International Journal of Intelligent Systems and Applications (IJISA)
IJISA Vol. 6, No. 5, 8 Apr. 2014
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A New Inaccuracy Measure for Fuzzy Sets and its Application in Multi-Criteria Decision Making
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Author(s)
Rajkumar Verma
1,*
Bhu Dev Sharma
1
Index Terms
Fuzzy Sets, Fuzzy Entropy, Fuzzy Inaccuracy Measure, Fuzzy Divergence Measure
Abstract
In the present paper, a new fuzzy inaccuracy measure is proposed to measure the inaccuracy of a fuzzy set with respect to another fuzzy set. This measure is a modified version of fuzzy inaccuracy proposed in our earlier work. The measure is demonstrated to satisfy some interesting properties, which prepare ground for applications in multi-criteria decision making problems. A method to solve multi-criteria decision making problems with the help of new measure is developed. Finally, a numerical example is given to illustrate the proposed method to solve multi-criteria decision-making problem under fuzzy environment.
Cite This Paper
Rajkumar Verma, Bhu Dev Sharma, "A New Inaccuracy Measure for Fuzzy Sets and its Application in Multi-Criteria Decision Making", International Journal of Intelligent Systems and Applications(IJISA), vol.6, no.5, pp.62-69, 2014. DOI:10.5815/ijisa.2014.05.06
Reference
[1]L.A. Zadeh, Fuzzy sets, Information and Control, vol. 8, no. 3, 1965, 338-353.
[2]L.A. Zadeh, Probability measure of fuzzy event, Journal of Mathematical Analysis and Applications, vol. 23, no. 2, 1968, 421-427.
[3]C.E. Shannon, A mathematical theory of communication, Bell System Technical Journal, vol. 27, 1948, 379-423; 623-656.
[4]A. De Luca and S. Termini, A definition of non-probabilistic entropy in the setting of fuzzy set theory, Information and Control, vol. 20, no. 4, 1972, 301-312.
[5]D. Bhandari and N.R. Pal, Some new information measure for fuzzy sets, Information Science, vol. 67, no. 3, 1993, 209-228.
[6]S. Kullback and R.A. Leibler, On information and sufficiency, The Annals Mathematical Statistics, vol. 22, no. 1, 1951, 79–86.
[7]S. Kullback, Information Theory and Statistics, Dover Publication, 1968.
[8]J. Lin, Divergence measure based on Shannon entropy, IEEE Transaction on Information Theory, vol. 37, no. 1, 1991, 145-151.
[9]X. Shang and G. Jiang, A note on fuzzy information measures, Pattern Recognition Letters, vol. 18, no. 5, 1997, pp. 425-432.
[10]D. Kerridge, Inaccuracy and inference, Journal of Royal Statistical Society B, vol. 23, no. 1, 1961, 184-194.
[11]R.K. Verma and B.D. Sharma, A measure of inaccuracy between two fuzzy sets, Cybernetics and Information Technologies, vol. 11, no. 2, 2011, 13-23.