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Please Define Three Relevant Continuous Mathematical Fuzzy Membership Functions

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Abstract

The idea of a fuzzy set is formally modeled by a membership function that plays the same role as the characteristic function for an ordinary set, except that the membership function takes intermediary values between full membership and no membership. In this short note we first provide some references about the historical emergence of this notion, then discuss the nature of the scale for membership grades, and finally review their elicitation in relation with their intended meaning as a matter of similarity, uncertainty or preference.

Notes

  1. 1.

    We omit references here, for the sake of conciseness; readers can find a lot of them by searching for the corresponding key-words.

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Dedication

The authors are very glad to dedicate this chapter to Bernadette for her continuous and endless efforts to develop and promote the fuzzy set methodology in an open-minded way through her publications, and also for the launching of important international conferences she organized such as IPMU, which have been essential forums for exchanges between various approaches to uncertainty and vagueness, including fuzzy set theory, over more than four decades. Thank you so much, Bernadette.

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  1. IRIT, Université Paul Sabatier, 118 Route de Narbonne, 31062, Toulouse Cedex 9, France

    Didier Dubois & Henri Prade

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Correspondence to Didier Dubois .

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  1. Sorbonne Université, CNRS, LIP6, Paris, France

    Marie-Jeanne Lesot

  2. Sorbonne Université, CNRS, LIP6, Paris, France

    Christophe Marsala

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Dubois, D., Prade, H. (2021). Membership Functions. In: Lesot, MJ., Marsala, C. (eds) Fuzzy Approaches for Soft Computing and Approximate Reasoning: Theories and Applications. Studies in Fuzziness and Soft Computing, vol 394. Springer, Cham. https://doi.org/10.1007/978-3-030-54341-9_2

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