The linguistic intuitionistic fuzzy set TOPSIS method for linguistic multi-criteria decision makings

Abstract

In the paper, we express uncertain assessments information in linguistic multi-criteria decision makings (LMCDMs) as linguistic intuitionistic fuzzy sets, i.e., the decision maker provides membership and nonmembership fuzzy linguistic terms to represent uncertain assessments information of alternatives in LMCDMs, and present Hamming distance between two linguistic intuitionistic fuzzy sets. Then we propose the linguistic intuitionistic fuzzy set TOPSIS method for LMCDMs, compared with the traditional TOP-SIS method, we provide different the positive ideal solution, the negative ideal solution and the relative closeness degrees of alternatives, in addition, we design an algorithm to finish the linguistic intuitionistic fuzzy set TOPSIS method for LMCDMs. We utilize a LMCDM problem to illustrate the performance, usefulness and effectiveness of the linguistic intuitionistic fuzzy set TOPSIS method, and compare it with the hesitant fuzzy linguistic multi-criteria optimization and compromise solution (HFL-VIKOR) method, the symbolic aggregation-based method and the hesitant fuzzy linguistic TOPSIS (HFL-TOPSIS) method in the example, results show that the linguistic intuitionistic fuzzy set TOPSIS method is a useful and alternative method for LMCDMs.

Constructing Novel Operational Laws and Information Measures for Proportional Hesitant Fuzzy Linguistic Term Sets with Extension to PHFL-VIKOR for Group Decision Making

“…Determine the objective weights of attributes based on entropy measure according to Eqs. (20) and (21). Then, we have the objective weights vector of attributes O = (0.2427, 0.0808, 0.1336, 0.5429) T .…”

“…The selection of decision-making approach is another important issue in MAGDM problems. A variety of MAGDM methods have been developed and applied for different decision environments for examples, the TOPSIS method [19][20][21][22][23], the PROMETHEE method [24,25], the TODIM method [16,26,27], and the VIKOR method [28,29]. Among these mentioned methods, VIKOR is an ideal point-based MAGDM method for dealing with discrete decision problems with non-commensurable and conflicting criteria [30].…”

Novel Transformation Methods Among Intuitionistic Fuzzy Models for Mixed Intuitionistic Fuzzy Decision Making Problems

“…Recently, because linguistic terms provide a more direct way to qualitatively express fuzzy information in decision making, linguistic decision making (LDM, assessments of alternatives provided by decision makers are represented by fuzzy linguistic terms) is closest to human beings' cognitive process that occurs in daily life, and many researchers have paid attention to LDM problems [1], [5], [27]- [32]. Inspired by IFS, the concept of LIFS has been proposed and applied in LDM problems [33], operations of LIFSs and their fundamental properties are widely researched [34], [35]. In [36]- [38], Meng provided linguistic intuitionistic fuzzy preference relations, multiplicative linguistic intuitionistic fuzzy preference relations, heterogeneous intuitionistic fuzzy preference relations for linguistic intuitionistic fuzzy decision problems, furthermore an additive consistency and its desirable properties of these preference relations have been analyzed.…”

A multi-attribute decision making method based on the third generation prospect theory and grey correlation degree

“…Liu [12] extended the partitioned Heronian means (HM) to LIFNs. Ou et al [13] proposed the TOPSIS method for LIFS. Peng et al [14] proposed a linguistic intuitionistic MADM approach based on the Heronian operator with Frank operations and applied it to evaluate coal mine safety.…”