Abstract
The theory of interval-valued intuitionistic fuzzy sets (IVIFSs) has been an impactful and convenient tool in the construction of advanced multiple attribute group decision making (MAGDM) models to counter the uncertainty in the developing complex decision support system. To satisfy much more demands from fuzzy decision making problems, we propose a method to solve the MAGDM problem in which all the information supplied by the decision makers is expressed as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by an interval-valued intuitionistic fuzzy number, and the information about the weights of both decision makers and attributes may be completely unknown or partially known. Firstly, we introduce a consensus-based method to quantify the weights of all decision makers based on all interval-valued intuitionistic fuzzy decision matrices. Secondly, we utilize the interval-valued intuitionistic fuzzy weighted arithmetic (IVIFWA) operator to aggregate all interval-valued intuitionistic fuzzy decision matrices into the collective one. Thirdly, we establish an optimization model to determine the weights of attributes depending on the collective decision matrix and the given attribute weight information. Fourthly, we adopt the weighted correlation coefficient of IVIFSs to rank all the alternatives from the perspective of TOPSIS via the collective decision matrix and the obtained weights of attributes. Finally, some examples are used to illustrate the validity and feasibility of our proposed approach by comparison with some existing models.
Highlights
Atanassov [1] introduced intuitionistic fuzzy sets (IFSs) as an extension of conventional fuzzy set proposed by Zadeh in 1965 [2]
To satisfy much more demands from fuzzy decision making problems, we propose a method to solve the multiple attribute group decision making (MAGDM) problem in which all the information supplied by the decision makers is expressed as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by an interval-valued intuitionistic fuzzy number, and the information about the weights of both decision makers and attributes may be completely unknown or partially known
It should be emphasized that multiple attribute decision making (MADM) and multiple attribute group decision making (MAGDM) on IFSs/intervalvalued intuitionistic fuzzy sets (IVIFSs) have been two especially important branches of operations research
Summary
Atanassov [1] introduced intuitionistic fuzzy sets (IFSs) as an extension of conventional fuzzy set proposed by Zadeh in 1965 [2]. As described in [20, 21], the provided partially known constraint condition may be constructed with the following forms: a weak ranking, a strict ranking, a ranking with multiples, an interval form, a ranking of differences, and an intervalvalued intuitionistic fuzzy numbers Some models, such as multiple-objective programming model [20, 22], fractional programming method [23], nonlinear programming model [24], linear programming model [25], and grey relational analysis [21], have been successfully developed from different perspectives to determine the weight vector of attributes.
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