**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31106

##### Applications of Trigonometic Measures of Fuzzy Entropy to Geometry

**Authors:**
Om Parkash,
C.P.Gandhi

**Abstract:**

**Keywords:**
Uncertainty,
Entropy,
Symmetry,
fuzzy entropy,
concavity

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1060145

**References:**

[1] Bhandari, D. and Pal, N.R. (1993): "Some new information measures for fuzzy sets", Inform. Sci., 67, 209-228.

[2] De Luca, A. and Termini, S. (1972): "A definition of non-probabilistic entropy in setting of fuzzy set theory ", Inform. and Control, 20, 301-312.

[3] Ebanks, B.R.(1983): "On measures of fuzziness and thei representations", Jour. of Mathematical Analysis and Applications, 94, 24-37.

[4] Guo, X. Z. and Xin, X. L. (2006): "Some new generalized entropy formulas of fuzzy sets", J. Northwest Univ.,36 (4), 529-532.

[5] Havrada, J.H. and Charvat, F. (1967): "Quantification methods of classification process: Concept of structural ─▒-entropy", Kybernetika, 3, 30-35.

[6] Hu,Q.and Yu, D. (2004): "Entropies of fuzzy indiscernibility relation and its operations", Internat. J. Uncertain. Fuzziness Knowledge-Based Systems, 12 (5), 575-589.

[7] Kapur, J.N. (1997): "Measures of Fuzzy Information", Mathematical Sciences Trust Society, New Delhi.

[8] Klir, G.J. and Folger, T.A. (1988): "Fuzzy Sets, Uncertainty and Indetermination", Prentice Hall, New York.

[9] Liu, S.T. and Kao, C. (2002): "Fuzzy measures for correlation coefficient of fuzzy numbers", Fuzzy Sets and Systems, 128, 267-275.

[10] Parkash, O. (1998): "A new parametric measure of fuzzy entropy," Inform. Process. and Management of Uncertainty, 2, pp. 1732-1737.

[11] Parkash, O. and Gandhi, C. P. (2005): "Generating measures of fuzzy entropy through fuzzy directed divergence", Ultra Scientist of Physical Sci., 17(3), 419-428.

[12] Parkash, O. and Sharma, P. K. (2004): "Noiseless coding theorems corresponding to fuzzy entropies", Southeast Asian Bulletin of Maths., 27, 1073-1080.

[13] 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.

[14] Parkash, O., Sharma, P. K. and Mahajan, R (2008): "Optimization principle for weighted fuzzy entropy using unequal constraints", Southeast Asian Bulletin Maths.(Accepted).

[15] Renyi, A. (1961): "On measures of entropy and information", Proc. 4th Ber. Symp. Math. Stat. and Prob., 1, 547-561.

[16] Rudas, I.J.(2001):"Measures of fuzziness : theory and applications ," Advance in fuzzy systems and evolutionary computation, 187-192, Artfi. Intell. Series (Athens) World Science Eng. Soc. Press, Athens.

[17] Shannon, C. E. (1948):"A mathematical theory of communication", Bell. Sys. Tech. Jr., 27, 379-423, 623-659.

[18] Zadeh,L.A.(1968): "Probability measures of fuzzy events", Jr. Math. Ann. Appli., 23, 421-427.