Binary Behavior of Fuzzy Programming With Piecewise Linear Membership Functions

• Published in: IEEE transactions on fuzzy systems Vol. 15; no. 3; pp. 342 - 349
• Main Author: Chang, Ching-Ter
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2007; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Crisps; Decision making; Delta modulation; Functional programming; Fuzzy; Fuzzy logic; Fuzzy programming; Fuzzy set theory; Linear programming; Mathematical analysis; Mathematical models; Mathematical programming; Natural languages; nonlinear membership function; Packaging; Piecewise linear techniques; Programming; Programming profession; Studies; Testing
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2006.886606

The nature of vagueness, imprecision and uncertainly is fuzzy rather than crisp and/or random, especially for a multiple objectives decision-making problem. A key component of fuzzy programming is the membership function that represents a mathematical expression of level function for the decision-maker's preference. In fact, a decision-making problem involves the achievement of fuzzy goals, some of which are met while others are not because these fuzzy goals are subject to real-world constraints. To represent this situation, the binary piecewise linear membership function is then employed. In order to solve the problem, we propose a new idea of how to formulate the binary piecewise linear membership function. The formulated problem can be easily solved using common integer programming packages. In addition, an illustrative example is included for demonstrating the usefulness of the proposed model. Finally, the analytical superiority of the proposed method in terms of the execution time can be seen, through a computation experiment conduced on a set of generated test examples.