International Journal of Intelligent Systems and Applications(IJISA)
ISSN: 2074-904X (Print), ISSN: 2074-9058 (Online)
Published By: MECS Press
IJISA Vol.5, No.8, Jul. 2013
The Complement of Normal Fuzzy Numbers: An Exposition
Full Text (PDF, 445KB), PP.73-82
In this article, our main intention is to revisit the existing definition of complementation of fuzzy sets and thereafter various theories associated with it are also commented on. The main contribution of this paper is to suggest a new definition of complementation of fuzzy sets on the basis of reference function. Some other results have also been introduced whenever possible by using this new definition of complementation.
Cite This Paper
Mamoni Dhar, Hemanta .K. Baruah,"The Complement of Normal Fuzzy Numbers: An Exposition", International Journal of Intelligent Systems and Applications(IJISA), vol.5, no.8, pp.73-82, 2013.DOI: 10.5815/ijisa.2013.08.09
Zadeh L. A,Fuzzy Sets, Inform and Control, 1965,8: 338-353
Baruah H K, Fuzzy Membership with respect to a Reference Function, Journal of the Assam Science Society, 1999, 40(.3):65-73.
Baruah H.K, Twards Forming a field of fuzzy sets, IJEIC, 2(1), 2011, 16-20
Baruah H.K, Theory of Fuzzy sets Beliefs and Realities, IJEIC, 2 (2), 2011, 1-22.
Dhar.M, Fuzzy Sets Towards Forming Boolean Algebra, IJEIC, Korea, Vol.2, Issue 4, 2011, p-137-142.
De Luca A, Termini S, A definition of non probabilistic entropy in the settings of fuzzy set theory, Information and Control, 1972, 20:301-312.
Dhar.M, On Cardinality of Fuzzy sets, accepted for publication in IJISA
Kosko, Fuzzy entropy and conditioning, Inform. Sci. 40 (2) (1986) 165–174.
Kosko, Fuzziness vs. probability, Internat. J. General Systems 17 (2–3) (1990) 211–240
Yager.R.R, On measures of fuzziness and negation part 1: Membership in unit interval. International Journal of General Systems, 5 (1979), 221-229.
Hwang C.M and Yang M.S, On entropy of fuzzy sets, International Journal of Uncertainty: Fuzziness and Knowledge Based systems, 16(4), 2008, 519-527.
Polit M, Artificial Intelligence Research and Development, IOS Press, 2006, p-85
Hegalson C.N and Jobe T.H, Fuzzy measure of symmetry breaking of conditions , similarity and comparision: Non statistical information for single patient,The Open Cybernetics and System Journal, Vol2, 11-19, 2008
Dhar.M, On Separation Index of Fuzzy Sets, IJMA, Vol.3, No.3, 2012, p-932-934.
Dhar.M, On Fuzzy Measures of Symmetry Breaking of Conditions, Similarity and Comparisons: Non Statistical Information for the Single Patient. IJMA, 2516-2519, 3(7), 2012.
Dhar. M, On Hwang and Yang’s definition of Entropy of Fuzzy sets, IJLTC, UK, Vol.2, No.4, 2011, p-496-497.
Soyer A, Kabak. O and Asan U, A fuzzy approach to value and culture assessement and application, International Journal of approximate reasoing, 44(2007), 182-196.
Shang X.G and Jiang W.S, A Note on fuzzy information measures, Pattern Recognition Letters, 1997,18(5),425-432.
Fan Jiu Lan and Ma Yuang Liang, Some new fuzzy entropy formulas, Fuzzy Sets and Systems, 128(2002), 277-284.
Dhar. M, A Note on existing Definition of Fuzzy Entropy, IJEIC, Korea, Vol.3, Issue 1, 2012, p-17-21.
Baruah H.K, The Randomness-Fuzzuness Consistency Principles, IJEIC, Vol. 1, Issue 1, 37-48, 2010
Dhar.M, On Some properties of entropy of fuzzy numbers, accepted for publication in IJISA
Dhar.M, A Note on Subsethood measure of Fuzzy sets, IJEIC, Korea.,55-61, 3(3)
Dhar.M, On Geometrical Representation of Fuzzy Numbers, IJEIC, Korea, Vol.3, Issue 2, 2012, p-29-34.
Dubois D and Prade H, Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, 1980.
Kosko B, Fuzzy Engineering, Prentice Hall, 1996
Dhar. M, Representation of fuzzy matrices Based on Reference Function, I.J. Intelligence Systems and Applications, 2012, 5(2), 84-90.F. Alt, Marshall C.Yovits, Advances in Computers, New York(1993)315-318
Dhar.M, A Note on Determinant and Adjoint of Fuzzy Square Matrix ,accepted for publication in IJISA