Fuzzy programming approach to multi-level programming problems

Sinha, Sujata

doi:10.1016/s0165-0114(02)00362-7

Cited by 91 publications

(64 citation statements)

References 28 publications

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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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Section: Introductionmentioning

confidence: 99%

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

Pramanik¹

2015

IJCA

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“…In order to overcome the problem in their methods, by eliminating the fuzzy goals for the decision variables, Sakawa et al have proposed interactive fuzzy programming for two-level or multi-level linear programming problems to obtain a satisfactory solution for DMs [29,30]. The subsequent works on two-level or multi-level programming have been developing [14,26,27,31,32,40,18,1,19,28]. In actual decision making situations, however, we must often make a decision on the basis of vague information or uncertain data.…”

Section: Introductionmentioning

confidence: 99%

Interactive Fuzzy Programming for Stochastic Two-level Linear Programming Problems through Probability Maximization

Sakawa

Matsui²

2013

AIR

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ForewordIn this paper, we focus on stochastic two-level linear programming problems involving random variable coefficients both in objective functions and constraints. Using the concept of chance constraints, stochastic constraints are transformed into deterministic ones. Following the probability maximization model, the minimization of each stochastic objective function is replaced with the maximization of the probability that each objective function is less than or equal to a certain value. Under some appropriate assumptions for distribution functions, the formulated stochastic two-level linear programming problems are transformed into deterministic ones. Taking into account vagueness of judgments of the decision makers, we present interactive fuzzy programming. In the proposed interactive method, after determining the fuzzy goals of the decision makers at both levels, a satisfactory solution is derived efficiently by updating the satisfactory degree of the decision maker at the upper level with considerations of overall satisfactory balance among both levels. It should be emphasized here that the transformed deterministic problems for deriving an overall satisfactory solution can be easily solved through the combined use of the bisection method and the phase one of the simplex method. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method.-iii - AbstractThis paper considers stochastic two-level linear programming problems. Using the concept of chance constraints and probability maximization, original problems are transformed into deterministic ones. An interactive fuzzy programming method is presented for deriving a satisfactory solution efficiently with considerations of overall satisfactory balance.

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“…This makes the solution process a lengthy one [9]. Fuzzy programming approach to multi-level programming problems was studied by Sinha [11]. The Baky investigated the problem of Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems [12].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy linear fractional bi-level multi-objective programming problems

Safaei¹,

Saraj²

2012

International Journal of Applied Mathematical Research

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The Kuhn-Tuker condition has become nowadays an important tool in the hands of investigation for checking the optimality in optimization literature. In the present paper with use of a Taylor series and KuhnTucker conditions approach, we solve a fuzzy linear fractional bilevel multi-objective programming (FLFBL-MOP) problem. The Taylor series is an expansion of a series that represents a function. In the proposed approach, membership functions associated with each level(s) of the objective(s) of FLFBL-MOP problems are transformed and unified by using a Taylor series approach. By using the Kuhn-Tucker conditions, the problem is reduced to a single objective and finally, numerical example is given to illustrates the efficiency and superiority of the proposed approach.

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Fuzzy programming approach to multi-level programming problems

Cited by 91 publications

References 28 publications

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

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

Interactive Fuzzy Programming for Stochastic Two-level Linear Programming Problems through Probability Maximization

Fuzzy linear fractional bi-level multi-objective programming problems

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