Linguistic Intuitionistic Fuzzy Sets and Application in MAGDM

Abstract

To better deal with imprecise and uncertain information in decision making, the definition of linguistic intuitionistic fuzzy sets (LIFSs) is introduced, which is characterized by a linguistic membership degree and a linguistic nonmembership degree, respectively. To compare any two linguistic intuitionistic fuzzy values (LIFVs), the score function and accuracy function are defined. Then, based ont-norm andt-conorm, several aggregation operators are proposed to aggregate linguistic intuitionistic fuzzy information, which avoid the limitations in exiting linguistic operation. In addition, the desired properties of these linguistic intuitionistic fuzzy aggregation operators are discussed. Finally, a numerical example is provided to illustrate the efficiency of the proposed method in multiple attribute group decision making (MAGDM).

A new trapezoidal Pythagorean fuzzy linguistic entropic combined ordered weighted averaging operator and its application for enterprise location

“…Inspired by Yager's work and Zhang's work, we propose the TrPFLOWA operator, then we further propose the TrPFLECOWA operator.…”

“…These information are more accurate and detailed. So Zhang defined the intuitionistic fuzzy linguistic sets and applied them to solve MAGDM problems.…”

“…To further apply the PFSs to the practical application, we define the trapezoidal Pythagorean fuzzy linguistic variables (TrPFLVs) by extending the PFSs to the linguistic environment and develop the operational rules, value index, and ambiguity index of TrPFLVs. Inspired by the work of Yager, Zhang, and Burillo and Bustince, we introduce a new trapezoidal Pythagorean fuzzy linguistic entropic combined ordered weighted averaging (TrPFLECOWA) operator to solve the above problems. The existing methods fail to solve the MAGDM problems with the trapezoidal Pythagorean fuzzy linguistic information, so we propose a novel method based on the TrPFLECOWA operator to help DMs make an ideal decision.…”

The Linguistic Interval-Valued Intuitionistic Fuzzy Aggregation Operators Based on Extended Hamacher T-Norm and S-Norm and Their Application

“…It is worth noting that the above-mentioned DLTSs focus on the qualitative representation of membership degree, and do not pay attention to the non-membership degree that can feedback experts' negation. In order to comprehensively consider the advantages of membership and non-membership in characterizing experts' psychological characteristics, scholars extended the concept of intuitionistic fuzzy sets (IFSs) [20] to linguistic information environment and proposed linguistic intuitionistic fuzzy sets (LIFSs) [21,22]. LIFSs could qualitatively represent membership or non-membership through linguistic variables.…”

Linguistic Neutrosophic Cubic Numbers and Their Multiple Attribute Decision-Making Method

“…Due to the incompleteness and uncertainty of linguistic decision environments, uncertain linguistic variables and their various aggregation operators were developed and applied to uncertain linguistic decision-making problems [6][7][8][9][10][11]. As to the extension of linguistic variables, the concept of linguistic intuitionistic fuzzy numbers and their linguistic intuitionistic multicriteria group decision-making methods were introduced in the literature [12,13], and then linguistic intuitionistic multicriteria decision-making method was proposed based on the Frank Heronian mean operator [14]. Recently, the concept of a neutrosophic linguistic number, which indicates a changeable uncertain linguistic number corresponding to some specified indeterminate range, and some weighted aggregation operators of neutrosophic linguistic numbers, were presented to solve multiple attribute group decision-making problems with neutrosophic linguistic numbers [15].…”