Decision making method based on Pythagorean fuzzy sets and its application to solid waste management

Abstract

The fuzzy decision-making trial and evaluation laboratory (fuzzy DEMATEL) has been used to solve various multi-criteria group decision-making problems where triangular fuzzy numbers are utilized in defining decision makers' linguistic judgements. Most of the fuzzy DEMATEL modifications are built from linguistic variables based on fuzzy sets. Recent literature suggests that Pythagorean fuzzy sets (PFS) can offer a better alternative particularly when fuzzy sets have some extent of limitations in handling vagueness and uncertainty. This paper proposes a modification fuzzy DEMATEL characterized by PFS for linguistic variables. Differently from the typical fuzzy DEMATEL which directly utilizes triangular fuzzy numbers with a single membership, this modification introduces membership and non-membership of PFS to enhance judgements in the group decision-making environment. The proposed method has a number of attractive features. It includes linguistic variables, expert's weights, and score function, in which all of these features are expressed by PFS. The proposed modification is applied to a case of solid waste management (SWM) where ten criteria are considered in assessment. Six experts in SWM were invited to provide linguistic judgments with respect to the criteria, and the eleven-step computational procedure of the proposed method was implemented without losing the general structure of the DEMATEL method. The results unveiled that four criteria are identified as 'cause group' and six criteria are identified as 'effect group' in SWM. The grouping of criteria would help policy makers in identifying the criteria that could enhance the efficiency of SWM. Keywords Pythagorean fuzzy set • DEMATEL • Causal diagram • Decision making • Solid waste management Develop seven-scale linguistic variable Construct direct-relation matrix with Pythagorean Fuzzy number Phase 2 PF-DEMATEL Construct an aggregated matrix Construct Weighted the Pythagorean Fuzzy matrix with different weigth of expert. Construct total average crisp matrix Construct normalized the average crisp matrix Construct total-relation matrix Calculate sum of row and column base on total-relation matrix Construct causal diagram Phase 3 Causal Diagram Network relationship map Phase 1 Define Linguistic variable

Attribute Reduction Methods Based on Pythagorean Fuzzy Covering Information Systems

“…We conclude that the approximate accuracy of the fuzzy λ-covering rough set for X is 1 3 , which is relatively small. Now, we reconsider the above example by using the PF λ-covering rough set.…”

“…Remark 1: In general, the smaller the approximate accuracy is, the less knowledge information is known for set X . From the above examples, it can be seen that since the approximate accuracy for X increases from 1 3 to 1 based on two different methods, we can obtain more knowledge information by using the PF λ-covering rough set rather than the fuzzy λ-covering rough set. For some reason, the fuzzy λ-covering rough set proposed by Ma [15] only considers the degree of membership and does not take into account the effects of other factors, so available knowledge information is insufficient in the decision-making process based on the fuzzy λ-covering rough set.…”

“…Compared with the intuitionistic fuzzy set, PFS is more comprehensive and scientific with respect to modeling uncertainty because it requires that the square sum of its membership and nonmembership does not exceed 1. Since its emergence, the field of PFS has attracted increasing attention from researchers [1]- [3], [5], [17], [18], [25], [33]- [35], [38], [39]. This new mathematical model not only promotes the development of fuzzy mathematics but also provides improved solutions for many practical problems, such as career orientation selection [44], internet stock investment [19] and software development investment [20].…”

Pythagorean Fuzzy Analytical Network Process (ANP) and Its Application to Warehouse Location Selection Problem

“…In this study, by following the same process, the network structure for 10 criteria recommended by experts for the storage location selection problem was determined by the Pythagorean fuzzy DEMATEL (PFDEMATEL) method and then the weight values of the criteria were determined through the proposed Pythagorean fuzzy ANP (PFANP) method. Preliminaries of PFS, and detailed calculation steps of PFDEMATEL, which were used in calculation steps of this study, can be found in [34,35] respectively. The use of the ANP method with the PFSs and its extensions has not proposed in the literature, and also the application of PFS based ANP has never been used in a medical sector WLSP before.…”

An Intuitionistic Fuzzy Decision-Making for Developing Cause and Effect Criteria of Subcontractors Selection

“…Furthermore, the proposed IF-DEMATEL also considers the importance weight of experts. It was noticed that there are no weights of experts assumed in most of the DEMATEL based methods [24][25][26][27]. In response to this issue, this proposed method introduced relative weights of experts based on the three numbers of IFNs of five linguistic terms.…”