Intuitionistic Fuzzy Interval-Valued Linguistic Entropic Combined Weighted Averaging Operator for Linguistic Group Decision Making

Abstract

Entropy, a basic concept of measuring the amount of information and the degree of confusion, has been applied in many weighted averaging operators in the linguistic group decision making. In the paper, we construct an intuitionistic fuzzy linguistic entropy based on the intuitionistic fuzzy entropy and the intuitionistic fuzzy linguistic variable. Then, inspired by operations of concentration and dilation (De SK, Biswas R, and Roy AR, Fuzzy Sets Syst. 2000;114(3):477ȓ484), we extend the intuitionistic fuzzy linguistic entropy to the intuitionistic fuzzy interval‐valued linguistic entropy. After that, the intuitionistic fuzzy interval‐valued linguistic entropic combined weighted averaging (IFIVLECWA) operator is proposed for multiple attribute linguistic group decision making. Finally, a numerical example about the selection of optimal alternative(s) is presented to illustrate the applicability and effectiveness of the proposed method.

Linguistic‐induced ordered weighted averaging operator for multiple attribute group decision‐making

“…In the next, we are going to present the ordering of the engineers in Table 12. Fair F ( ) [3,5,5,7] MediumGood MG ( ) [5,7,7,9] Good G ( ) [7,9,9,10] VeryGood VG ( ) [9,9,9,10] T A B L E 5 Linguistic variables for the confidence (12, ( [5, 7, 7, 9]; [0.7, 0.9, 0.9, 1.0] , (0.3, 0.3, 0.5, 0.7; 1))) 〈 〉 (13, ( [7, 9, 9, 10]; [0.9, 0.9, 1.0, 1.0] , (0.5, 0.7, 0.7, 0.9; 1))) A 2 〈 〉 (12, ( [7, 9, 9, 10]; [0.7, 0.9, 0.9, 1.0] , (0.9, 0.9, 1.0, 1.0; 1))) 〈 〉 (15, ( [9, 9, 9, 10]; [0.9, 0.9, 1.0, 1.0] , (0.5, 0.7, 0.7, 0.9; 1))) A 3 〈 〉 (13, ( [9, 9, 9, 10]; [0.7, 0.9, 0.9, 1.0] ,(0.9, 0.9, 1.0, 1.0; 1))) 〈 〉 (11, ( [5, 7, 7, 9]; [0.9, 0.9, 1.0, 1.0] , (0.3, 0.3, 0.5, 0.7; 1)))…”

“…) = ([1,5,6,8]; [0.2, 0.4, 0.6, 0.8]1 1 , (0.3, 0.5, 0.7, 0.8;1)), 〈 = ( , ) = ([2,3,6,9]; [0.2, 0.5, 0.7, 1.0] 2 2 2…”

Interval 2‐tuple Pythagorean fuzzy linguistic MULTIMOORA method with CIA and their application to MCGDM

“…For example, when one people evaluate the risk level of the stock market, linguistic term “low,” “medium,” and “high” can be used. Therefore, Zadeh proposed the fuzzy linguistic approach, in which the evaluations are taken as linguistic terms rather than crisp numbers to make the representation of information much closer to people's expression habits, and aroused growing concerns in recent years . Wang and Li combined the IFS with linguistic terms and proposed intuitionistic linguistic set (ILS).…”

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

“…proposed a new intuitionistic fuzzy linguistic hybrid aggregation operator to aggregate the information. Xian et al . presented the intuitionistic fuzzy interval‐valued linguistic entropic combined weighted averaging operator for dealing with linguistic group decision making.…”