Convergence of Optimal Solutions about Approximation Scheme for Fuzzy Programming with Minimum-Risk Criteria

Two-stage fuzzy minimum-risk problems (FMRPs) include fuzzy variable parameters defined through a possibility distribution, they are inherently infinite-dimensional optimization problems that can rarely be solved directly. Therefore, algorithms to solve such optimization problems must rely on intelligent computing as well as approximating scheme, which results in approximating finite-dimensional FMRPs. The purpose of this paper is to establish conditions under which the optimal objective value and optimal solution of such approximating two-stage FMRP converges to the optimal objective value and optimal solution of the original two-stage FMRP, respectively.

[1]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

[2]  George J. Klir,et al.  On fuzzy-set interpretation of possibility theory , 1999, Fuzzy Sets Syst..

[3]  Y.-K. Liu,et al.  Convergent results about the use of fuzzy simulation in fuzzy optimization problems , 2006, IEEE Transactions on Fuzzy Systems.

[4]  Hidetomo Ichihashi,et al.  Modality constrained programming problems: A unified approach to fuzzy mathematical programming problems in the setting of possibility theory , 1993, Inf. Sci..

[5]  Baoding Liu,et al.  A survey of credibility theory , 2006, Fuzzy Optim. Decis. Mak..

[6]  Baoding Liu,et al.  Theory and Practice of Uncertain Programming , 2003, Studies in Fuzziness and Soft Computing.

[7]  C. Hwang,et al.  Fuzzy Mathematical Programming: Methods and Applications , 1995 .

[8]  Didier Dubois,et al.  Possibility theory , 2018, Scholarpedia.

[9]  Yian-Kui Liu.  Fuzzy Programming with Recourse , 2005, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[10]  Hsiao-Fan Wang,et al.  Linear programming with fuzzy coefficients in constraints , 1999 .

[11]  Baoding Liu.  Uncertainty Theory: An Introduction to its Axiomatic Foundations , 2004 .

[12]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[13]  Peter Kall,et al.  Stochastic Linear Programming , 1975 .

[14]  Ichiro Nishizaki,et al.  On computational methods for solutions of multiobjective linear production programming games , 2001, Eur. J. Oper. Res..

[15]  Pei Wang,et al.  Fuzzy contactibility and fuzzy variables , 1982 .

[16]  James G. Morris,et al.  Decision Problems Under Risk and Chance Constrained Programming: Dilemmas in the Transition , 1981 .

[17]  Andrey I. Kibzun,et al.  Stochastic Programming Problems with Probability and Quantile Functions , 1996 .