ELSEVIER Fuzzy Sets and Systems 88 (1997) 173-181 FUZZY sets and systems Fuzzy programming approachto multi-objective stochastic linear programming problems Suwarna Hulsurkar, M.P. Biswal, S.B. Sinha * Department of Mathematics, Indian Institute of Technology, Kharagpur-2, India Received November 1994 Abstract This paper presents an application of fuzzy programming approach to the multi-objective stochastic linear programming problem. After converting the proposed stochastic programming problem into a deterministic problem (which may be linear or non-linear), fuzzy programming approach is applied to find the compromise solution. Assuming the coefficients of the decision variables in the objective functions and in the constraints, and the right-hand-side parameters in the constraints as normal random variables, a methodology is presented to convert the probabilistic problem into a deterministic problem. Then fuzzy programming is applied using linear as well as non-linear membership functions. The method leads to an efficient solution as well as an optimal compromise solution. Numerical example is also presented to illustrate the methodology. (~)1997 Elsevier Science B.V. Keywords: Chance constrained programming; Two-stage programming; Fuzzy programming; Linear and non-linear membership functions 1. Introduction Stochastic or probabilistic programming deals with situations where some or all the parameters of a mathematical programming problem are described by stochastic variables rather than by deterministic quantities. Several models have been presented in the field of stochastic programming [12]. Contini [2] developed an algorithm for stochastic goal pro- gramming when the random variables are normally distributed with known means and variances. He transformed the stochastic problem into an equiva- lent deterministic quadratic programming problem, where the objective functions consisted of maxi- mizing the probability of a vector of goals lying in * Corresponding author. E-mail: sbsinha@maths.iitkgp.ernet.in the confidence region of a predefined size. Sullivan and Fitzsimmoms [13] suggested an algorithm using probabilistic goals based on the concept of chance constraints of Charnes and Cooper [ 1 ] where the goals can be stated in terms of probability of satisfying the aspiration levels. Teghem et al. [14] and Leclercq [9] have presented interactive methods in stochastic programming. Two major approaches to stochastic programming [3, 7] are recognized as: 1. Chance constrained programming, 2. two-stage programming. The chance constrained programming (CCP) tech- nique is one which can be used to solve problems involving chance constraints i.e., constraints having finite probability of being violated. The CCP was orig- inally developed by Charnes and Cooper [ 1 ] and has 0165-0114/97/$17.00 (~) 1997 Elsevier Science B.V. All rights reserved PH SO 1 65-0 11 4(96 )00056-5