Separable programming problems with the max-product fuzzy relation equation constraints

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Hedayatfar B.; Abbasi Molai A.; Aliannezhadi S.

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Journal: Iranian Journal of Fuzzy Systems Year:2019 | Volume:16 | Issue:1 Page(s): 1-15

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Title

Separable programming problems with the max-product fuzzy relation equation constraints

Author(s)

Hedayatfar B. | Abbasi Molai A. | Aliannezhadi S. | Issue Writer Certificate

Keywords

Separable programming problemQ2

Fuzzy relation equationsQ2

Max-product compositionQ2

Fuzzy optimizationQ2

Abstract

In this paper, the Separable programming problem subject to Fuzzy Relation Equation (FRE) constraints is studied. It is decomposed to two subproblems with decreasing and increasing objective functions with the same constraints. They are solved by the maximum solution and one of minimal solutions of its feasible domain, respectively. Their combination produces the original optimal solution. The detection of the optimal solution of the second subproblem by finding all the minimal solutions will be very time-consuming because of its NP-hardness. To overcome such difficulty, two types of sufficient conditions are proposed to find some of its optimal components or all of them. Under the first type sufficient conditions, some procedures are given to simplify the original problem. Also, a value matrix is defined and an algorithm is proposed to compute an initial upper bound on its optimal objective value using the matrix. Then, a branch-and-bound method is extended using the matrix and initial upper bound to solve the simplified problem without finding all the minimal solutions.

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APA: Copy

Hedayatfar, B., Abbasi Molai, A., & Aliannezhadi, S.. (2019). Separable programming problems with the max-product fuzzy relation equation constraints. IRANIAN JOURNAL OF FUZZY SYSTEMS, 16(1 ), 1-15. SID. https://sid.ir/paper/113244/en

Vancouver: Copy

Hedayatfar B., Abbasi Molai A., Aliannezhadi S.. Separable programming problems with the max-product fuzzy relation equation constraints. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2019;16(1 ):1-15. Available from: https://sid.ir/paper/113244/en

IEEE: Copy

B. Hedayatfar, A. Abbasi Molai, and S. Aliannezhadi, “Separable programming problems with the max-product fuzzy relation equation constraints,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 16, no. 1 , pp. 1–15, 2019, [Online]. Available: https://sid.ir/paper/113244/en

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