Abstract
In this paper, a robust optimization approach to possibilistic linear programming problems is studied. After necessity measures and generation processes of logical connectives are reviewed, the necessity fractile optimization model of possibilistic linear programming problem is introduced as a robust optimization model. This problem is reduced to a linear semi-infinite programming problem. Assuming the convexity of the right parts of membership functions of fuzzy coefficients and the concavity of membership functions of fuzzy constraints, we investigate conditions on logical connectives for the problems to be reduced to linear programming problems. Several examples are given to demonstrate that necessity fractile optimization models are often reduced to linear programming problems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Rommelfanger, H., Słowiński, R.: Fuzzy Linear Programming with Single or Multiple Objective Functions. In: Słowiński, R. (ed.) Fuzzy Sets in Decision Analysis, Operations Research and Statistics, pp. 179–213. Kluwer, Boston (1998)
Inuiguchi, M., Ramík, J.: 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, 29–45 (2000)
Inuiguchi, M.: A Semi-infinite Programming Approach to Possibilistic Optimization under Necessity Measure Constraints. In: Proceedings of 2009 IFSA World Congress and 2009 EUSFLAT Conference, Lisbon, Portugal, pp. 873–878 (2009)
Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)
Dubois, D., Prade, H.: A Theorem on Implication Functions Defined from Triangular Norms. Stochastica 8, 267–279 (1984)
Inuiguchi, M., Sakawa, M.: On the Closure of Generation Processes of Implication Functions from a Conjunction Function. In: Yamakawa, T., Matsumoto, G. (eds.) Methodologies for the Conception, Design, and Application of Intelligent Systems, vol. 1, pp. 327–330. World Scientific, Singapore (1996)
Dubois, D., Prade, H.: Fuzzy Numbers: An Overview. In: Bezdek, J.C. (ed.) Analysis of Fuzzy Information. Mathematics and Logic, vol. I, pp. 3–39. CRC Press, Boca Raton (1987)
Inuiguchi, M., Greco, S., Słowiński, R., Tanino, T.: Possibility and Necessity Measure Specification Using Modifiers for Decision Making under Fuzziness. Fuzzy Sets and Systems 137, 151–175 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Inuiguchi, M. (2011). Possibilistic Linear Programming Using General Necessity Measures Preserves the Linearity. In: Torra, V., Narakawa, Y., Yin, J., Long, J. (eds) Modeling Decision for Artificial Intelligence. MDAI 2011. Lecture Notes in Computer Science(), vol 6820. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22589-5_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-22589-5_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22588-8
Online ISBN: 978-3-642-22589-5
eBook Packages: Computer ScienceComputer Science (R0)