GOAL PROGRAMMING IN A FUZZY ENVIRONMENT

TLDR

In fuzzy environments, goal‑programming goals are stated imprecisely, unlike typical problems. The paper applies fuzzy subset concepts to goal programming, first addressing equal‑weight multiple goals and then extending to unequal fuzzy weights. The authors develop a linear‑programming solution for fuzzy goal‑programming, handling both equal‑weight and unequal‑weight multiple goals. Numerical examples illustrate the solution procedure for both equal‑weight and unequal‑weight fuzzy goal‑programming cases.

Abstract

Abstract This paper illustrates the application of “fuzzy subsets” concepts to goal programming in a fuzzy environment. In contrast to a typical goal‐programming problem, the goals are stated imprecisely when the decision environment is fuzzy. The paper first considers a fuzzy goal‐programming problem with multiple goals having equal weights associated with them. A solution approach based on linear programming is developed. Next, the solution approach is extended to the case where unequal fuzzy weights are associated with multiple goals. Numerical examples are provided for both cases to illustrate the solution procedure.