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COSINE ENTROPY AND SIMILARITY MEASURES FOR FUZZY SETS

Year 2015, Volume: 3 Issue: 1, 83 - 93, 01.04.2015

Abstract

In the present paper, based on the cosine function, a new fuzzy entropy measure is de ned. Some interesting properties of this measure are analyzed. Furthermore, a new fuzzy similarity measure has been proposed with its elegant properties. A relation between the proposed fuzzy entropy and fuzzy similarity measure has also been proved.

References

  • [1] D. Bhandari and N.R. Pal, Some new information measures for fuzzy sets, Information Sci- ences Vol: 67, No.2 (1993), 204-228.
  • [2] S.M. Chen, S.M. Yeh and P.H. Hsiao, A comparison of similarity measures of fuzzy values, Fuzzy Sets and Systems, Fuzzy Sets and Systems Vol: 72, No.1 (1995), 79-89.
  • [3] A. De Luca and S. Termini, A de nition of non-probabilistic entropy in the setting of fuzzy set theory, Information and Control Vol: 20, No.4 (1972), 301-312.
  • [4] J. Fan and W. Xie, Some notes on similarity measure and proximity measure, Fuzzy Sets and Systems Vol: 101, No.3 (1999), 403-412.
  • [5] Kaufmann,A., Introduction to the Theory of Fuzzy Subsets, Academic Press, New York, 1975.
  • [6] X. Liu, Entropy, distance measure and similarity measure of fuzzy sets and their relations, Fuzzy Sets and Systems Vol: 52, No.3 (1992), 305-318.
  • [7] N.R. Pal and S.K. Pal, Object background segmentation using new de nitions of IEEE Pro- ceedings E- Computers and Digital Techniques Vol: 366,(1989), 284-318.
  • [8] C.P. Pappis and N.I. Karacapilidis, A comparative assessment of measures of similarity of fuzzy values, Fuzzy Sets and Systems Vol: 56, No.2 (1993), 171-174.
  • [9] O. Prakash, P.K. Sharma and R. Mahajan, New measures of weighted fuzzy entropy and their applications for the study of maximum weighted fuzzy entropy principle, Information Sciences Vol: 178, No.11 (2008), 2839-2395.
  • [10] C.E. Shannon, A mathematical theory of communication, Bell System Technical Journal Vol: 27, (1948), 379-423,623-656.
  • [11] G. Salton and M.J. McGrill, Introduction to Modern Information Retrieval, McGraw {Hill Book Company, New York, (1983).
  • [12] R. Verma and B.D. Sharma, On generalized exponential fuzzy entropy, World Academy of Science, Engineering and Technology Vol: 60, (2011), 1402-1405.
  • [13] Wang, P.Z., Theory of Fuzzy Sets and their Applications, Shanghai Science and Technology Publishing House, Shanghai, 1982.
  • [14] W.J. Wang, New similarity measures on fuzzy sets and on elements, Fuzzy Sets Systems Vol: 85, No.3 (1997), 305-309.
  • [15] R.R. Yager, On the measure of fuzziness and negation Part-I membership degree in the unit interval, International Journal of General Systems Vol: 5, No.4 (1979), 221-229.
  • [16] R.R. Yager, Entropy and speci city in a mathematical theory of evidence, International Journal of General Systems Vol: 9, No.4 (1983), 249-260.
  • [17] R.R. Yager, Measures of entropy and fuzziness related to aggregation operators, Information Sciences Vol: 82, No.3-4 (1983), 147-166.
  • [18] R.R. Yager, On the entropy of fuzzy measures, IEEE Transactions on Fuzzy Systems Vol: 8, No.4 (2000), 453-461.
  • [19] L.A. Zadeh, Fuzzy Sets, Information and Control Vol: 8, No.3 (1965), 338-353.
  • [20] L.A. Zadeh, Probability measure of fuzzy events, Journal of Mathematical Analysis and Applications Vol: 23, No.2 (1968), 421-427.
  • [21] R. Zwick, E. Carlstein and D.V. Budesco, Measures of similarity amongst fuzzy concepts: A comparative analysis, International Journal of Approximate Reasoning Vol: 1, No.2 (1987), 221-242.
Year 2015, Volume: 3 Issue: 1, 83 - 93, 01.04.2015

