International Journal of Information Engineering and Electronic Business (IJIEEB)
IJIEEB Vol. 5, No. 3, 8 Sep. 2013
Cover page and Table of Contents: PDF (size: 190KB)
Author(s)
Index Terms
Reference Function, Membership Value, The Randomness-Fuzziness Consistency Principles
Abstract
In this article, we would like to revisit and comment on the definition of complementation of fuzzy sets and also on some of the theories and formulas associated with this. Furthermore, the existing probability-possibility consistency principles are also revisited and related results are viewed from the standpoint of the Randomness-Fuzziness consistency principles. It is found that the existing definition of complementation as well as the probability – possibility consistency principles is not well defined. Consequently the results obtained from these would be inappropriate from our standpoints. Hence we would like to suggest some new definitions for some of the terms often used in the theory of fuzzy sets whenever possible.
Cite This Paper
Mamoni Dhar, Hemanta .K. Baruah, "Theory of Fuzzy Sets: An Overview", International Journal of Information Engineering and Electronic Business(IJIEEB), vol.5, no.3, pp.22-33, 2013. DOI:10.5815/ijieeb.2013.03.03
Reference
[1]Zadeh L A, Inform and Control, 1965,8: 338-353
[2]BaruahH.K, Set Superimposition and Its Application to the Theory of Fuzzy Sets, Journal of the Assam Science Society, 40(1 & 2), (1999) 25-31.
[3]Baruah H.K, The Randomness-Fuzzuness Consistency Principles, IJEIC, 1(1), (2010)37-48.
[4]BaruahH.K, Twards Forming a field of fuzzy sets, IJEIC, 2(1), 2011, 16-20
[5]BaruahH.K, Theory of Fuzzy sets Beliefs and Realities, IJEIC, 2 (2), 2011, 1-22.
[6]BaruahH.K, In Search of Root of Fuzziness: Measure Theoritic Meaning of Partial Presence, Annals of Fuzzy Mathematics and Informatics, 2( 1), (2011)57-68
[7]BaruahH.K, Construction of membership functions of a Fuzzy Number, ICICI Express Letters, 5(2), and (2011)545-549.
[8]BaruahH.K, Construction of Normal Fuzzy Numbers Using Mathematics of Partial Presence, 1(1), (2012) 9-15.
[9]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.
[10]Dhar.M, On Cardinality of Fuzzy sets, accepted for publication in IJISA
[11]Kosko, Fuzzy entropy and conditioning, Inform. Sci. 40 (2) (1986) 165–174.
[12]Kosko, Fuzziness vs. probability, Internat. J. General Systems 17 (2–3) (1990) 211–240
[13]S Yager R.R, A procedure for ordering fuzzy subsets of the unit interval, Information Science, 24(1981), 143-161
[14]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.
[15]Polit M, Artificial Intelligence Research and Development, IOS Press, 2006, p-85
[16]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
[17]Dhar.M, On Separation Index of Fuzzy Sets, IJMA, Vol.3, No.3, 2012, p-932-934.
[18]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.
[19]Dhar. M, On Hwang and Yang’s definition of Entropy of Fuzzy sets, IJLTC, UK, Vol.2, No.4, 2011, p-496-497.
[20]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
[21]L. A. Zadeh: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and System, 1,(1978) 3-28, 1978
[22]G. J. Klir, Probability- possibility transformations: a comparison, International Journal of General Systems, 21(1992) 291-310.
[23]D. Dubois and H. Prade, On possibility- probability transformations, Fuzzy Logic, (1993) 103-112
[24]Dhar.M, Probability- Possibility Transformation: A Brief revisit, Accepted for publication in AFMI journal, Korea, 2012.
[25]Dhar.M, A Note on Variable transformations, AFMI,5(2), 371-376,2013
[26]Dhar M, Probability- Possibility Transformations: An Overview, IJMA,3(8),2887-2890,2012
[27]Dhar.M, On Yager’s Probability-Possibility Transformations, IJBSS, 1(3), 2012.
[28]Dhar.M, A Revisit to Probability - Possibility Consistency Principles, IJISA,p-90-99, 5(4),2013
[29]Dhar.M, A Note on the Coherence between Probability and Possibility Measures, IJCA, USA, Vol.43, No.7, 2012, p-28-29.
[30]Devillez.A, Mouchaweh M.S and Billaudel.P, A process monotoring module based on fuzzy logic and Pattern Recognition, International Journal of Approximate Reasoning, 379 (1),( 2004) 43-70
[31]Dhar. M, A Note on existing Definition of Fuzzy Entropy, IJEIC, Korea, Vol.3, Issue 1, 2012, p-17-21.
[32]Dhar.M, On Some properties of entropy of fuzzy numbers, IJISA,5(3),66-73
[33]Lee .Kwang Hyung, First Course of Fuzzy Set Theory and Applications, Springer-Verlag, Berlin, Heidelberg,2005
[34]Yager, R.R, A procedure for ordering fuzzy subsets of the unit interval, Information Sciences, 24, 1981,143-161
[35]Bender .M and Simonovic. S, Fuzzy Compromise Programming, Water Resources Research Report, No.034, University of Monitoba, Winnipeg,1996
[36]Bender .M and Simonovic. S,A fuzzy Compromise approach to water resource systems planning under uncertainty, Fuzzy Sets and Systems, 115, 35-44, 2000
[37]Cheng, C.H, A new approach to ranking fuzzy numbers by distance method, Fuzzy Sets and Systems, 95, 307-317,1998