On Some Results Based on Geometrical Representation of Fuzzy Sets

Full Text (PDF, 236KB), PP.57-62

Author(s)

Mamoni Dhar 1,*

1. Science College, Kokrajhar, Assam, India

* Corresponding author.

Received: 20 Sep. 2012 / Revised: 11 Jan. 2013 / Accepted: 17 Mar. 2013 / Published: 8 Jun. 2013

Index Terms

Reference Function, Membership Function, Entropy of Fuzzy Sets, The Randomness-Fuzziness Consistency Principles

Abstract

The main purpose of this article is to highlight the fact that there are some drawbacks in the existing definition of complementation of fuzzy sets and hence the geometrical representation of fuzzy sets on the basis of such definition which itself is defective would have no meaning. As a result the theorems or formulas which were rooted in the geometrical representation would become unacceptable and it is realized that in most cases of practical significance it is desirable to consider an additional requirement in defining fuzzy complement. It is important to mention here the fact that all these existing properties are being seen through the application of complementation of fuzzy sets which is rooted in the reference function. The current definition of complementation would infact remove those drawbacks and cosequently produce the results which seems to be logical.

Cite This Paper

Mamoni Dhar, "On Some Results Based on Geometrical Representation of Fuzzy Sets", International Journal of Intelligent Systems and Applications(IJISA), vol.5, no.7, pp.57-62, 2013. DOI:10.5815/ijisa.2013.07.08

Reference

[1]Zadeh.L.A, Towards Theory of Fuzzy Systems, InAspects of Network and System Theory, R.E. Kalman N.D. Claris, New York: Holt, Rinehart and Winston, 1971.

[2]Shimoda M, A natural interpretation of fuzzy sets and fuzzy relations, “Fuzzy Sets and System”Vol.128, No.2, 2002.

[3]Pieget A, A new definition of Fuzzy sets , Int. J. Appl. Math. Comput. Sci., Vol.15, No1, 2005

[4]Qing-Shi Gao, Xiao-Yu Gao and Yue Hu, A new fuzzy set theory satisfying all classical set formulas, Journal of Computer Science and Technology, Vol.24, No.4, 2009.

[5]Kosko.B, Neural Networks and Fuzzy System, A Dynamic System Approach to Machine Intelligence, Eagle Wood Cliffs, Ng, Prentice Hall, 1992.

[6]Kosko.B, Fuzziness Vs Probability, Int. J. General System, Vol. 17, 211-240 , 1990.

[7]Baruah. H.K, Fuzzy Membership with respect to a Reference Function ,Journal of the Assam Science Society, Vol.40,No.3, ,65-73, 1999.

[8]Baruah.H.K, Towards Forming a field of Fuzzy sets, IJEIC, Vol. 2, Issue 1, 16-20, 2011

[9]Baruah H.K, Theory of Fuzzy sets Beliefs and Realities , IJEIC, Vol. 2 ,Issue 2,1-22,2011

[10]Dhar .M, Hwang and Yang’s definition of Entropy of Fuzzy sets, IJLTC, Vol.2, No.4, 496-497, 2011.

[11]Dhar.M, Fuzzy Sets Towards Forming Boolean Algebra , IJEIC, Vol.2, Issue 4,137-142, 2011.

[12]Dhar.M, On Separation Index of Fuzzy Sets, IJMA, Vol.3, No.3, 932-934, 2012.

[13]Dhar.M, On Geometrical Representation of Fuzzy Numbers, IJEIC, Vol.3, Issue 2, 29-34, 2012.

[14]Dhar.M, On Fuzzy Measures of Symmetry Breaking of Conditions, Similarity and Comparisons: Non Statistical Information for the Single Patient., Accepted for publication in IJMA journal, 2012.

[15]Dhar.M, A Note on Subsethood measure of Fuzzy sets, accepted for publication in IJEIC in August, Korea.

[16]Dhar. M, Representation of fuzzy matrices Based on Reference Function, I.J. Intelligence Systems and Applications, 2012, 5(2), 84-90.

[17]Dhar.M, A Note on Determinant and Adjoint of Fuzzy Square Matrix ,accepted for publication in IJISA

[18]Dhar.M, On Cardinality of Fuzzy sets, accepted for publication in IJISA

[19]Dhar M, On Some properties of entropy of fuzzy numbers, accepted for publication in IJISA

[20]Dhar.M, A Note on existing Definition of Fuzzy Entropy, IJEIC, Vol.3, Issue 1,17-21, 2012.