Linear programming method for MADM with interval-valued intuitionistic fuzzy sets

Fuzziness is inherent in decision data and decision making process. In this paper, interval-valued intuitionistic fuzzy (IVIF) sets are used to capture fuzziness in multiattribute decision making (MADM) problems. The purpose of this paper is to develop a methodology for solving MADM problems with bo...

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Vydáno v:Expert systems with applications Ročník 37; číslo 8; s. 5939 - 5945
Hlavní autor: Li, Deng-Feng
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.08.2010
Témata:
Decision making
Expert systems
Fuzzy set theory
Intermediate frequency
Interval-valued intuitionistic fuzzy set
Intervals
Intuitionistic fuzzy set
Linear programming
Mathematical models
Mathematical programming
Methodology
Multiattribute decision making
Uncertainty
Interval-valued intuitionistic fuzzy set
Multiattribute decision making
Intuitionistic fuzzy set
Uncertainty
Mathematical programming
ISSN:0957-4174, 1873-6793
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Shrnutí:Fuzziness is inherent in decision data and decision making process. In this paper, interval-valued intuitionistic fuzzy (IVIF) sets are used to capture fuzziness in multiattribute decision making (MADM) problems. The purpose of this paper is to develop a methodology for solving MADM problems with both ratings of alternatives on attributes and weights being expressed with IVIF sets. In this methodology, a weighted absolute distance between IF sets is defined using weights of IF sets. Based on the concept of the relative closeness coefficients, we construct a pair of nonlinear fractional programming models which can be transformed into two simpler auxiliary linear programming models being used to calculate the relative closeness coefficient intervals of alternatives to the IVIF positive ideal solution, which can be employed to generate ranking order of alternatives based on the concept of likelihood of interval numbers. The proposed method is illustrated with a real example.
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ISSN:0957-4174
1873-6793
DOI:10.1016/j.eswa.2010.02.011