Using Gradual Numbers for Solving Fuzzy-Valued Combinatorial Optimization Problems

Authors:
Adam Kasperski;Paweł Zieliński
Affiliations:
Institute of Industrial Engineering and Management, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland;Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Venue:
IFSA '07 Proceedings of the 12th international Fuzzy Systems Association world congress on Foundations of Fuzzy Logic and Soft Computing
Year:
2007

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Abstract

In this paper a general approach to combinatorial optimization problems with fuzzy weights is discussed. The results, valid for the interval-valued problems, are extended to the fuzzy-valued ones by exploiting the very recent notion of a gradual number. Some methods for determining the exact degrees of possible and necessary optimality and the possibility distributions of deviations of solutions and elements are proposed. The introduced notions are illustrated by practical examples.