A dual approach to solve the fuzzy linear programming problem

Jose L Verdegay
1984 Fuzzy sets and systems (Print)  
Introduction Linear Programming (LP) is one of the most versatile, powerful, and useful techniques for making managerial decisions. Linear programming technique may be used for solving broad range of problems arising in business, government, industry, hospitals, libraries, etc. Whenever we want to allocate the available limited resources for various competing activities for achieving our desired objective, the technique helps us is linear programming. As a decision making tool, it has
more » ... ed its value in various field such as production, finance, marketing, research and development, and personal management. In conventional LP problems, it is assumed that the data have precise values. This means that the elements are crisp numbers, inequality is defined in the crisp sense, and objective function is a strict imperative. However, the observed values of the data in real-life problems are often imprecise because of incomplete or non-obtainable information. In such situations, fuzzy sets theory is an idea approach to handle imprecise in LP by generalizing the notion of membership in a set and this leads to the concept of fuzzy LP problems. Fuzzy Linear Programming (FLP) problems allow working with imprecise data and constraints, leading to more realistic models. They have often been used for solving a wide variety of problems in sciences and engineering. Fuzzy mathematical programming has been researched by a number of authors. One of the earliest works on fuzzy mathematics programming A B S T R A C T P A P E R I N F O Today, human decisions are more than ever based on information. But most of this information is not definitive, and in this situation, logical decision making is very difficult based on this uncertainty. Different methods are used to represent this uncertainty, including the fuzzy numbers. The fuzzy linear programming problem is one of the interesting concepts to be addressed in fuzzy optimization. Fully Fuzzy Linear Programming Problems (FFLP) are issues in which all parameters of the coefficients of the variables in the target functions, the coefficients of the variables in the constraints, the right-hand side of the constraints, and the decision variables in them are fuzzy. In this paper, we show that Definition 2.6 which is used by Ezzati et al. [1], failed to compare any arbitrary triangular fuzzy numbers. We demonstrate that their presented method is not well in general, thus the proposed method finds the fuzzy optimal solution of fully fuzzy linear programming problems by Ezzati et al. [1] . Then a new approach is proposed for solving this FFLP problem. An example is also presented to demonstrate the new method. Chronicle:
doi:10.1016/0165-0114(84)90096-4 fatcat:ruabgkj3prch3a7n7bgfygimvu