Separable programming problems with the max-product fuzzy relation equation constraints
Publish place: Iranian Journal of Fuzzy Systems، Vol: 16، Issue: 1
Publish Year: 1398
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_IJFS-16-1_002
تاریخ نمایه سازی: 17 آبان 1400
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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Authors
Behnaz Hedayatfar
School of Mathematics and Computer Sciences, Damghan University, P.O.Box ۳۶۷۱۵-۳۶۴, Damghan, Iran
Ali Abbasi Molai
School of Mathematics and Computer Sciences, Damghan University, P.O.Box ۳۶۷۱۵-۳۶۴, Damghan, Iran
Samaneh Aliannezhadi
School of Mathematics and Computer Sciences, Damghan University, P.O.Box ۳۶۷۱۵-۳۶۴, Damghan, Iran
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