Preference Approach to Fuzzy Linear Inequalities and Optimizations

Abstract

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.

Reasoning and querying bounds on differences with layered preferences

“…4 Actually, there are also other approaches coping with the more general class of linear inequalities. For instance, the work in [72] proposes an approach coping with fuzzy linear inequalities. However, in this section we only focus on BoDs.…”

Soft-sensing of level of satisfaction in TOC product-mix decision heuristic using robust fuzzy-LP

“…(1) was indicated as Scurve MF by Goguen [12] and Zadeh [36]. A preference approach to fuzzy linear constraints and optimizations was suggested by Wang and Wu [32]. …”

FCVLP: A Fuzzy Random Conditional Value-at-Risk-Based Linear Programming Model for Municipal Solid Waste Management

“…Therefore, many inexact optimization methods, such as interval, fuzzy, and stochastic programming methods, have been proposed for dealing with uncertainties that exist in MSW management problems [13][14][15][16][17][18][19][20][21][22][23][24]. Among them, the fuzzy linear programming (FLP) method, which is recognized as an effective alternative to tackle uncertainties expressed as fuzzy sets, has been widely studied over the past decades [25][26][27][28][29][30][31][32][33][34]. For example, Huang et al [26] proposed a grey fuzzy linear programming approach for MSW management planning.…”