International Journal of Intelligent Systems and Applications (IJISA)
IJISA Vol. 5, No. 4, 8 Mar. 2013
Cover page and Table of Contents: PDF (size: 331KB)
A Revisit to Probability - Possibility Consistency Principles
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Author(s)
Mamoni Dhar
1,*
Index Terms
Superimposition of Sets, Glivenko- Cantelli’s Theorem, Dubois and Prade Definition of a Normal Fuzzy Number, FMF, PDF
Abstract
In this article, our main intention is to highlight the fact that the probable links between probability and possibility which were established by different authors at different point of time on the basis of some well known consistency principles cannot provide the desired result. That is why the paper discussed some prominent works for transformations between probability and possibility and finally aimed to suggest a new principle because none of the existing principles because none of them found the unique transformation. The new consistency principle which is suggested hereby would in turn replace all others that exist in the literature references by providing a reliable estimate of consistency between the two.Furthermore some properties of entropy of fuzzy numbers are also presented in this article.
Cite This Paper
Mamoni Dhar, "A Revisit to Probability - Possibility Consistency Principles", International Journal of Intelligent Systems and Applications(IJISA), vol.5, no.4, pp.90-99, 2013. DOI:10.5815/ijisa.2013.04.09
Reference
[1]L. A. Zadeh, Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and System, 1,(1978) 3-28, 1978
[2]R. Krishnapuram, J.M. Keller, A possibilistic approach to clustering, IEEE transcation on fuzzy systems, 1(2), (1993) 98-109.
[3]G.J.Klir, Information preserving probability-possibility transformation, recent developments, Fuzzy Logic,(1993), 417-428.
[4]G.J. Klir, Probability-possibility TransformationsL A comparision, Unternational Journal of General System Vol 21, 291-310, 1992
[5]D. Dubois and H. Prade, On possibility/probability transformations, Fuzzy Logic, 103- 112, 1993
[6]F. Alt and Marshall C.Yovits, Advances in Computers, New York (1993)315-318 .
[7]Elina Castineira,Susana Cubillo,Enric Trillas,On the Coherence between Probability and Posibility Measures,International Journal of Information Theories and Applications ,Vol. 14,303-310,2007
[8]Liu Du, Kyung K. Choi, Byeng D. Youn, AIAA Journal,2005.
[9]Moamar Sayed Mouchaweb, Mohamed Said Bouguelid, Patrice Billaudel and Bernard RiERA: Variable Probability-Possibility transformation, 25th European Annual Conference on Human Decision -Making and Manual Control (EAM”06), September 27-29, Valenciennes, France
[10]Ronald R. Yager, Entropy Conserving Probability Transform and the entailment Principles, Fuzy Sets and Systems, Vol. 158, 1397-1405,2007
[11]K.D.Lee and J. llinas, hybrid Model for Intent estimation, Proceedings, Sixth International Conference of Information Fusion, Cairo, July, 2001, 1215-1220.
[12]H. K. Baruah, Set Superimposition and Its Application to the Theory of Fuzzy Sets, Journal of the Assam Science Society, Vol. 40, Nos. 1 & 2, 1999, 25-31.
[13]H. K. Baruah, the Randomness-Fuzzuness Consistency Principles, IJEIC, Vol. 1, Issue 1, 37-48, 2010
[14]H.K.Baruah , Theory of Fuzzy sets Beliefs and Realities ,IJEIC, Vol. 2 ,Issue 2,1-22,2011
[15]Mamoni Dhar, Rituparno Chutia and Supahi Mahanta, A Note on existing Definition of Fuzzy Entropy, IJEIC, Korea, Vol.3, Issue 1, 2012, p-17-21.
[16]Mamoni Dhar, A Note on the Coherence between Probability and Possibility Measures, IJCA, USA, Vol.43, No.7, 2012, p-28-29.
[17]Mamoni Dhar, Probability- Possibility Transformation: A Brief revisit, Accepted for publication in AFMI journal, Korea, 2012.
[18]Mamoni Dhar, A Note on Variable transformations, Accepted for publication in AFMI journal, Korea, 2012.
[19]Mamoni Dhar, Probability- Possibility Transformations: An Overview, Accepted for publication in IJMA journal, India, 2012.