Preference Approach to Fuzzy Linear Inequalities and Optimizations

In this study we first present the preference structures in decision making as a generalized non-linear function. Then, we incorporate it into a fuzzy linear inequality of which the progressive and conservative manners are described by the concept of target hyperplanes. Thus, one’s preference domain is said to be bounded by such soft constraint. When facing different situations, a membership function is defined as an evaluation function for incorporating one’s optimistic or pessimistic attitude into this soft constraint. Once a goal is pursued, the problem is transformed into a symmetric fuzzy linear program. Based on max–min principle, an auxiliary crisp model in the form of a generalized fractional program is derived. Then, Dinkelbach-type-2 and the bisection algorithms are adopted for solution. Finally their simulation results of an uncertain production scheduling problem are reported.