Neural Network-Based Fuzzy Multi-objective Optimisation for Efficiency Evaluation

Abstract

Multi-objective optimisation handles the optimisation of multiple objectives on a multi-dimensional space (Lootsma in Fuzzy Multi-Objective Optimization. Springer, Boston, 1997 [1]). There are various classical methods and a wide variety of genetic algorithms for determining the Pareto-optimal front in MOOP. Most of the MOOP algorithms dealing with fuzzy systems treat fuzzy parameters (Young-Jou and Ching-Lai in Fuzzy multiple objective decision making: Methods and applications, Springer, Berlin, 1994 [2]), fuzzy inequalities (Chuntian in Hydrological Sciences Journal 44(4): 573–582, 1999 [3]) and fuzzy objective function (Young Jou and Ching-Lai in Fuzzy Sets and Systems 54(2): 135–146, 1993 [4]). In this article, an algorithm for multi-objective optimisation using neural network is presented where the variables are fuzzy. The paper deals with the core of the issue that is the fuzzy variables in multi-objective optimisation. Here, the variables are treated as triangular fuzzy variables. The arithmetic on these fuzzy variables is defined, according to the existing available work. As a numerical illustration, the new algorithm has been tested on two fractional functions. The results obtained after implementing the new algorithm using MATLAB code is presented. The algorithm uses neural network to approximate the Pareto front. This proposed algorithm is an illustration of possible optimisation technique in the fuzzy domain using Neural Network.