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JACIII Vol.22 No.3 pp. 359-368
doi: 10.20965/jaciii.2018.p0359
(2018)

Paper:

Multiobjective Two-Level Fuzzy Random Programming Problems with Simple Recourses and Estimated Pareto Stackelberg Solutions

Hitoshi Yano

Graduate School of Humanities and Social Sciences, Nagoya City University
1 Yamanohata, Mizuho-cho, Mizuho-ku, Nagoya, Aichi 467-8501, Japan

Received:
December 13, 2017
Accepted:
March 22, 2018
Published:
May 20, 2018
Keywords:
two-level programming problems, simple recourse programming problems, estimated Pareto Stackelberg solutions, weighting method, possibility measure
Abstract

In this paper, we focus on multiobjective two-level fuzzy random programming problems with simple recourses, in which multiple objective functions are involved in each level, shortages and excesses resulting from the violation of the constraints with fuzzy random variables are penalized, and sums of the objective functions and expectation of the amount of the penalties are minimized. To deal with such problems, the concept of estimated Pareto Stackelberg solutions of the leader is introduced under the assumption that the leader can estimate the preference of the follower as a weighting vector of the weighting problems. Employing the possibility measure for fuzzy numbers, weighting method for multiobjective programming problems, and Kuhn-Tucker approach for two-level programming problems, a nonlinear optimization problem under complementarity conditions is formulated to obtain the estimated Pareto Stackelberg solutions for the leader. A numerical example illustrates the proposed method for a multiobjective two-level fuzzy random programming problem with simple recourses. Several types of estimated Pareto Stackelberg solutions are derived corresponding to the weighting vectors and permissible possibility levels specified by the leader.

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Cite this article as:
Hitoshi Yano, “Multiobjective Two-Level Fuzzy Random Programming Problems with Simple Recourses and Estimated Pareto Stackelberg Solutions,” J. Adv. Comput. Intell. Intell. Inform., Vol.22, No.3, pp. 359-368, 2018
Hitoshi Yano, J. Adv. Comput. Intell. Intell. Inform., Vol.22, No.3, pp. 359-368, 2018

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Last updated on Jun. 22, 2018