{"title":"Normalization and Constrained Optimization of Measures of Fuzzy Entropy","authors":"K.C. Deshmukh, P.G. Khot, Nikhil","volume":51,"journal":"International Journal of Physical and Mathematical Sciences","pagesStart":300,"pagesEnd":305,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/8541","abstract":"In the literature of information theory, there is\r\nnecessity for comparing the different measures of fuzzy entropy and\r\nthis consequently, gives rise to the need for normalizing measures of\r\nfuzzy entropy. In this paper, we have discussed this need and hence\r\ndeveloped some normalized measures of fuzzy entropy. It is also\r\ndesirable to maximize entropy and to minimize directed divergence\r\nor distance. Keeping in mind this idea, we have explained the method\r\nof optimizing different measures of fuzzy entropy.","references":"[1] Bhandari, D. and Pal, N.R. (1993). Some new information measures for\r\nfuzzy sets. Information Sciences 67: 209-228.\r\n[2] De Luca, A. and Termini, S. (1972). A definition of non-probabilistic\r\nentropy in setting of fuzzy set theory. Information and Control 20: 301-\r\n312.\r\n[3] Emptoz, H. (1981). Non-probabilistic entropies and indetermination\r\nprocess in the setting of fuzzy set theory. Fuzzy Sets and Systems 5:\r\n307-317.\r\n[4] Hu,Q.and Yu, D. (2004). Entropies of fuzzy indiscernibility relation and\r\nits operations. International Journal of Uncertainty, Fuzziness and\r\nKnowledge-Based Systems 12: 575-589.\r\n[5] Kandel, A. (1986). Fuzzy Mathematical Techniques with Applications.\r\nAddison-wesley.\r\n[6] Kapur, J.N. (1997). Measures of Fuzzy Information. Mathematical\r\nSciences Trust Society, New Delhi.\r\n[7] Klir, G.J. and Folger, T.A. (1988). Fuzzy Sets, Uncertainty and\r\nIndetermination. Prentice Hall, New York.\r\n[8] Lowen, R. (1996). Fuzzy Set Theory-Basic Concepts, Techniques and\r\nBibliography. Kluwer Academic Publishers, Boston.\r\n[9] Pal, N.R. and Bezdek, J.C. (1994). Measuring fuzzy uncertainty. IEEE\r\nTransaction on Fuzzy Systems 2: 107-118.\r\n[10] Parkash, O. (1998). A new parametric measure of fuzzy entropy.\r\nInformation Processing and Management of Uncertainty 2:1732-1737.\r\n[11] Parkash, O. and Sharma, P.K. (2004). Measures of fuzzy entropy and\r\ntheir relations. Inernationa. Journal of Management & Systems 20 : 65-\r\n72.\r\n[12] Parkash, O. and Sharma, P. K. (2004). Noiseless coding theorems\r\ncorresponding to fuzzy entropies. Southeast Asian Bulletin of\r\nMathematics 27: 1073-1080.\r\n[13] Parkash, O., Sharma, P. K. and Kumar, J. (2008). Characterization of\r\nfuzzy measures via concavity and recursivity. Oriental Journal of\r\nMathematical Sciences 1:107-117.\r\n[14] Parkash, O, Sharma, P. K. and Mahajan, R (2008). New measures of\r\nweighted fuzzy entropy and their applications for the study\r\nof maximum weighted fuzzy entropy principle. Information Sciences\r\n178: 2389-2395.\r\n[15] Parkash, O., Sharma, P. K. and Mahajan, R (2010). Optimization\r\nprinciple for weighted fuzzy entropy using unequal constraints.\r\nSoutheast Asian Bulletin of Mathematics 34: 155-161.\r\n[16] Shannon, C. E. (1948). A mathematical theory of communication. Bell\r\nSystem Technical Journal 27: 379-423, 623-659.\r\n[17] Zadeh, L. A. (1965). Fuzzy sets. Information and Control 8: 338-353.\r\n[18] Zimmermann, H. J. (2001). Fuzzy Set Theory and its Applications.\r\nKluwer Academic Publishers, Boston.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 51, 2011"}