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Fuzzy Optimization and Decision Making

Erschienen in:

10.02.2020

A scalarization method for fuzzy set optimization problems

verfasst von: Masamichi Kon

Erschienen in: Fuzzy Optimization and Decision Making | Ausgabe 2/2020

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Abstract

In the present paper, we consider fuzzy optimization problems which involve fuzzy sets only in the objective mappings, and give two concepts of optimal solutions which are non-dominated solutions and weak non-dominated solutions based on orderings of fuzzy sets. First, by using level sets of fuzzy sets, the fuzzy optimization problems treated in this paper are reduced to set optimization problems, and relationships between (weak) non-dominated solutions of the fuzzy optimization problems and the reduced set optimization problems are derived. Next, the set optimization problems are reduced to scalar optimization problems which can be regarded as scalarization of the fuzzy optimization problems. Then, relationships between non-dominated solutions of the fuzzy optimization problems and optimal solutions of the reduced scalar optimization problems are derived.

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Bellman, R. E., & Zadeh, L. A. (1970). Decision making in a fuzzy environment. Management Science, 17, 141–164.MathSciNetCrossRef

Dubois, D., Ostasiewicz, W., & Prade, H. (2000). Fuzzy sets: History and basic notions. In D. Dubois & H. Prade (Eds.), Fundamentals of fuzzy sets (pp. 21–124). Boston: Kluwer.CrossRef

Gupta, S. K., & Dangar, D. (2014). Duality for a class of fuzzy nonlinear optimization problem under generalized convexity. Fuzzy Optimization and Decision Making, 13, 131–150.MathSciNetCrossRef

Hernández, H., & Rodríguez-Marín, L. (2007). Nonconvex scalarization in set optimization with set-valued maps. Journal of Mathematical Analysis and Applications, 325, 1–18.MathSciNetCrossRef

Inuiguchi, M. (2005). Multiple objective linear programming with fuzzy coefficients. In J. Figueira, S. Greco, & M. Ehrgott (Eds.), Multiple criteria decision analysis: State of the art surveys (pp. 723–760). New York: Springer.CrossRef

Inuiguchi, M. (2007). On possibilistic/fuzzy optimization. In P. Melin, O. Castillo, L. T. Aguilar, & W. Pedrycz (Eds.), Foundations of fuzzy logic and soft computing (pp. 351–360). Berlin Heidelberg: Springer.CrossRef

Inuiguchi, M., & Ramík, J. (2000). Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets and Systems, 111, 3–28.MathSciNetCrossRef

Jahn, J., & Ha, T. X. D. (2011). New order relations in set optimization. Journal of Optimization Theory and Applications, 148, 209–236.MathSciNetCrossRef

Jamison, K. D., & Lodwick, W. A. (1999). Minimizing unconstrained fuzzy functions. Fuzzy Sets and Systems, 103, 457–464.MathSciNetCrossRef

Kon, M. (2014). Operation and ordering of fuzzy sets, and fuzzy set-valued convex mappings, Journal of Fuzzy Set Valued Analysis, Article ID jfsva-00202.

Kon, M. (2013). On degree of non-convexity of fuzzy sets. Scientiae Mathematicae Japonicae, 76, 417–425.MathSciNetMATH

Kurano, M., Yasuda, M., Nakagami, J., & Yoshida, Y. (2000). Ordering of convex fuzzy sets—A brief survey and new results. Journal of the Operations Research Society of Japan, 43, 138–148.MathSciNetMATH

Kuroiwa, D., Tanaka, T., & Ha, T. X. D. (1997). On cone convexity of set-valued maps. Nonlinear Analysis: Theory, Methods & Applications, 30, 1487–1496.MathSciNetCrossRef

Maeda, T. (2008). On characterization of fuzzy vectors and its applications to fuzzy mathematical programming problems. Fuzzy Sets and Systems, 159, 3333–3346.MathSciNetCrossRef

Maeda, T. (2012). On optimization problems with set-valued objective maps: Existence and optimality. Journal of Optimization Theory and Applications, 153, 263–279.MathSciNetCrossRef

Ramík, J., & Řimánek, J. (1985). Inequality relation between fuzzy numbers and its use in fuzzy optimization. Fuzzy Sets and Systems, 16, 123–138.MathSciNetCrossRef

Wu, H.-C. (2006). Scalarization of the fuzzy optimization problems. Fuzzy Optimization and Decision Making, 5, 331–353.MathSciNetCrossRef

Wu, H.-C. (2007). Duality theory in fuzzy optimization problems formulated by the Wolfe’s primal and dual pair. Fuzzy Optimization and Decision Making, 6, 179–198.MathSciNetCrossRef

Wu, H.-C. (2008). The optimality conditions for optimization problems with fuzzy-valued objective functions. Optimization, 57, 473–489.MathSciNetCrossRef

Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.MathSciNetCrossRef

Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning-I. Information Sciences, 8, 199–249.MathSciNetCrossRef

Titel: A scalarization method for fuzzy set optimization problems
verfasst von: Masamichi Kon
Publikationsdatum: 10.02.2020
Verlag: Springer US
Erschienen in: Fuzzy Optimization and Decision Making / Ausgabe 2/2020
Print ISSN: 1568-4539
Elektronische ISSN: 1573-2908
DOI: https://doi.org/10.1007/s10700-020-09313-0

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