Using fuzzy numbers in linear programming

Abstract

Managers, decision makers, and experts dealing with optimization problems often have a lack of information on the exact values of some parameters used in their problems. To deal with this kind of imprecise data, fuzzy sets provide a powerful tool to model and solve these problems. This paper studies a linear programming (LP) problem in which all its elements are defined as fuzzy sets. Special cases of this general model are found and reproduced, and it is shown that they coincide with the particular problems proposed in the literature by different authors and distinct approaches. Solution methods are also provided. They show how it is possible to address and solve linear programming problems with data given in a qualitative form, instead of the usual quantitative and precise way.

Applying Fuzzy Linear Programming to Supply Chain Planning with Demand, Process and Supply Uncertainty

“…According to Table 2, and in order to address the fuzzy coefficients of the FMILP model, it is necessary to consider the fuzzy mathematical programming approaches that integrally consider the fuzzy coefficients of the objective function and the fuzzy constraints: technological and right-hand side coefficients. In this context, several research works exist in the literature, and readers are referred to them (Buckley, 1989;Cadenas & Verdegay, 1997;Carlsson & Korhonen, 1986;Gen et al, 1992;Herrera & Verdegay, 1995;Jiménez et al, 2007;Lai & Hwang, 1992;Vasant, 2005). In this paper, we adopt the approach by Cadenas and Verdegay (1997;.…”

“…In this context, several research works exist in the literature, and readers are referred to them (Buckley, 1989;Cadenas & Verdegay, 1997;Carlsson & Korhonen, 1986;Gen et al, 1992;Herrera & Verdegay, 1995;Jiménez et al, 2007;Lai & Hwang, 1992;Vasant, 2005). In this paper, we adopt the approach by Cadenas and Verdegay (1997;. The authors propose a general model for fuzzy linear programming that considers fuzzy cost coefficients, fuzzy technological coefficients and fuzzy right-hand side terms in constraints.…”

“…(21) is transformed into the crisp equivalent linear programming problem defined in Eq. (23) (Cadenas and Verdegay, 1997) . (1 ) 3 …”

New Approach to Solve Fuzzy Linear Programming Problems by the Ranking Function

“…Bellman & Zadeh, (1970) [4] proposed the concept of decision making in fuzzy environment. Cadenas & Verdegay, (1997) [5] studied a linear programming problem in which all its elements are defined as fuzzy sets. (Chanas, 1983) [6] Proposed the possibility of the identification of a complete fuzzy decision in fuzzy linear Programming by use of the parametric programming technique.…”

A New Method for Solving Fuzzy Linear Programs with Trapezoidal Fuzzy Numbers

“…Inuiguchi et al [13] dealt with the fuzzy linear programming problems with continuous piecewise linear membership function. Cadenas and Verdegay [5] studied a linear programming problem in which all its elements are defined as fuzzy sets. Fang et al [10] presented a method for solving linear programming problems with fuzzy coefficients in constraints.…”