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Multi-fuzzy sets: An extension of fuzzy sets

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Fuzzy Information and Engineering

Abstract

In this paper we propose a method to construct more general fuzzy sets using ordinary fuzzy sets as building blocks. We introduce the concept of multi-fuzzy sets in terms of ordered sequences of membership functions. The family of operations T, S, M of multi-fuzzy sets are introduced by coordinate wise t-norms, s-norms and aggregation operations. We define the notion of coordinate wise conjugation of multifuzzy sets, a method for obtaining Atanassov’s intuitionistic fuzzy operations from multi-fuzzy sets. We show that various binary operations in Atanassov’s intuitionistic fuzzy sets are equivalent to some operations in multi-fuzzy sets like M operations, 2-conjugates of the T and S operations. It is concluded that multi-fuzzy set theory is an extension of Zadeh’s fuzzy set theory, Atanassov’s intuitionsitic fuzzy set theory and L-fuzzy set theory.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Kannur University, Mangattuparamba, Kannur, 670567, Kerala, India

    Sabu Sebastian & T. V. Ramakrishnan

Authors
  1. Sabu Sebastian
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  2. T. V. Ramakrishnan
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Correspondence to Sabu Sebastian.

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Sebastian, S., Ramakrishnan, T.V. Multi-fuzzy sets: An extension of fuzzy sets. Fuzzy Inf. Eng. 3, 35–43 (2011). https://doi.org/10.1007/s12543-011-0064-y

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  • DOI: https://doi.org/10.1007/s12543-011-0064-y

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