Generalized Measures of Fuzzy Entropy and their Properties

Authors: K.C. Deshmukh, P.G. Khot, Nikhil

Abstract:

In the present communication, we have proposed some new generalized measure of fuzzy entropy based upon real parameters, discussed their and desirable properties, and presented these measures graphically. An important property, that is, monotonicity of the proposed measures has also been studied.

Keywords: Fuzzy numbers, Fuzzy entropy, Characteristicfunction, Crisp set, Monotonicity.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1057991

References:

[1] De Luca, A. and Termini, S. (1972). A definition of non-probabilistic entropy in setting of fuzzy set theory. Information and Control 20: 301- 312.
[2] Ebanks, B.R. (1983). On measures of fuzziness and their representations. Journal of Mathematical Analysis and Applications 94: 24-37.
[3] Emptoz, H. (1981). Non-probabilistic entropies and indetermination process in the setting of fuzzy set theory. Fuzzy Sets and Systems 5: 307-317.
[4] Guo, X. Z. and Xin, X. L. (2006). Some new generalized entropy formulas of fuzzy sets. Journal of the Northwest Univewrsity 36: 529- 532.
[5] Hu,Q.and Yu, D. (2004). Entropies of fuzzy indiscernibility relation and its operations. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12: 575-589.
[6] Kapur, J.N. (1997). Measures of Fuzzy Information. Mathematical Sciences Trust Society, New Delhi.
[7] Kaufmann, A. (1975). Introduction to Theory of Fuzzy Subsets. Academic Press, New York.
[8] Parkash, O. and Sharma, P.K. (2004). Measures of fuzzy entropy and their relations. Inernationa. Journal of Management & Systems 20 : 65- 72.
[9] Shannon, C. E.(1948). A mathematical theory of communication. Bell System Technical Journal 27: 379-423, 623-659.
[10] Singpurwalla, N. D. and Booker, J.M. (2004). Membership functions and probability measures of fuzzy sets. Journal of the American Statistical Association 99: 867-889.
[11] Zadeh, L. A. (1965). Fuzzy sets. Information and Control 8: 338-353.
[12] Zadeh,L.A.(1968). Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications 23: 421-427.