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An Introduction to a Family of Fuzzy Subsets forming Boolean algebra

by Dwiraj Talukdar, Sisir Kumar Rajbongshi
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 68 - Number 24
Year of Publication: 2013
Authors: Dwiraj Talukdar, Sisir Kumar Rajbongshi
10.5120/11724-6770

Dwiraj Talukdar, Sisir Kumar Rajbongshi . An Introduction to a Family of Fuzzy Subsets forming Boolean algebra. International Journal of Computer Applications. 68, 24 ( April 2013), 1-6. DOI=10.5120/11724-6770

@article{ 10.5120/11724-6770,
author = { Dwiraj Talukdar, Sisir Kumar Rajbongshi },
title = { An Introduction to a Family of Fuzzy Subsets forming Boolean algebra },
journal = { International Journal of Computer Applications },
issue_date = { April 2013 },
volume = { 68 },
number = { 24 },
month = { April },
year = { 2013 },
issn = { 0975-8887 },
pages = { 1-6 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume68/number24/11724-6770/ },
doi = { 10.5120/11724-6770 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:28:45.120552+05:30
%A Dwiraj Talukdar
%A Sisir Kumar Rajbongshi
%T An Introduction to a Family of Fuzzy Subsets forming Boolean algebra
%J International Journal of Computer Applications
%@ 0975-8887
%V 68
%N 24
%P 1-6
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

It has been established that the fuzzy sets do not hold the Complement laws of Boolean algebra. The aim of this article is to introduce and study a kind of family of fuzzy subsets of a finite set which holds the Complement laws. The complement operation has redefined for this purpose. Further, it has been established that the introduced fuzzy subsets can form Boolean lattice and also Boolean algebra.

References
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  2. G. Bojadziev, M. Bojadziev, Fuzzy Sets, Fuzzy Logic, Applications: Advances in Fuzzy Systems, World Scientific, vol. 5.
  3. L. A. , Zadeh, Fuzzy sets, Information and Control, 8 (1965) 338-353.
  4. G. Birkhoff, Lattice theory, American Mathematical Society, Providence, RI, 1984.
  5. V. Murali, and B. B. Makamba, Finite Fuzzy Sets, Int. J. Gen. Systems, 34 (2005) 61-75.
  6. M. Dhar, Fuzzy Sets towards Forming Boolean Algebra, International Journal of energy, Information and Communication, vol. 2, issue 4, Nov. 2011.
  7. T. J. Neog, D. K. Sut, Complement of an Extended Fuzzy Set, IJCA (0975-8887), Volume 29-No 3, Sep. 2011.
  8. B. Seselja, A. Tepavcevic, Lattice and Poset Valued fuzzy structures-theory and applications, University of Novi Sad, Ser. , August 20, 2009.
Index Terms

Computer Science
Information Sciences

Keywords

fuzzy subset membership value the complement operation the complement laws Boolean lattice subsets of a fuzzy subset fuzzy power set

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