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Über dieses Buch

In the last 25 years, the fuzzy set theory has been applied in many disciplines such as operations research, management science, control theory,artificial intelligence/expert system, etc. In this volume, methods and applications of fuzzy mathematical programming and possibilistic mathematical programming are first systematically and thoroughly reviewed and classified. This state-of-the-art survey provides readers with a capsule look into the existing methods, and their characteristics and applicability to analysis of fuzzy and possibilistic programming problems. To realize practical fuzzy modelling, we present solutions for real-world problems including production/manufacturing, transportation, assignment, game, environmental management, resource allocation, project investment, banking/finance, and agricultural economics. To improve flexibility and robustness of fuzzy mathematical programming techniques, we also present our expert decision-making support system IFLP which considers and solves all possibilities of a specific domain of (fuzzy) linear programming problems. Basic fuzzy set theories, membership functions, fuzzy decisions, operators and fuzzy arithmetic are introduced with simple numerical examples in aneasy-to-read and easy-to-follow manner. An updated bibliographical listing of 60 books, monographs or conference proceedings, and about 300 selected papers, reports or theses is presented in the end of this study.

Inhaltsverzeichnis

Frontmatter

1. Introduction

Abstract
At the turn of the century, reducing complex real-world systems into precise mathematical models was the main trend in science and engineering. In the middle of this century, Operations Research (OR) began to be applied to real-world decision-making problems and thus became one of the most important fields in science and engineering. Unfortunately, real-world situations are often not so deterministic. Thus precise mathematical models are not enough to tackle all practical problems.
Young-Jou Lai, Ching-Lai Hwang

2. Fuzzy Set Theory

Abstract
The term “fuzzy” was proposed by Zadeh in 1962 [273]. In 1965, Zadeh formally published the famous paper “Fuzzy Sets”[274]. The fuzzy set theory is developed to improve the oversimplified model, thereby developing a more robust and flexible model in order to solve real-world complex systems involving human aspects. Furthermore, it helps the decision maker not only to consider the existing alternatives under given constraints (optimize a given system), but also to develop new alternatives (design a system).
Young-Jou Lai, Ching-Lai Hwang

3. Fuzzy Mathematical Programming

Abstract
Fuzzy set theory was first developed for solving the imprecise/vague problems in the field of artificial intelligence, especially for imprecise reasoning and modelling linguistic terms. In solving decision making problems, the pioneer work came from Bellman and Zadeh [12], Tanaka, Okuda and Asai [236][237], Negoita et al. [176][178][179], Zimmermann [296][298], Orlovsky [192], Yager [266] and Freeling [92].
Young-Jou Lai, Ching-Lai Hwang

4. Possibilistic Programming

Abstract
Stochastic programming has been used since the late 1950s for decision models where input data (coefficients in LP problems) have been given probability distributions. The pioneer works were done by Dantzig [47], Beale [9], Tintner [247], Simon [223], Charnes, Cooper and Symonds [39], and Charnes and Cooper [40]. Since then, a number of stochastic programming models have been formulated in inventory theory, system maintenance, micro-economics, and banking and finance. The most recent summaries of the development of stochastic programming methods are Stancu-Minasian [BM48] and Wets [260].
Young-Jou Lai, Ching-Lai Hwang

5. Concluding Remarks

Abstract
During the last 25 years, the fuzzy set theory has been applied in many disciplines such as operations research, management science, artificial intelligence/expert system, control theory, statistics, etc. In this study, we concentrate on fuzzy mathematical programming which is one of the most important fields in operations research and management science. This study provides readers and researchers with a capsule look into the existing methods, their characteristics and their applicability to analysis of single-objective mathematical programming under fuzziness/imprecision.
Young-Jou Lai, Ching-Lai Hwang

Backmatter

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