Fuzzy mathematical programming applied to multi-level programming problems

Sinha, Sujata

doi:10.1016/s0305-0548(02)00061-8

Cited by 53 publications

(39 citation statements)

References 10 publications

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“…Over the last three decades, tremendous amount of research efforts have been made on MLPP for hierarchical decentralised planning problems leading to the publication of many interesting results in the literature [3][4][5][6][7][8][9][10][11] and many methodologies have been proposed to solve MLPP's which potentially arise in various fields such as Agriculture, Bio fuel production, Economic systems, Finance, Government policy, Network designs etc. In 1997, Fuzzy goal programming technique (FGP) introduced by Mohamed [12] for proper distribution of decision powers to the DMs to arrive at a satisfying decision for the overall benefits of the organization was developed to overcome the difficulties associated with MLP structure.…”

Section: Literature Reviewmentioning

confidence: 99%

Modified FGP approach for multi-level multi objective linear fractional programming problems

Lachhwani

2015

Applied Mathematics and Computation

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Section: Literature Reviewmentioning

confidence: 99%

Modified FGP approach for multi-level multi objective linear fractional programming problems

Lachhwani

2015

Applied Mathematics and Computation

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“…Sinha [12,13] studied alternative fuzzy mathematical programming approach to solve MLPP. In Sinha's approach, last (lowest) level is most important and decision of the lowest level remains either unchanged or closest to individual best decision, which reflects the paradox that the decision power of the lowest level DM dominates the higher level decision maker.…”

Section: Introductionmentioning

confidence: 99%

Multilevel Programming Problems with Fuzzy Parameters: A Fuzzy Goal Programming Approach

Pramanik¹

2015

IJCA

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This paper presents fuzzy goal programming approach for solving multilevel programming problems with fuzzy parameters. The proposed approach is based on  -cut and fuzzy goal programming. In the proposed approach, the tolerance membership functions for the fuzzily described objective functions are defined by determining individual best solution of the objective function of every decision maker. Since the objectives of the level decision makers are potentially conflicting in nature, decision deadlock may arise due to the dissatisfaction of the solution of upper level decision makers. Sometimes upper level decision makers insist to work more than stipulated working hours or overtime duty in order to meet the heavy demand of the market arising for festivals or emergency reasons. In order to survive in the open competitive market, the relaxations of lower level decision makers are very crucial for the upper level decision makers and for the organization. So in the proposed model relaxation of decision for each level decision maker is considered. The relaxation of decision is performed by providing preference bounds on the decision variables for avoiding decision deadlock. Then three fuzzy goal programming models for multilevel programming are formulated. In general, the fuzzy goal programming models offer different solutions. In order to find the best compromise solution Euclidean function is used. An illustrative numerical example is provided to demonstrate the efficiency of the proposed approach.

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“…Zhang, et al [3] developed a tri-level Kth-Best algorithm to solve linear tri-level programming problems. Lai [15], Shih, et al [16] and Sinha [17,18] developed fuzzy approaches to find solutions to linear multilevel programming problems involving tri-level programming problems, and further, Pramanik and Roy [19] proposed another fuzzy approach using linear goal programming to solve such problems. However, the existing solution approaches are limited to solving tri-level programming problems in the linear version or in a special situation where all decision entities share the same constraint conditions.…”

Section: Introductionmentioning

confidence: 99%

Solving tri-level programming problems using a particle swarm optimization algorithm

Han

Zhang

et al. 2015

2015 IEEE 10th Conference on Industrial Electronics and Applications (ICIEA)

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Abstract-Tri-level programming, a special case of multilevel programming, arises to deal with decentralized decision-making problems that feature interacting decision entities distributed throughout three hierarchical levels. As tri-level programming problems are strongly NP-hard and the existing solution approaches lack universality in solving such problems, the purpose of this study is to propose an intelligence-based heuristic algorithm to solve tri-level programming problems involving linear and nonlinear versions. In this paper, we first propose a general tri-level programming problem and discuss related theoretical properties. A particle swarm optimization (PSO) algorithm is then developed to solve the tri-level programming problem. Lastly, a numerical example is adopted to illustrate the effectiveness of the proposed PSO algorithm.Keywords-tri-level programming; bi-level programming; computational intelligence; particle swarm optimization; KuhnTucker conditions.

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Fuzzy mathematical programming applied to multi-level programming problems

Cited by 53 publications

References 10 publications

Modified FGP approach for multi-level multi objective linear fractional programming problems

Modified FGP approach for multi-level multi objective linear fractional programming problems

Multilevel Programming Problems with Fuzzy Parameters: A Fuzzy Goal Programming Approach

Solving tri-level programming problems using a particle swarm optimization algorithm

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