Extension of the VIKOR method for group decision making with interval-valued intuitionistic fuzzy information |
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Authors: | Jin Han Park Hyun Ju Cho Young Chel Kwun |
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Institution: | 1. Division of Mathematical Sciences, Pukyong National University, Pusan, 608-737, Republic of Korea 2. Department of Mathematics, Dong-A University, Pusan, 604-714, Republic of Korea
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Abstract: | The aim of this paper is to extend the VIKOR method for multiple attribute group decision making in interval-valued intuitionistic
fuzzy environment, in which all the preference information provided by the decision-makers is presented as interval-valued
intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy
number, and the information about attribute weights is partially known, which is an important research field in decision science
and operation research. First, we use the interval-valued intuitionistic fuzzy hybrid geometric operator to aggregate all
individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued
intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and
construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and
the given attribute weight information, we establish an optimization model to determine the weights of attributes, and then
determine the interval-valued intuitionistic positive-ideal solution and interval-valued intuitionistic negative-ideal solution.
We use the different distances to calculate the particular measure of closeness of each alternative to the interval-valued
intuitionistic positive-ideal solution. According to values of the particular measure, we rank the alternatives and then select
the most desirable one(s). Finally, a numerical example is used to illustrate the applicability of the proposed approach. |
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