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Multi-fuzzy sets: An extension of fuzzy sets

Author

Listed:
  • Sabu Sebastian

    (Kannur University)

  • T. V. Ramakrishnan

    (Kannur University)

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.

Suggested Citation

  • Sabu Sebastian & T. V. Ramakrishnan, 2011. "Multi-fuzzy sets: An extension of fuzzy sets," Fuzzy Information and Engineering, Springer, vol. 3(1), pages 35-43, March.
    • Handle: RePEc:spr:fuzinf:v:3:y:2011:i:1:d:10.1007_s12543-011-0064-y
    DOI: 10.1007/s12543-011-0064-y
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    Cited by:

    1. Osman Kazancı & Sarka Hoskova-Mayerova & Bijan Davvaz, 2022. "Algebraic Hyperstructure of Multi-Fuzzy Soft Sets Related to Polygroups," Mathematics, MDPI, vol. 10(13), pages 1-16, June.
    2. Sabeena Begam S & Vimala J & Ganeshsree Selvachandran & Tran Thi Ngan & Rohit Sharma, 2020. "Similarity Measure of Lattice Ordered Multi-Fuzzy Soft Sets Based on Set Theoretic Approach and Its Application in Decision Making," Mathematics, MDPI, vol. 8(8), pages 1-15, July.
    3. Osman Kazancı & Sarka Hoskova-Mayerova & Bijan Davvaz, 2021. "Application Multi-Fuzzy Soft Sets in Hypermodules," Mathematics, MDPI, vol. 9(18), pages 1-14, September.
    4. Sana Habib & Harish Garg & Yufeng Nie & Faiz Muhammad Khan, 2019. "An Innovative Approach towards Possibility Fuzzy Soft Ordered Semigroups for Ideals and Its Application," Mathematics, MDPI, vol. 7(12), pages 1-16, December.
    5. Sabeena Begam, S. & Vimala, J., 2022. "Compositions on lattice ordered multi-fuzzy soft matrix and its simulated application in medical diagnosis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 555-563.

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