\ \hfill C_i^{*}=1\mathit{if}{A}_i=A^{+}\hfill \\ \hfill C_i^{*}=0\mathit{if}{A}_i=A^{-}\hfill \\ \hfill \hfill \end{array}$(6)

Step 6: Rank the preference order. A set of alternatives can now be preferentially ranked according to the descending order of $C_i^{*}$.

4 Development methodology

In this study, four distinct districts from Khyber Pakhtunkhwa (KPK) are selected for site selection by PRCS: Hangu, Nowshehra, Lower Dir and Charsadda. Hangu and Lower Dir share disaster characteristics, as do Nowshehra and Charsadda. Table 1 depicts conditional attributes, classifications of conditional attributes according to corresponding factors and corresponding decision levels in which H represents High, M represents Medium, L represents Low and N represents Neutral. The differences between the first two districts and the last two districts are shown in Table 2, i.e., the varying nature of their conditional attributes (d), (e) and (f).

Attributes and classification of conditional attributes are selected via a deductive method, i.e., a long session of interviews was conducted with PRCS experts. PRCS officials suggested a number of attributes, but the given nine were determined to be of top priority. Data is quantified by assigning 1 to High, 2 to Medium, 3 to low and 4 to neutral characteristics. Two districts (Hangu and Lower Dir) have nearly identical classifications, as do Nowshehra and Charsadda, depending on the nature of the area. A maximum of 80 sites were considered in all four districts, and all sites were mapped with conditional attributes, their classifications and decision levels as shown in Tables 1 and 2. Distribution of food took place in these 80 sites, provided by the top management of PRCS. According to Table 3, the decision levels are selected as the highest priority, from high to low. A total of 9 attributes form a to i; the corresponding decision levels are taken as mod () of the 9 given attributes.

5 Algorithms used to generate rules and evaluation measures

Data mining techniques use many algorithms to generate decision rules from the given data. In this study, four different algorithms are applied to generate rules: the exhaustive algorithm [7], genetic algorithm [9, 25], covering algorithm [11] and LEM 2 algorithm [9, 11]. The following evaluation measures were then used to evaluate the results.

Sensitivity = TP/TP+FN, also called “recall”

Specificity = TN/TN+FP, where 1-specificity = FP/TN+FPPrecision = TP/(TP + FP)

Accuracy = (TP + TN) / (TP + FN) + (TN + FP)

Misclassification Error (MisErr) = 1 –Accuracy

Type-I Error = 1–specificity = FP/(FP+TN)

Type-II Error = 1–sensitivity = FN/(TP+FN)

F-measure = 2.(Precision.Recall)/(Precision+ Recall)

COV = (number of cases satisfying Condition and Decision)/(number of cases satisfying Decision)

6 Results and discussion of rough set theory

6.1 Results algorithms applied

Four algorithms are applied to the given dataset which include the exhaustive, genetic, covering and LEM2 algorithms. Results are calculated and thoroughly analyzed.

Comparison of all algorithms is shown in Table 3. Based on resultant analysis, the genetic algorithm is selected for the proposed dataset because it demonstrates the best accuracy in predicting the result by considering 100% data.

6.1.1 Reducts and rules

Two reduct sets are calculated, and a total of 40 sites are selected by applying rough set theory about the given data. A total of 482 rules are obtained, among which 222 rules support decision 1, (High), 147 rules support decision 2 (Medium) and 113 rules support decision 3 (Low). The rules take the form of “IF A then B”. It is not possible to show all rules related to this paper due to space limitations, but rules are selected in descending order as shown in Table 4.

Although rough set theory provided the best overall result, which indicates that all sites that satisfy the decision criteria for a designation of “High” should be considered for food distribution, the top-priority site has yet to be determined. This problem is solved by applying the TOPSIS method, as mentioned in section 3.2.

6.2 Results of TOPSIS method

By applying the TOPSIS method steps to the result provided by the rough set approach to 40 sites, it was demonstrated that the TOPSIS method is able to successfully predict the best and worst sites for future food distribution. The results are shown in Table 5. This work takes into account all four districts, and one site is selected to represent the top priority.

7 Strengths and weakness

Rough set theory can evaluate the importance of particular attributes and eliminate redundant attributes from a decision table. It can be constructed from minimal subsets of independent attributes, and ensures the same quality of classification as the entire set, i.e., reducts of the set of attributes. Intersections of these reducts provide a core of attributes, which cannot be eliminated without disturbing the ability to approximate the classification, and the generation of logical rules from the reduced decision table. Alternatively, TOPSIS is a simple soft computing method that can be easily implemented using any type of quantitativedata.

Along with the above mentioned strengths, there are some weaknesses inherent to these techniques. Selecting appropriate data for these techniques requires extensive study; any addition or deletion can affect the overall accuracy, which may lead to inaccurate results. For site selection, it is expected that the information provided must be accurate and repeatedly revised, leading lead to fewer opportunities for error.

8 Conclusion and future work

This study presents a systematic and flexible approach to deal with rule-based multi-criteria decision making problems, and provides a foundation for decision making regarding appropriate site selection. The successful integration of an RST data mining technique and a multi-criteria decision making method (TOPSIS) has led to successful prediction of sites for PRCS in the four studied districts.

Rough set theory has been used to evaluate the feasibility of different site selection applications, demonstrating 98% accuracy, while the TOPSIS method determines the top priority sites for food distribution. Most PRCS problems involving site selection can be solved according to the proposed method. The advantage of using this method over others is to provide ease, rapid and accurate evaluation of appropriate sites for future food distribution. As rough set theory is a data mining technique, it can demonstrate more accurate results with large changes in data, while the TOPSIS method can be applied to any data.

For future work, variations in rough set theory (i.e., fuzzy rough sets) and in the TOPSIS method (i.e., fuzzy TOPSIS) can also be applied to such data to induce greater accuracy. The evaluation of more sites and attributes are also suggested for incorporationinto the suggested technique.