Abstract
AbstractIn this paper, we propose new methods to represent interdependence among alternative attributes and experts’ opinions by constructing Choquet integral using interval-valued intuitionistic fuzzy numbers. In the sequel, we apply these methods to solve the multiple attribute group decision-making (MAGDM) problems under interval-valued intuitionistic fuzzy environment. First, the concept of interval-valued intuitionistic fuzzy Choquet integral is defined, and some elementary properties are studied in detail. Next, an axiomatic system of interval-valued intuitionistic fuzzy measure is established by delivering a series of mathematical proofs. Then, with fuzzy entropy and Shapely-values in game theory, we propose the interval-valued intuitionistic fuzzy measure development methods in order to form the importance measure of attributes and correlation measure of the experts, respectively. Based on the results of theoretical analysis, a new method is proposed to handle the interval-valued intuitionistic fuz...
Highlights
With the increasing complexity and uncertainty of the social-economic environment and various limitations, such as time pressure, lack of knowledge of problem domain, difficulties in information extraction etc., there are numerous uncertain phenomena existing in our daily life
Based on the analysis presented before, we develop a new method for multiple attribute group decision-making (MAGDM) problems under interval-valued intuitionistic fuzzy environment
The main advantage of our method is that we develop a new method to determine the fuzzy measures directly based on decision information, while in Tan’s method, the fuzzy measures need provided by the decision maker which maybe difficult to the decision makers (DMs) and is closely related the subjective preferences of the DMs, or even lead to inconsistent results
Summary
With the increasing complexity and uncertainty of the social-economic environment and various limitations, such as time pressure, lack of knowledge of problem domain, difficulties in information extraction etc., there are numerous uncertain phenomena existing in our daily life. Xu 40 investigated Choquet integral to propose some intuitionistic fuzzy aggregation operators, and applied them to solve intuitionistic fuzzy multiple attribute decision making problems. Meng et al 45 defined some new hybrid Choquet integral aggregation operators, and proposed a method to solve multiple criteria group decision making (MCGDM) based on intuitionistic fuzzy Choquet integral with respect to the generalized λ -Shapely index. When Choquet integral is used to handle MADM problems under interval-valued intuitionistic fuzzy environment, the most challenging difficulty is how to determine fuzzy measure with an effective and accurate method. The motivation of this study is to develop a new method of constructing fuzzy measures based on interval-valued intuitionistic information and apply them to the group decision making problems.
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