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ISSN: 2321-9653
Estd : 2013
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Ijraset Journal For Research in Applied Science and Engineering Technology

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On Some Theoretic Aspects of Fuzzy Subsets

Authors: Dr. Sisir Kumar Rajbongshi, Prasanta Gogoi

DOI Link: https://doi.org/10.22214/ijraset.2023.48934

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Abstract

This article proposes some important theoretic aspects of -fuzzy power set of a finite set. Here, we take a non-empty fi-nite set and an ordered subset of the closed interval , then the set of mappings from to denoted by is defined as -fuzzy power set. Considering the disjunctive union ‘ ’ operations between fuzzy subsets of , the struc-ture forms a groupoid, which is defined as special fuzzy groupoid. Later, we try to introduce the product of special fuzzy groupoids and their properties.

Introduction

Conclusion

The proposed work presented some important properties of -fuzzy power set. Considering the disjunctive union ‘ ’ op-erations between two fuzzy subsets of the -fuzzy power set, it forms a groupoid, which is defined as special fuzzy groupoid. Throughout this article different properties of the -fuzzy power set and special fuzzy groupoid are studied. We hope the results established in this article would find some applications and enrich the theory of fuzzy algebra.

References

[1] Zadeh, L, A. Fuzzy sets, Infor. And Control, 1965, 8, pp. 338-353. [2] Goguen, J, A. L-fuzzy sets, J. Math. Anal. Appl., 1967, 18, pp. 145-174. [3] Sanchez, E. Resolution of Composite fuzzy relation equation, Infor. And Control, 1976, 30, pp. 38-48. [4] Rosenfeld, A. Fuzzy Groups, J Math Anal Appl., 1971, 35, pp. 512-517. [5] Bhutani, K. R., Fuzzy Sets, fuzzy relations and fuzzy groups: some interrelations, Inform. Sci., 73, 107-115 (1993). [6] Rosenfeld, A. Fuzzy Groups, J Math Anal Appl., 1971, 35, pp. 512-517. [7] Rajbongshi, S. K.; Talukdar, D. Some aspects of Special fuzzy Boolean algebra, Proceeding of International Conference on Frontiers in Mathematics Gauhati University, Guwahati, Assam, India, 2015, pp. 26-28. [8] Rajbongshi, S. K.; Talukdar, D. An Introduction to a family of fuzzy subsets forming Boolean algebra, International Journal of Computer Applications, 2013, (0975-8887), 68(24). [9] Atif, M.; Mishref, A., On the free product, Fuzzy Sets and Systems, 1996, 81, 287-289. [10] Tepavacevic, A.; Trajkovski, G. L-fuzzy lattices: an introduction, Fuzzy Sets Syst., 2001, vol. 123, pp. 209-216. [11] Bhutani, K. R., Fuzzy Sets, fuzzy relations and fuzzy groups: some interrelations, Inform. Sci., 73, 107-115 (1993). [12] Emami R.; Fuzzy Logic Application in Chemical Processes, The Journal of Mathematics and Computer Science Vol .1 No.4 (2010) 339-348.

Copyright

Copyright © 2023 Dr. Sisir Kumar Rajbongshi, Prasanta Gogoi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Paper Id : IJRASET48934

Publish Date : 2023-01-31

ISSN : 2321-9653

Publisher Name : IJRASET

DOI Link : Click Here