A note on entropy subsethood relationship

Abstract

We comment on subsethood measure defined by Kosko and Young and give some new aspects of these measures. Finally we would like to discard the entropy subsethood relationship established by the authirs. We present some properties of subsethood measure from set theoretic approach and also from axiomatic approach with the expectation that these would help in removing the shortcomings that currently exist in these definitions.

Keywords

• membership value; membership function;fuzzy entropy

Kaynakça

1. Zadeh L A, Fuzzy Sets, Inform. and Control, 1965,8: 338-353.
2. B. Kosko, Fuzziness Vs Probability, Int.J.General Systems,17(1990),211-240
3. V.R.Young, Fuzzy Subsethood, Fuzzy Sets and Systems, 77(1996),371-384.
4. D. Sinha and E.R. Doughtery, Fuzzification of set inclusion: theory and applications, Fuzzy Sets and Systems, 55(1993), 15-42
5. 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.
6. Yager R.R, A procedure for ordering fuzzy subsets of the unit interval, Information Science, 24(1981), 143-161.
7. Baruah H K, Towards Forming a Field of Fuzzy Sets, International Journal of Energy Information and Communications, 2011, 2(1): 16 – 20.
8. Baruah H K, Theory of Fuzzy sets Beliefs and Realities, International Journal of Energy, Information and Communications, 2011, 2(2): 1-22.

9. L.Kitainik, Fuzy inclusions and fuzzydictonomous decision procedures in Optimization Models Using Fuzzy Sets and Possibility, eds, J. Kacprzyk and S.Orlovski (Reidel, Dordrecht, 1987),pp-154-170
10. Dubious and Prade, Fuzzy sets and systems: Theory and Applications, Academic Press, New York(1980)
11. W. Bandler and L.Kohout, Fuzzy power set and fuzzy implication operators, Fuzzy Sets and Systems, 4(1980), 13-30.
12. Dhar M, On Hwang and Yang’s definition of Entropy of Fuzzy sets, International Journal of Latest Trend Computing, 2011, 2(4): 496-497.
13. Dhar M, A Note on existing Definition of Fuzzy Entropy, International Journal of Energy Information and Communications, 2012, 3( 1): 17-21.
14. Dhar M, On Separation Index of Fuzzy Sets, International Journal of Mathematical Archives, 2012, .3(3): 932-934.
15. Dhar M, On Geometrical Representation of Fuzzy Numbers, International Journal of Energy Information and Communications, 2012, 3(2): 29-34.