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Symmetry 2017, 9(11), 254; https://doi.org/10.3390/sym9110254

Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random Variables

1
Department of Industrial Engineering, Faculty of Engineering, Kanagawa University, 3-27-1 Rokkakubashi, Yokohama-shi, Kanagawa 221-8686, Japan
2
Department of Computer Science, Hiroshima Institute of Technology, 2-1-1 Miyake, Saeki-ku, Hiroshima 731-5193, Japan
3
Department of Mathematical Science, Graduate School of Technology, Industrial and Social Science, Tokushima University, 2-1, Minamijosanjima-cho, Tokushima-shi, Tokushima 770-8506, Japan
*
Author to whom correspondence should be addressed.
Received: 7 September 2017 / Revised: 6 October 2017 / Accepted: 6 October 2017 / Published: 30 October 2017
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making)
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Abstract

This paper considers linear programming problems (LPPs) where the objective functions involve discrete fuzzy random variables (fuzzy set-valued discrete random variables). New decision making models, which are useful in fuzzy stochastic environments, are proposed based on both possibility theory and probability theory. In multi-objective cases, Pareto optimal solutions of the proposed models are newly defined. Computational algorithms for obtaining the Pareto optimal solutions of the proposed models are provided. It is shown that problems involving discrete fuzzy random variables can be transformed into deterministic nonlinear mathematical programming problems which can be solved through a conventional mathematical programming solver under practically reasonable assumptions. A numerical example of agriculture production problems is given to demonstrate the applicability of the proposed models to real-world problems in fuzzy stochastic environments. View Full-Text
Keywords: discrete fuzzy random variable; linear programming; possibility measure; necessity measure; expectation model; Pareto optimal solution discrete fuzzy random variable; linear programming; possibility measure; necessity measure; expectation model; Pareto optimal solution
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Katagiri, H.; Kato, K.; Uno, T. Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random Variables. Symmetry 2017, 9, 254.

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