tailieunhanh - Fuzzy optimization of primal-dual pair using piecewise linear membership functions

Present paper improves the model of Bector and Chandra on duality in fuzzy linear programming by using non-linear membership functions. Numerical problem discussed by these authors has also been worked out through our non–linear model to demonstrate the obtain improvements. | Yugoslav Journal of Operations Research 21 (2011), Number 2, 97-106 DOI: FUZZY OPTIMIZATION OF PRIMAL-DUAL PAIR USING PIECEWISE LINEAR MEMBERSHIP FUNCTIONS D. PANDEY, S. KUMAR Department of Mathematics, , Meerut-250004 India Received: May 2009 / Accepted: April 2012 Abstract: Present paper improves the model of Bector and Chandra on duality in fuzzy linear programming by using non-linear membership functions. Numerical problem discussed by these authors has also been worked out through our non–linear model to demonstrate the obtain improvements. Keywords: Linear primal-dual problems, Fuzzy environment, tolerance, Non-linear membership function. MSC: 03E72, 49N15 1. INTRODUCTION Theories in economics indicate that abundance of resources correlates inversely with their market values. Any study pertaining to resource allocation is therefore useful only when the resources are limited. Solutions of Linear Programming (LP) problems give answer to the allocation of resources through the solution of the primal problem [2]. The solution to the dual problem does the market valuation of the resources. In crisp environment, solution of primal (dual) implicitly provides the solution of dual (primal). In fuzzy environment, instead of optimization, the goal is to find optimal satisfaction of aspiration levels for both primal and dual problems. The concept of Fuzzy Linear Programming (FLP) was introduced by Zimmermann [5]. In FLP, both optimization of primal-dual pair and reaching aspiration value in each case as close as possible are important. The primal-dual theory can be considered as a theory of industry-market problems and has numerous economic, business and industrial interpretations and applications [1]. Quite a lot of literature is available on fuzzy linear programming, but there are comparatively very few works on fuzzy dual problems. The first work on duality of fuzzy linear programming was done by Rodder and Zimmermann [3], .