A Note on New Definition of Fuzzy Compact Space on the Basis of Reference Function
Main Article Content
Abstract
 It is believed that the union of a fuzzy set and its complement may not be equal to the whole universal set. But it is seen that when we discussed fuzzy set on the basis of reference function then union of fuzzy set and its complement is equal to the whole universal set. In this article we will try to give definition of fuzzy compact on the basis of reference function.
Downloads
Article Details
Open Access: This is an open-access journal. All articles published in the Journal of Global Research in Mathematical Archives(JGRMA) are made immediately and permanently available under the Creative Commons Attribution 4.0 International (CC BY 4.0) License. Authors retain the copyright of their work and grant Journal of Global Research in Mathematical Archives(JGRMA) the right of first publication. This license permits unrestricted use, distribution, adaptation, and reproduction in any medium or format, including commercial use, provided the original author(s), source, and license are properly acknowledged.
Google Scholar Indexed | DOI Enabled | OAI-PMH Compliant | Open Access Journal
References
L. A. Zadeh , Fuzzy sets, Information and Control, 8, 338-353 (1965)
C. L. Chang , Fuzzy Topological Space, Journal of Mathematical Analysis and Application 24, 182- 190 (1968)
K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and systems, 20, 87-96, (1986).
D. Coker, An introduction to Intuitionistic fuzzy topological spaces, Fuzzy sets and systems, 88, 81-89, (1997).
H. K. Baruah, Towards Forming a Field of Fuzzy Sets, Int. Jr. of Energy, Information and Communications, Vol. 2, issue 1, Feb. (2011).
H. K. Baruah, The Theory of Fuzzy Sets: Belief and Realities, Int. Jr. of Energy, Information and Communications, Vol. 2, issue 2, May (2011).
T. J. Neog and D. K. Sut, Complement of an Extended Fuzzy Set, Int. Jr. of Computer Application (0975 - 8887), Vol. 29-No.3 Sep. (2011).
W. Shi and K. Liu, A Fuzzy Topology for Computing the Interior, Boundary and Exterior of Spatial Objects Quantitatively in GIS, Computers and Geosciences 33 (2007) 898-915.
M. Dhar and H. K. Baruah, The Complement of Normal Fuzzy Numbers: An Exposition, I. J. Intelligent Systems and Applications, (2013), 08, 73-82, DOI:10.5815/ijisa.2013.08.09
P. Kakati, A Similarity Measure For Fuzzy Sets With the Extended Definition of Complementation, Int. Jr. of Soft Computing and Engineering, 2231-2307, Volume-3, issue-4, September ( 2013).
H. K. Baruah, The Randomness-Fuzziness Consistency Principle, Int. Jr. of Energy, Information and Communications, Vol. 1, Issue 1, November, (2010) .
H. K. Baruah, In Search of the Root of Fuzzyness: The Measure Theoretic Meaning of Partial Presence, Annals of Fuzzy Mathematics and Informatics, Vol. 2 No. 1, (July 2011), pp. 57-68.
M. Dhar, On Geometrical Representation of Fuzzy Numbers, IJEIC, Korea, Vol.3, Issue 2, 2012, P-29-34.
M. Dhar, Fuzzy sets Towards Forming Boolean Algebra, International Journal of Energy, Information and Communications, Vol. 2, Issue 4, (2011), pp. 1-22.
T. J. Neog and D. K. Sut, An Extended Approach to Generalized Fuzzy Soft Sets, International Journal of Energy, Information and Communications, Vol. 3, Issue 2, May, 2012.