Abstract
As an extension of classical fuzzy set, intuitionistic fuzzy set (IFS) has been widely utilized in decision making. Based on IFS, intuitionistic fuzzy value (IFV) and linguistic intuitionistic fuzzy set (LIFS) have also been proposed to represent uncertain assessments of alternatives in different intuitionistic fuzzy decision environment. Theoretically, IFV, IFS or LIFS own themselves processing methods in decision making. However, they may be utilized to represent intuitionistic fuzzy assessments of alternatives in the same decision problem, i.e., multi-decision makers provide IFVs, IFSs or LIFSs to represent uncertain assessments of alternatives in the decision problem. In such case, the significant challenge is to unify IFVs, IFSs and LIFSs in the decision making matrices. In the paper, novel transformation methods are presented to unify IFVs, IFSs and LIFSs. To this end, mixed intuitionistic fuzzy decision matrix is presented to represent IFV, IFS or LIFS assessments of alternatives provided by decision makers, then transformation functions are developed to unify IFVs, IFSs and LIFSs in the decision making matrices, their properties are also analysed. The decision making method is presented to solve the intuitionistic fuzzy decision making problems with IFVs, IFSs or LIFSs, which is consisted of six main phases, accordingly the algorithm is designed to carry out the problems. Illustrative examples show that transformation functions are useful in intuitionistic fuzzy decision environment, the proposed decision making method is an effective and alternative tool for the intuitionistic fuzzy decision making problems with IFVs, IFSs or LIFSs.
Highlights
Due to the lack of knowledge or information, there is pervasive uncertainty when the real world physical objects are represented by the human cognition, such as in big data, there is uncertain information when decision makers provide assessments of alternatives, this makes that decision problems become difficult and complex [1]
From intuitionistic fuzzy value (IFV) to intuitionistic fuzzy set (IFS) and linguistic intuitionistic fuzzy set (LIFS), different intuitionistic fuzzy assessments of alternatives are provided by decision makers depending on their knowledge level, background or experience, the situation can arises especially in large-scale decision making environment based on big data, in which there are a huge number of decision makers, alternatives and criteria for intuitionistic fuzzy decision problems
Due to knowledge level, background or experience of decision makers, IFVs, IFSs or LIFSs may be utilized by decision makers to assess alternatives with respect to criteria in the mixed intuitionistic fuzzy decision making
Summary
Due to the lack of knowledge or information, there is pervasive uncertainty when the real world physical objects are represented by the human cognition, such as in big data, there is uncertain information when decision makers provide assessments of alternatives, this makes that decision problems become difficult and complex [1]. Many fuzzy decision making methods have been proposed [3]–[6], in which assessments of alternatives provided by decision makers are represented by fuzzy sets or linguistic values. From IFVs to IFSs and LIFSs, different intuitionistic fuzzy assessments of alternatives are provided by decision makers depending on their knowledge level, background or experience, the situation can arises especially in large-scale decision making environment based on big data, in which there are a huge number of decision makers, alternatives and criteria for intuitionistic fuzzy decision problems. The transformation functions can be utilized to unify mixed intuitionistic fuzzy decision matrix, intuitionistic fuzzy aggregation operators or ordering methods can be utilized to carry out MIFDM problems; 3) The MIFDM method is presented by six main phases, an algorithm is designed.
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