Commenced in January 2007
Paper Count: 30843
Normalization and Constrained Optimization of Measures of Fuzzy Entropy
Abstract:In the literature of information theory, there is necessity for comparing the different measures of fuzzy entropy and this consequently, gives rise to the need for normalizing measures of fuzzy entropy. In this paper, we have discussed this need and hence developed some normalized measures of fuzzy entropy. It is also desirable to maximize entropy and to minimize directed divergence or distance. Keeping in mind this idea, we have explained the method of optimizing different measures of fuzzy entropy.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1071081Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1095
 Bhandari, D. and Pal, N.R. (1993). Some new information measures for fuzzy sets. Information Sciences 67: 209-228.
 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.
 Emptoz, H. (1981). Non-probabilistic entropies and indetermination process in the setting of fuzzy set theory. Fuzzy Sets and Systems 5: 307-317.
 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.
 Kandel, A. (1986). Fuzzy Mathematical Techniques with Applications. Addison-wesley.
 Kapur, J.N. (1997). Measures of Fuzzy Information. Mathematical Sciences Trust Society, New Delhi.
 Klir, G.J. and Folger, T.A. (1988). Fuzzy Sets, Uncertainty and Indetermination. Prentice Hall, New York.
 Lowen, R. (1996). Fuzzy Set Theory-Basic Concepts, Techniques and Bibliography. Kluwer Academic Publishers, Boston.
 Pal, N.R. and Bezdek, J.C. (1994). Measuring fuzzy uncertainty. IEEE Transaction on Fuzzy Systems 2: 107-118.
 Parkash, O. (1998). A new parametric measure of fuzzy entropy. Information Processing and Management of Uncertainty 2:1732-1737.
 Parkash, O. and Sharma, P.K. (2004). Measures of fuzzy entropy and their relations. Inernationa. Journal of Management & Systems 20 : 65- 72.
 Parkash, O. and Sharma, P. K. (2004). Noiseless coding theorems corresponding to fuzzy entropies. Southeast Asian Bulletin of Mathematics 27: 1073-1080.
 Parkash, O., Sharma, P. K. and Kumar, J. (2008). Characterization of fuzzy measures via concavity and recursivity. Oriental Journal of Mathematical Sciences 1:107-117.
 Parkash, O, Sharma, P. K. and Mahajan, R (2008). New measures of weighted fuzzy entropy and their applications for the study of maximum weighted fuzzy entropy principle. Information Sciences 178: 2389-2395.
 Parkash, O., Sharma, P. K. and Mahajan, R (2010). Optimization principle for weighted fuzzy entropy using unequal constraints. Southeast Asian Bulletin of Mathematics 34: 155-161.
 Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal 27: 379-423, 623-659.
 Zadeh, L. A. (1965). Fuzzy sets. Information and Control 8: 338-353.
 Zimmermann, H. J. (2001). Fuzzy Set Theory and its Applications. Kluwer Academic Publishers, Boston.