Minimizing a linear function under a fuzzy max–min relational equation constraint

Wu, Yan-Kuen; Guu, Sy-Ming

doi:10.1016/j.fss.2004.09.010

Cited by 113 publications

(29 citation statements)

References 22 publications

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“…The procedure checks much fewer nodes in the solution tree than Fang and Li's method. Wu and Guu (2005) suggested a necessary condition for finding an optimal solution. Three rules were proposed to simplify the computation of the optimal solution based on the condition.…”

Section: Relevant Literature Review and Motivationsmentioning

confidence: 99%

Linear optimization with mixed fuzzy relation inequality constraints using the pseudo-t-norms and its application

Molai

2014

Soft Comput

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This paper studies the minimization problem of a linear objective function subject to mixed fuzzy relation inequalities (MFRIs) over finite support with regard to max-T 1 and max-T 2 composition operators, where T 1 and T 2 are two pseudo-t-norms. We first determine the structure of its feasible domain and then show that the solution set of a MFRI system is determined by a maximum solution and a finite number of minimal solutions. Moreover, sufficient and necessary conditions are proposed to check whether the feasible domain of the problem is empty or not. The MFRI path is defined to determine the minimal solutions of its feasible domain. The resolution process of the optimization problem is also designed based on the structure of its feasible domain. Procedures are proposed to reduce the size of the problem. With regard to the above points and the procedures, an algorithm is designed to solve the problem. Its application is expressed in the area of investing and covering. Finally, the algorithm is compared with other approaches.

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Section: Relevant Literature Review and Motivationsmentioning

confidence: 99%

Linear optimization with mixed fuzzy relation inequality constraints using the pseudo-t-norms and its application

Molai

2014

Soft Comput

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“…(2) can be determined completely by a unique maximum solution and a finite number of minimal solutions [12]. Wu & Guu [13] proposed the necessary condition for optimal solution of the problems with positive cost coefficients in the objective function. Based on this necessary condition, three rules have been applied in simplifying the finding of optimal solutions.…”

Section: Minimizementioning

confidence: 99%

A New Algorithm for Optimization of the Fuzzy Relation Equation With Maxalgebraic Sum Composition

Zharfi¹,

Mirzazadeh²

2011

The South African Journal of Industrial Engineering

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This paper considers an optimization problem with a linear objective function under the constraints expressed by a system of fuzzy relation equations using max-as (Algebraic Sum) composition. First, some properties of minimal solutions of the system with fuzzy relation equations and max-as composition are shown. Then, a new algorithm for solving the optimization problem is derived. The numerical examples have been provided to illustrate the theoretical results. OPSOMMINGHierdie artikel bestudeer 'n optimiseringsprobleem met 'n lineêre doelwitfunksie en wasige randvoorwaardes met 'n algebraïese somsamestelling. Aanvanklik word sommige eienskappe van die minimale oplossings van die wasige vergelykings en die algebraïese samestelling getoon. Daarna word 'n nuwe algoritme vir die oplossing van die optimiseringsprobleem afgelei. Numeriese voorbeelde word voorsien om die teoretiese resultate te ondersteun.

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“…The branch and bound method with jump-tracking technique was applied to solve the integer programming problem. This problem was improved by Wu et al [35] and Wu and Guu [34] by providing the proper upper bounds for the branch and bound procedure. Fang and Li's problem was studied with the max-product composition by Loetamonphong and Fang [22].…”

Section: Introductionmentioning

confidence: 99%

Linear optimization with bipolar max-parametric hamacher fuzzy relation equation constraints

Aliannezhadi¹,

Molai²,

Hedayatfar³

2016

Kybernetika

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Minimizing a linear function under a fuzzy max–min relational equation constraint

Cited by 113 publications

References 22 publications

Linear optimization with mixed fuzzy relation inequality constraints using the pseudo-t-norms and its application

Linear optimization with mixed fuzzy relation inequality constraints using the pseudo-t-norms and its application

A New Algorithm for Optimization of the Fuzzy Relation Equation With Maxalgebraic Sum Composition

Linear optimization with bipolar max-parametric hamacher fuzzy relation equation constraints

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