Linguistic Intuitionistic Fuzzy Aggregation Operators Research Articles

Multiple attribute group decision making based on 2-dimension linguistic intuitionistic fuzzy aggregation operators

The 2-dimension linguistic variables (2-DLVs) add a subjective evaluation on the reliability of the evaluation results provided by decision makers, so 2-DLVs are very useful tools for describing uncertain or fuzzy information. This work extends the idea of 2-DLVs by introducing 2-dimension linguistic intuitionistic fuzzy variables (2-DLIFVs) in which 1 class and 2 class information describe in the form of linguistic intuitionistic fuzzy numbers. The paper defines some operational laws, score, and accuracy functions for 2-DLIFVs. Further, we develop some arithmetic and geometric aggregation operators for aggregating 2-DLIF information and prove a number of valuable properties associated with them. Using the proposed aggregation operators, an approach for multiple attribute group decision making with 2-DLIF information is formulated. Finally, an illustrated example is given to verify and prove the validity of the developed method. The computed results are also compared with the existing results.

Group decision-making method based on prioritized linguistic intuitionistic fuzzy aggregation operators and its fundamental properties

Linguistic intuitionistic fuzzy set (LIFS) is one of the effective tools to represent the data in form of membership degrees in a qualitative rather than the quantitative aspects. Under this environment, the present paper develops some prioritized aggregation operators which considered the prioritized relationship between the attributes. To achieve it, first, some operational laws on LIF numbers are presented, and hence, based on these, some prioritized aggregation operators, namely, the LIF prioritized weighted, ordered weighted averaging, and geometric aggregation operators, have proposed. The fundamental properties of these operators are also investigated in detail. Furthermore, an approach to solve decision-making problem under LIFS environment has been presented and its efficiency has been verified with an illustrative example.

Linguistic Intuitionistic Fuzzy Group Decision Making Based on Aggregation Operators

This paper researches decision making with linguistic intuitionistic fuzzy variables. Several linguistic intuitionistic fuzzy operations are first defined. Then, several linguistic intuitionistic fuzzy aggregation operators are provided, including the linguistic intuitionistic fuzzy hybrid weighted arithmetical averaging operator, and the linguistic intuitionistic fuzzy hybrid weighted geometric mean operator. Considering the interactive characteristics between the weights of elements in a set, several linguistic intuitionistic fuzzy Shapley aggregation operators are presented, including the linguistic intuitionistic fuzzy hybrid Shapley arithmetical averaging operator, and the linguistic intuitionistic fuzzy hybrid Shapley geometric mean operator. To ensure the application reasonably, several desirable properties are discussed. When the weighting information is incompletely known, models for the optimal fuzzy and additive measures are constructed. After that, an approach to multi-criteria group decision making with linguistic intuitionistic fuzzy information is performed. Finally, a practical example about evaluating different types of engines is provided to illustrate the developed procedure.

Some Improved Linguistic Intuitionistic Fuzzy Aggregation Operators and Their Applications to Multiple-Attribute Decision Making

Linguistic intuitionistic fuzzy numbers (LIFNs) is a new concept in describing the intuitionistic fuzzy information, which membership and non-membership are expressed by linguistic terms, so it can more easily express the fuzzy information, and some research results on LIFNs have been achieved. However, in the existing researches, some linguistic intuitionistic fuzzy aggregation operators are based on the traditional operational rules, and they have some drawbacks for multi-attribute decision making (MADM) in the practical application. In order to overcome these problems, in this paper, we proposed some improved operational rules based on LIFNs and verified their some properties. Then we developed some aggregation operators to fuse the decision information represented by LIFNs, including the improved linguistic intuitionistic fuzzy weighted averaging (ILIFWA) operator and the improved linguistic intuitionistic fuzzy weighted power average (ILIFWPA) operator. Further, we proved their some desirable properties. Based on the ILIFWA operator and the ILIFWPA operator, we presented some new methods to deal with the multi-attribute group decision making (MAGDM) problems under the linguistic intuitionistic fuzzy environment. Finally, we used some practical examples to illustrate the validity and feasibility of the proposed methods by comparing with other methods.

Linguistic Intuitionistic Fuzzy Sets and Application in MAGDM

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).