TOPSIS Method Based on Correlation Coefficient and Entropy Measure for Linguistic Pythagorean Fuzzy Sets and Its Application to Multiple Attribute Decision Making

Mingwei Lin,Zeshui Xu,Chao Huang

doi:10.1155/2019/6967390

Abstract

The linguistic Pythagorean fuzzy set (LPFS) is an important implement for modeling the uncertain and imprecise information. In this paper, a novel TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method is proposed for LPFSs based on correlation coefficient and entropy measure. To this end, the correlation coefficient is proposed for the relationship measurement between LPFSs. Afterwards, two entropy measures are developed to calculate the attribute weight information. Then, a novel linguistic Pythagorean fuzzy TOPSIS (LPF-TOPSIS) method is proposed to solve multiple attribute decision-making problems. Finally, the LPF-TOPSIS method is applied to handle a case concerning the selection of firewall productions, and then, a case concerning the security evaluation of computer systems is given to conduct the comparative analysis between the proposed LPF-TOPSIS method and previous decision-making methods for validating the superiority of the proposed LPF-TOPSIS method.

Highlights

As for the MADM methods for linguistic Pythagorean fuzzy set (LPFS), there exist some deficiencies that are analyzed as follows:
The data structure contained in LPFSs is different from that of the previous fuzzy information. erefore, the previous TOPSIS methods cannot be directly used for LPFSs
Our contributions can be summarized as follows: (1) We propose the equations of correlation coefficient and weighted correlation coefficient for LPFSs based on MD, NMD, and hesitance degree, and their properties are discussed

Summary

Preliminaries

We briefly review some basic knowledge about LPFSs and classical TOPSIS method. Each pair of MD and NMD (sp(x), sq(x)) is simplified as α (sp, sq), which is named an linguistic Pythagorean fuzzy number (LPFN). Garg [41] put forward a comparison method consisting of score function and accuracy function to compare LPFNs. Definition 2 (see [41]). Given an LPFN A (sp, sq) with sp and sq being the elements of a continuous LTS. If. To aggregate LPFNs Ai (spi, sqi), i 1, 2, . N in which sp and sq belong to a continuous LTS S 􏽮sβ | β ∈ [0, τ]􏽯, the LPFWG aggregation operator is a function that is defined as LPFWG A1, A2, . E weight vector satisfies 0 ≤ ω ≤ 1 j of attributes is ω and 􏽐nj 1ωj 1.

Correlation Coefficient and Entropy Measure

Novel TOPSIS Method Based on Correlation Coefficient and Entropy Measure

Case Study and Comparative Analyses

Conclusions