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Choice Functions in Fuzzy Environment: An Overview

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35 Years of Fuzzy Set Theory

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 261))

Abstract

In this chapter, we present an overview of choice functions. Firstly, we introduce some important research topics on classic choices which serve as a guideline for the fuzzification research of choice functions. Then we begin with the fuzzy choice function defined by Banerjee. After a brief introduction to Banerjee’s work, various preferences derived from a choice function are investigated. Main rationality conditions are presented and the relationships between them are presented. Some necessary and sufficient conditions for T-transitive rationality are summarized. Afterwards, we turn to a special family of choice functions which are associated with fuzzy preferences. In this case, the final choices can be exact or fuzzy. For the former, various characterizations of the Orlovsky choice function are primary topics. For the latter, Roubens’s work is mainly introduced. Finally, the research around Georgescu fuzzy choice functions is surveyed. The investigation includes three parts: rationality characterization, rationality conditions and rationality indicators. In the first part, G-rationality, G-normality, M-rationality and M-normality are discussed. In the second part, some important fuzzy versions of rationality conditions are displayed and their interrelationships are presented. The third part is devoted to the introduction of various rationality and rationality condition indicators.

The work is supported by Shanxi Natural Science Foundation 200901106.

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Authors and Affiliations

  1. Department of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, P.R. China

    Xuzhu Wang, Caiping Wu & Xia Wu

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  1. Xuzhu Wang
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  2. Caiping Wu
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  3. Xia Wu
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Editors and Affiliations

  1. Ghent University, Gent, Belgium

    Chris Cornelis , Glad Deschrijver , Mike Nachtegael , Steven Schockaert  & Yun Shi , , ,  & 

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Wang, X., Wu, C., Wu, X. (2010). Choice Functions in Fuzzy Environment: An Overview. In: Cornelis, C., Deschrijver, G., Nachtegael, M., Schockaert, S., Shi, Y. (eds) 35 Years of Fuzzy Set Theory. Studies in Fuzziness and Soft Computing, vol 261. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16629-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-16629-7_8

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