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Complement of an Extended Fuzzy Set

by Tridiv Jyoti Neog, Dusmanta Kumar Sut
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 29 - Number 3
Year of Publication: 2011
Authors: Tridiv Jyoti Neog, Dusmanta Kumar Sut
10.5120/3543-4852

Tridiv Jyoti Neog, Dusmanta Kumar Sut . Complement of an Extended Fuzzy Set. International Journal of Computer Applications. 29, 3 ( September 2011), 39-45. DOI=10.5120/3543-4852

@article{ 10.5120/3543-4852,
author = { Tridiv Jyoti Neog, Dusmanta Kumar Sut },
title = { Complement of an Extended Fuzzy Set },
journal = { International Journal of Computer Applications },
issue_date = { September 2011 },
volume = { 29 },
number = { 3 },
month = { September },
year = { 2011 },
issn = { 0975-8887 },
pages = { 39-45 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume29/number3/3543-4852/ },
doi = { 10.5120/3543-4852 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:14:50.687198+05:30
%A Tridiv Jyoti Neog
%A Dusmanta Kumar Sut
%T Complement of an Extended Fuzzy Set
%J International Journal of Computer Applications
%@ 0975-8887
%V 29
%N 3
%P 39-45
%D 2011
%I Foundation of Computer Science (FCS), NY, USA
Abstract

It has been accepted that for a fuzzy set and its complement , neither is the null set, nor is the universal set. Whereas the operations of union and intersection of two crisp sets are indeed special cases of the corresponding operations of two fuzzy sets, they end up with peculiar results while defining and . In this regard, H. K. Baruah proposed that in the current definition of the complement of a fuzzy set, fuzzy membership function and fuzzy membership value had been taken to be the same, which led to the conclusion that the fuzzy sets do not follow the set theoretic axioms of exclusion and contradiction. H. K. Baruah has put forward an extended definition of fuzzy set and redefined the complement of a fuzzy set accordingly. In this paper, we are trying to improve the notion of union and intersection of fuzzy sets proposed by Baruah and generalize the concept of complement of a fuzzy set when the fuzzy reference function is not zero. We support our definition of complement of an extended fuzzy set with examples and show that indeed our definition satisfies all those properties that complement of a set really does in classical sense.

References
  1. Atanassov K, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, vol. 20, pp. 87-96, 1986.
  2. Atanassov K, Intuitionistic Fuzzy Sets–Theory and Applications, Physica–Verlag, A Springer–Verlag Company, New-York (1999)
  3. Baruah H K, “The Theory of Fuzzy Sets: Beliefs and Realities”, International Journal of Energy, Information and Communications, Vol. 2, Issue 2, pp. 1-22, May 2011.
  4. Baruah H K, “Towards Forming A Field Of Fuzzy Sets”, International Journal of Energy, Information and Communications, Vol. 2, Issue 1, pp. 16-20, February 2011.
  5. Zadeh L A, “Fuzzy Sets”, Information and Control, 8, pp. 338- 353, 1965.
Index Terms

Computer Science
Information Sciences

Keywords

Fuzzy set fuzzy membership function fuzzy reference function fuzzy membership value complement of an extended fuzzy set

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