Intuitionistic Fuzzy Hybrid Aggregation Operator Research Articles

Induced Atanassov's interval-valued intuitionistic fuzzy hybrid Choquet integral operators and their application in decision making

AbstractBased on the Choquet integral and the generalized Shapley function, two new induced Atanassov's interval-valued intuitionistic fuzzy hybrid aggregation operators are defined, which are named as the induced generalized Shapley Atanassov's interval-valued intuitionistic fuzzy hybrid Choquet arithmetical averaging (IGS-IVIFHCAA) operator and the induced generalized Shapley Atanassov's interval-valued intuitionistic fuzzy hybrid Choquet geometric mean (IGS-IVIFHCGM) operator. These operators do not only globally consider the importance of elements and their ordered positions, but also overall reflect the correlations among them and their ordered positions. Meantime, some important cases are examined, and some desirable properties are studied. Furthermore, if the information about the weighting vectors is incompletely known, the models for the optimal λ–fuzzy measures on attribute set and ordered set are established, respectively. Moreover, an approach to multi-attribute decision making under Atanassov...

Induced Interval‐Valued Intuitionistic Fuzzy Hybrid Aggregation Operators with TOPSIS Order‐Inducing Variables

Two induced aggregation operators with novelly designed TOPSIS order‐inducing variables are proposed: Induced Interval‐valued Intuitionistic Fuzzy Hybrid Averaging (I‐IIFHA) operator and Induced Interval‐valued Intuitionistic Fuzzy Hybrid Geometric (I‐IIFHG) operator. The merit of two aggregation operators is that they can consider additional preference information of decision maker’s attitudinal characteristics besides argument‐dependent information and argument‐independent information. Some desirable properties of I‐IIFHA and I‐IIFHG are studied and theoretical analysis also shows that they can include a wide range of aggregation operators as special cases. Further, we extend these operators to form a novel group decision‐making method for selecting the most desirable alternative in multiple attribute multi‐interest group decision‐making problems with attribute values and decision maker’s interest values taking the form of interval‐valued intuitionistic fuzzy numbers, and application research to real estate purchase selection shows its practicality.

A Deviation-Based Approach to Intuitionistic Fuzzy Multiple Attribute Group Decision Making

The aim of this article is to investigate the approach to multiple attribute group decision making (MAGDM) with intuitionistic fuzzy information. We first introduce a deviation measure between two intuitionistic fuzzy numbers, and then utilize the intuitionistic fuzzy hybrid aggregation operator to aggregate all individual intuitionistic fuzzy decision matrices into a collective intuitionistic fuzzy decision matrix. Based on the deviation measure, we develop an optimization model by which a straightforward formula for deriving attribute weights can be obtained. Furthermore, based on the intuitionistic fuzzy weighted averaging operator and information theory, we utilize the score function and accuracy function to give an approach to ranking the given alternatives and then selecting the most desirable one(s). In addition, we extend the above results to MAGDM with interval-valued intuitionistic fuzzy information.

Intuitionistic Fuzzy Aggregation Operators

An intuitionistic fuzzy set, characterized by a membership function and a non-membership function, is a generalization of fuzzy set. In this paper, based on score function and accuracy function, we introduce a method for the comparison between two intuitionistic fuzzy values and then develop some aggregation operators, such as the intuitionistic fuzzy weighted averaging operator, intuitionistic fuzzy ordered weighted averaging operator, and intuitionistic fuzzy hybrid aggregation operator, for aggregating intuitionistic fuzzy values and establish various properties of these operators.