Interval-Valued Intuitionistic Fuzzy Einstein Geometric Choquet Integral Operator and Its Application to Multiattribute Group Decision-Making

Abstract

With respect to the multiattribute decision-making (MADM) problem in which the attributes have interdependent or interactive phenomena under the interval-valued intuitionistic fuzzy environment, we propose a group decision-making approach based on the interval-valued intuitionistic fuzzy Einstein geometric Choquet integral operator (IVIFEGC). Firstly, the Einstein operational laws and some basic principle on interval-valued intuitionistic fuzzy sets are introduced. Then, the IVIFEGC is developed and some desirable properties of the operator are studied. Further, an approach to multiattribute group decision-making with interval-valued intuitionistic fuzzy information is developed, where the attributes have interdependent phenomena. Finally, an illustrative example is used to illustrate the developed approach.

Interval-Valued q-Rung Orthopair Fuzzy Choquet Integral Operators and Their Application in Group Decision-Making

“…e comprehensive attribute values of each alternative are obtained through equation (40), and the results are obtained as follows: (43) erefore, the ranking of alternatives is x 3 > x 2 > x 1 > x 4 > x 5 , and x 3 is the optimal selection, which means the doctor is required for timely follow-up to promote management of blood pressure of this patient who receives yellow warning.…”

“…where a ′(t) ij represents the IVq-ROFNs in the decision matrix given by the t-th expert. (4) en, the collective value r i of x i is derived by equation (40), which aggregates the fuzzy information corresponding to attributes:…”

“…In this subsection, the proposed method is used to solve the case in [32], which is compared with the method given in [32,40]. ere are 5 alternatives with 4 attributes C 1 , C 2 , C 3 , and C 4 for 3 experts e 1 , e 2 , and e 3 to make a decision, and the evaluation matrices A (1) , A (2) , and A (3)…”

“…Score or closeness Alternative ranking Proposed method Score: S(x 1 ) � 0.16S(x 2 ) � 0.71S(x 3 ) � 0.74S(x 4 ) � 0.38S(x 5 ) � 0.77 x > x 3 > x 2 > x 4 > x 1 IVIFEGC [40] Score: S(x 1 ) � 0.05S(x 2 ) � 0.66S(x 3 ) � 0.65S(x 4 ) � 0.26S(x 5 ) � 0.70 x > x 2 > x 3 > x 4 > x 1 Choquet integral-based TOPSIS (CITOPSIS) [32] Closeness: r(x 1 ) � 0.4817r(x 2 ) � 0.5465r(x 3 ) � 0.5297r(x 4 ) � 0.4990r(x 5 ) � 0.4958…”

Probabilistic Linguistic Aggregation Operators Based on Einstein t-Norm and t-Conorm and Their Application in Multi-Criteria Group Decision Making

“…Cai and Han [15] developed the induced interval-valued Einstein ordered weighted averaging operator. Wang and Sun [16] also examined the interval-valued intuitionistic fuzzy Einstein geometric Choquet integral operator. Rahman et al [17] focused on interval-valued Pythagorean fuzzy Einstein hybrid weighted averaging aggregation operator and their application to group decision making.…”