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On Exponential Interval Valued Intuitionistic Fuzzy Entropy of Order a and type ß and its Applications in Decision Making

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International Journal of Computer Applications
© 2014 by IJCA Journal
Volume 95 - Number 12
Year of Publication: 2014
Authors:
Rajeev Kaushik
Rakesh K Bajaj
10.5120/16643-6615

Rajeev Kaushik and Rakesh K Bajaj. Article: On Exponential Interval Valued Intuitionistic Fuzzy Entropy of Order a and type b and its Applications in Decision Making. International Journal of Computer Applications 95(12):1-6, June 2014. Full text available. BibTeX

@article{key:article,
	author = {Rajeev Kaushik and Rakesh K Bajaj},
	title = {Article: On Exponential Interval Valued Intuitionistic Fuzzy Entropy of Order a and type b and its Applications in Decision Making},
	journal = {International Journal of Computer Applications},
	year = {2014},
	volume = {95},
	number = {12},
	pages = {1-6},
	month = {June},
	note = {Full text available}
}

Abstract

In the present paper, a new entropy of order and type on Interval-Valued Intutionistic Fuzzy Sets (IVIFSs) along with their proofs of validity is proposed. It has been proved that the proposed entropy has monotonic decreasing behavior with respect to and . Further, a new algorithm for multiple attribute decision making method (MADM) has been provided using the benefit attributes and cost attribute weights on the proposed entropy, where the alternatives on attributes are expressed by interval-valued intuitionistic fuzzy sets (IVIFS). The information about attribute weight is unknown. Finally, numerical example for illustrating the proposed methodology has also been provided to illustrate the applicability and validity of the newly proposed method.

References

  • K. Atanassov, Intuitionistic fuzzy set, Fuzzy Sets and Systems, 1986, vol. 30, no. 1, 87-96.
  • K. Atanassov and G. Gargov, " Interval valued Intuitionistic fuzzy set," Fuzzy Sets and Systems,1989, vol. 31, no. 3, pp. 343-349.
  • L. A. Zadeh, Fuzzy Sets, Information and Control, 8, 338 – 353.
  • Bustince, H. , Burillo, P. , Entropy on Intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems, 1996, 78, 305-316.
  • Ying Jun Zhang, Pei Jun Ma, Xiao Hong Su ,Chi Ping Zhang "Entropy on Interval-valued Intuitionistic Fuzzy Sets and Its Application in Multi-attribute Decision Making" International Conference on Information Fusion, 2011.
  • A. De Luca and S. Termini, A Definition of a Nonprobabilistic Entropy in the Setting of fuzzy sets theory, Information and Control, 1972, 20, 301 -312.
  • Kaufmann, A. , Introduction to the Theory of Fuzzy Subsets– vol. 1, Fundamental Theoretical Elements, Academic Press, New York, 1975
  • HungW. , A note on entropy of intuitionistic fuzzy sets. International Journal of Uncertainty, Fuzziness and Knowledge- Based Systems, 2003, 11, 627-633.
  • Zhang H. , ZhangW. , Mei C. , Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure. Knowledge- Based Systems, 2009, 22, 449-454.
  • Vlachos I. , Sergiadis G. , Intuitionistic fuzzy information- Applications to pattern recognition. Pattern Recognition Letters, 2007, 28(2): 197-206.
  • Zeng, W. , Yu F. , Yu X. , Chen H. and Wu S. , Entropy of Intuitionistic fuzzy set based on similarity measure. International Journal of Innovative Computing, Information and Control, 2009, 5(12): 4737-4744.
  • Yager, R. R. , On the measure of fuzziness and negation. Part I: Membership in the unit interval, Intermat. J. General Systems, 5(1979), 189-200.
  • Hwang C L, Yoon K. Multiple attribute decision making methods and applications. Springer-Verlag, Berlin, 1981.
  • Yoon K. , The propagation of errors in multiple attribute decision analysis: a practical approach. Journal of the Operational Research Society, 1989, 40: 681–686.
  • Edwards W. , How to use multi-attribute utility measurement for social decision making. IEEE Trans. on Systems, Man and Cybernetics, 1977, 7: 326–340.
  • Saaty T L. , A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 1977, 15: 234–281.
  • Yang J B, Xu D L. , Nonlinear information aggregation via evidential reasoning in multi-attribute decision analysis under uncertainty. IEEE Trans. On Systems, Man and Cybernetics- