Title: Duality in fuzzy multi objective linear programming problem with multi constraint

Authors: Ananya Chakraborty; S.P. Tiwari; Amares Chattopadhyay; Kalyan Chatterjee

Addresses: Department of Mathematics, Vemana Institute of Technology, Kormangala 3rd Block, Bangalore-560034, Karnataka, India ' Department of Applied Mathematics, Indian School of Mines, Dhanbad-826004, Jharkhand, India ' Department of Applied Mathematics, Indian School of Mines, Dhanbad-826004, Jharkhand, India ' Department of Electrical Engineering, Indian School of Mines, Dhanbad-826004, Jharkhand, India

Abstract: In this paper, a pair of primal and dual problems is introduced for multi objective linear programming problems under a fuzzy environment. Duality takes central place in linear programming. The study of duality in a multi objective fuzzy programming are few. In the present study, we have generalised the duality results in a fuzzy multi objective linear programming problem. Linear and exponential membership functions have been used to deal with fuzzy objective and constraints. Few duality results have been developed for the above problems to prove the duality relationship between them. The problem is illustrated by an example.

Keywords: fuzzy programming; multi-objective linear programming; MOLP; duality; membership function; multiple constraints.

DOI: 10.1504/IJMOR.2014.060850

International Journal of Mathematics in Operational Research, 2014 Vol.6 No.3, pp.297 - 315

Received: 27 Aug 2012
Accepted: 15 Dec 2012
Published online: 28 Jun 2014 *

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