Abstract

References

  • [1] D. Bhandari and N.R. Pal, Some new information measures for fuzzy sets, Information Sci- ences Vol: 67, No.2 (1993), 204-228.
  • [2] S.M. Chen, S.M. Yeh and P.H. Hsiao, A comparison of similarity measures of fuzzy values, Fuzzy Sets and Systems, Fuzzy Sets and Systems Vol: 72, No.1 (1995), 79-89.
  • [3] A. De Luca and S. Termini, A de nition of non-probabilistic entropy in the setting of fuzzy set theory, Information and Control Vol: 20, No.4 (1972), 301-312.
  • [4] J. Fan and W. Xie, Some notes on similarity measure and proximity measure, Fuzzy Sets and Systems Vol: 101, No.3 (1999), 403-412.
  • [5] Kaufmann,A., Introduction to the Theory of Fuzzy Subsets, Academic Press, New York, 1975.
  • [6] X. Liu, Entropy, distance measure and similarity measure of fuzzy sets and their relations, Fuzzy Sets and Systems Vol: 52, No.3 (1992), 305-318.
  • [7] N.R. Pal and S.K. Pal, Object background segmentation using new de nitions of IEEE Pro- ceedings E- Computers and Digital Techniques Vol: 366,(1989), 284-318.
  • [8] C.P. Pappis and N.I. Karacapilidis, A comparative assessment of measures of similarity of fuzzy values, Fuzzy Sets and Systems Vol: 56, No.2 (1993), 171-174.
  • [9] O. Prakash, P.K. Sharma and R. Mahajan, New measures of weighted fuzzy entropy and their applications for the study of maximum weighted fuzzy entropy principle, Information Sciences Vol: 178, No.11 (2008), 2839-2395.
  • [10] C.E. Shannon, A mathematical theory of communication, Bell System Technical Journal Vol: 27, (1948), 379-423,623-656.
  • [11] G. Salton and M.J. McGrill, Introduction to Modern Information Retrieval, McGraw {Hill Book Company, New York, (1983).
  • [12] R. Verma and B.D. Sharma, On generalized exponential fuzzy entropy, World Academy of Science, Engineering and Technology Vol: 60, (2011), 1402-1405.
  • [13] Wang, P.Z., Theory of Fuzzy Sets and their Applications, Shanghai Science and Technology Publishing House, Shanghai, 1982.
  • [14] W.J. Wang, New similarity measures on fuzzy sets and on elements, Fuzzy Sets Systems Vol: 85, No.3 (1997), 305-309.
  • [15] R.R. Yager, On the measure of fuzziness and negation Part-I membership degree in the unit interval, International Journal of General Systems Vol: 5, No.4 (1979), 221-229.
  • [16] R.R. Yager, Entropy and speci city in a mathematical theory of evidence, International Journal of General Systems Vol: 9, No.4 (1983), 249-260.
  • [17] R.R. Yager, Measures of entropy and fuzziness related to aggregation operators, Information Sciences Vol: 82, No.3-4 (1983), 147-166.
  • [18] R.R. Yager, On the entropy of fuzzy measures, IEEE Transactions on Fuzzy Systems Vol: 8, No.4 (2000), 453-461.
  • [19] L.A. Zadeh, Fuzzy Sets, Information and Control Vol: 8, No.3 (1965), 338-353.
  • [20] L.A. Zadeh, Probability measure of fuzzy events, Journal of Mathematical Analysis and Applications Vol: 23, No.2 (1968), 421-427.
  • [21] R. Zwick, E. Carlstein and D.V. Budesco, Measures of similarity amongst fuzzy concepts: A comparative analysis, International Journal of Approximate Reasoning Vol: 1, No.2 (1987), 221-242.
There are 21 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Rajkumar Verma This is me

Publication Date April 1, 2015
Submission Date July 10, 2014
Published in Issue Year 2015 Volume: 3 Issue: 1

Cite

APA Verma, R. (2015). COSINE ENTROPY AND SIMILARITY MEASURES FOR FUZZY SETS. Konuralp Journal of Mathematics, 3(1), 83-93.
AMA Verma R. COSINE ENTROPY AND SIMILARITY MEASURES FOR FUZZY SETS. Konuralp J. Math. April 2015;3(1):83-93.
Chicago Verma, Rajkumar. “COSINE ENTROPY AND SIMILARITY MEASURES FOR FUZZY SETS”. Konuralp Journal of Mathematics 3, no. 1 (April 2015): 83-93.
EndNote Verma R (April 1, 2015) COSINE ENTROPY AND SIMILARITY MEASURES FOR FUZZY SETS. Konuralp Journal of Mathematics 3 1 83–93.
IEEE R. Verma, “COSINE ENTROPY AND SIMILARITY MEASURES FOR FUZZY SETS”, Konuralp J. Math., vol. 3, no. 1, pp. 83–93, 2015.
ISNAD Verma, Rajkumar. “COSINE ENTROPY AND SIMILARITY MEASURES FOR FUZZY SETS”. Konuralp Journal of Mathematics 3/1 (April 2015), 83-93.
JAMA Verma R. COSINE ENTROPY AND SIMILARITY MEASURES FOR FUZZY SETS. Konuralp J. Math. 2015;3:83–93.
MLA Verma, Rajkumar. “COSINE ENTROPY AND SIMILARITY MEASURES FOR FUZZY SETS”. Konuralp Journal of Mathematics, vol. 3, no. 1, 2015, pp. 83-93.
Vancouver Verma R. COSINE ENTROPY AND SIMILARITY MEASURES FOR FUZZY SETS. Konuralp J. Math. 2015;3(1):83-9.
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