Abstract-The paper aims to give computational algorithm to solve a multi objective linear programming problem using intuitionistic fuzzy optimization method. It also includes some basic properties of intuitionistic fuzzy set and operations on it. The development of algorithm is based on principle of optimal decision set obtained by intersection of various intuitionistic fuzzy decision sets which are obtained corresponding to each objective function. Further, as the intuitionistic fuzzy optimization technique utilizes degree of belonging and degree of non-belonging, we made a comparative study of linear and nonlinear membership function for belonging and nonbelonging to see its impact on optimization and to get insight in such optimization process. The developed algorithm has been illustrated by a numerical example.Index Terms-Intuitionistic fuzzy set, multi objective linear programming, membership function, non-membership function. I. INTRODUCTIONIn several optimization problems, it has been observed that a small violation in given constraints or conditions may lead to more efficient solution to the problem. Such situations appear in frequent way in real life modeling, as a matter of fact in optimization problems; many times it is not practical to fix accurate parameters as many of these are obtained through approximation or through some kind of human observation. For example in a production optimization problem, it is not necessary that all the produced are of good quality and are completely sellable on a fixed price. There is possibility that some of the products may be defective and are not sellable on the fixed price. Further prices of raw material as well as market price of finished product may vary depending on its surplus/deficiency in the market due to some uncontrollable situations. Thus it is evident that prices and/or productions are not purely deterministic but in general these are imprecise or nondeterministic and thus such problems of optimization are to be dealt with help of some non-classical methods.Modeling of most of real life problems involving optimization process turns out to be multi objective programming problem in a natural way. Such multi objective programming problems may in general comprise of conflicting objectives. For example, if we consider a Manuscript received August 9, 2013; revised October 13, 2013. The authors are with the Department of Mathematics, Banaras Hindu University,Varanasi-221005, India (e-mail: singh_shivaraj@rediffmail.com, skmaths.bhu@gmail.com).problem of agricultural production planning, the optimal model should have the objectives of maximizing the profit and minimizing the inputs and cost of cultivation. Thus these objectives are conflicting in nature and hence solution of such problems are in general compromise solutions which satisfy each objective function to a degree of satisfaction and a concept of belonging and non-belonging arises in such situations. In view of growing use of fuzzy set in modeling of problems under situations when information available...
This paper addresses a multi items volume flexible system for time dependent decaying items with the concept of machine breakdown and imprecise environment. In this study, partially backlogged shortages have been discussed. All the costs are fuzzified with signed distance method. Numerical examples are given to illustrate the theoretical results and sensitivity analysis is given to validate the results for various parameters
Present paper is an application study of intuitionistic fuzzy optimization technique in agricultural production planning problem particularly a case of smallholder farmer in north Bihar, India. Generally, the crop planning problem is formulated as linear programming problems. but in realistic situation there are many uncertain factors in agricultural production planning problems and hence future profits for crop are imprecise and uncertain values. Therefore, we propose a model of crop planning using intuitionistic fuzzy optimization technique. General TermsMulti-Objective linear programming, Crop production planning.
The paper presents a new method to find the optimal solution of a fully intuitionistic fuzzy linear programming (FIFLP) problem. It uses the sign distance between intuitionistic fuzzy numbers for their comparison. The proposed methods have been applied for solving a FIFLP problem with equality constraints. The proposed method is convenient for implementation to solution of FIFLP problems arising in real life situations. General TermsLinear programming, distance function. KeywordsIntuitionistic fuzzy sets, Triangular intuitionistic fuzzy numbers, Sign distance between intuitionistic fuzzy numbers, Fully intuitionistic fuzzy linear programming problem.
This paper is based on intuitionistic fuzzy sets, we introduce an extension of fuzzy TOPSIS for multi criteria decision making problem in intuitionistic fuzzy environment. Intuitionistic fuzzy sets are more suitable to deal with uncertainty than other generalized forms of fuzzy sets. The rating of each alternative and the weight of each criterion are expressed in intuitionistic fuzzy number. The normalized intuitionistic fuzzy number is calculated by using the concept of . Ranking function is used for determining the positive ideal solution and negative ideal solution. For application and verification, a numerical example is discussed at the end of this paper and compare with existing method. KeywordsIntuitionistic fuzzy number, ranking of intuitionistic fuzzy number, positive ideal solution, negative ideal solution, multicriteria decision making
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