ON THE STRUCTURE OF TWO - FOLD FUZZY SET

  • Naphtali B Jelten Department of Mathematics University of Jos, PMB 2084 Plateau State, Nigeria
  • Lois A. Ademola Department of Mathematics University of Jos PMB 2084 Plateau State, Nigeria.
  • Dachollom Sambo Department of Mathematics Morgan State University 1700 E Cold Spring Lane Baltimore, MD 21251 Maryland USA.
  • Musaddid Abdulkareem Dayyib Federal Capital Territory Abuja Nigeria
  • Audu Buba Departments of Mathematics and Statistics American University of Nigeria Yola
DOI: https://doi.org/10.5281/zenodo.17224467
Keywords: fuzzy operators, fuzzy set, membership, two-fold fuzzy set, uncertainty

Abstract

The traditional fuzzy set deals with single degree of membership which cannot capture matters exhibited by multi-dimensional uncertainty. This gap motivate is the motivation to our work. We extend the existing Boolean algebra of the traditional fuzzy set to the two-fold fuzzy set., to further make its application wider and easier. The results show the conformity of the two-fold fuzzy sets with the existing Boolean algebra in the theory of the traditional fuzzy sets. The basic operations of the traditional fuzzy set were investigated against the two-fold fuzzy sets. The axioms of fuzzy union, fuzzy intersection and fuzzy complement of the traditional fuzzy set were investigated and extended to that of the two-fold fuzzy set. Furthermore, the set having satisfied the axioms was proved to be commutative, associative, distributive, involutivity, absorptive point-wise, and in concord with De Morgan’s law. With this the two fold fuzzy set will be more relevant in modelling vagueness and imprecision than the traditional fuzzy set.

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References

P. Venkata Subba Reddy. (2020). Fuzzy Conditional Inference with Twofold Fuzzy Set on Fuzzy Intuitions: An Application to Data Analytics. Computer Science and Engineering, Sri Venkateswara University, Tirupati,517502

Zadeh, L.A. (1978): Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst., Vol. 1, No. 28, pp. 3–28.

Zadeh, L. A.(1965). Fuzzy sets. Information and Control, 8, 338-353.

Didier Dubois, Henri Prade,(1987). Twofold fuzzy sets and rough sets—Some issues in knowledge representation. Fuzzy Sets and Systems, V. 23, 3-18

Zimmermann H.J. (1996): Fuzzy Set Theory. — Boston: Kluwer.

Alhaji, J. Alkali, and Sylvanus, K. Samaila. (2021). A study of operators on fuzzy sets. Mathematics Letters. Vol.7, No.2, 2021,30-36

Dubois, Didier, and Prade, Henry. (1988). Twofold fuzzy sets

P.Venkata Subba Reddy. (2013) Generalized fuzzy logic for incomplete information, IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), IEEE Xplore, 1-6.

P. Venkata Subba Reddy. (2017).Fuzzy Logic Based on Belief and Disbelief Membership Function. Fuzzy Information and Engineering 9, 405-422

Mouzon, Olivier de., Dubois, Didier., and Prade, Henri.(2021). Twofold fuzzy sets in single and multiple fault diagnosis, using information about normal values. 10th IEEE International Conference on Fuzzy Systems, 1563-1566,

Published
2025-09-29
How to Cite
Jelten, N. B., Ademola, L. A., Sambo, D., Dayyib, M. A., & Buba, A. (2025). ON THE STRUCTURE OF TWO - FOLD FUZZY SET. GPH-International Journal of Mathematics, 8(8), 01-10. https://doi.org/10.5281/zenodo.17224467
Issue
Vol 8 No 8 (2025): GPH-International Journal of Mathematics
Section
Articles
Copyright (c) 2025 Naphtali B Jelten, Lois A. Ademola, Dachollom Sambo, Musaddid Abdulkareem Dayyib, Audu Buba

The authors and co-authors warrant that the article is their original work, does not infringe any copyright, and has not been published elsewhere. By submitting the article to GPH - International Journal of Mathematics, the authors agree that the journal has the right to retract or remove the article in case of proven ethical misconduct.