# (Ijcsis) International Journal Of Computer Science And Information Security, Vol. 6, No. 3, 2009 Application Of A Fuzzy Programming Technique To Production Planning In The Textile Industry

*I. Elamvazuthi , T. Ganesan, P. Vasant Universiti Technologi PETRONAS 
 Tronoh, Malaysia *
J. F. Webb Swinburne University of Technology Sarawak Campus, Kuching, Sarawak, Malaysia Abstract**—Many engineering optimization problems can be** considered as linear programming problems where all or some of the parameters involved are linguistic in nature. These can only be quantified using fuzzy sets. The aim of this paper is to solve a fuzzy linear programming problem in which the parameters involved are fuzzy quantities with logistic membership functions. To explore the applicability of the method a numerical example is considered to determine the monthly production planning quotas and profit of a home-textile group. 

Keywords: fuzzy set theory, fuzzy linear programming, logistic membership function, decision making 

## I. Introduction

Many problems in science and engineering have been considered from the point of view optimization. As the environment is much influenced by the disturbance of social and economic factors, the optimization approach is not always the best. This is because, under such turbulent conditions, many problems are ill-defined. Therefore, a degree-of-satisfaction approach may be better than optimization. Here, we discuss how to deal with decision making problems that are described by fuzzy linear programming (FLP) models and formulated with elements of imprecision and uncertainty. More precisely, we will study FLP models in which the parameters are known only partially to some degree of precision. 

Even though the information is incomplete, the model builder is able to provide realistic intervals for the parameters in these FLP models. We will demonstrate that the modeling complications can be handled with the help of some results which have been developed in fuzzy set theory. The FLP problem which we will be considering in this work is to find ways to handle fuzziness in the parameters. We will develop a FLP model in which the parameters are known with only some degree of precision. We will also show that the model can be parameterized in such a way that a satisfactory solution becomes a function of the membership values. The FLP model derived in this way is flexible and easy to handle computationally [1]. 

The first and most meaningful impetus towards the mathematical formalization of fuzziness was pioneered by Zadeh [2]. Its further development is in progress, with numerous attempts being made to explore the ability of fuzzy set theory to become a useful tool for adequate mathematical analysis of real-world problems [3]. The period of development of fuzzy theory from 1965 to 1977, is often referred to as the academic phase. The outcome was a rather small number of publications of a predominantly theoretical nature by a few contributors, mainly from the academic community. At this time, not much work in the area of fuzzy decision making was reported. The period from 1978 to 1988, has been called the transformation phase during which significant advances in fuzzy set theory were made and some real-life problems were solved. In this period, some important principles in fuzzy set theory and its applications were established. However, work on fuzzy decision making was not very active, in the area of engineering applications. Some earlier work on fuzzy decision making can be found in [4] and [5]. From 1989 to the present work on fuzzy techniques has boomed . In this period, many problems concerning applications in industry and business have been tackled successfully. In the early 1990s, fuzzy techniques were used to aid the solution of some soft computing problems. The aim of soft computing is to exploit, whenever possible, the tolerance for imprecision and uncertainty in order to achieve computational tractability, robustness, and low cost, by methods that produce approximate but acceptable solutions to complex problems which often have no precise solution. 

Currently, fuzzy techniques are often applied in the field of decision making. Fuzzy methods have been developed in virtually all branches of decision making, including multiobjective, multi-person, and multi-stage decision making [6]. 

Apart from this, other research work connected to fuzzy decision making includes applications of fuzzy theory in management, business and operational research [7]. Some representative publications can be found in [8], [9], [10], [11] 
and [12]. 

Decision making is an important and much studied application of mathematical methods in various fields of human activity. In real-world situations, decisions are nearly always made on the basis of information which, at least in part, is fuzzy in nature. In some cases fuzzy information is used as an approximation to more precise information. This form of approximation can be convenient and sufficient for making good enough decisions in some situations. In other cases, fuzzy information is the only form of information available. 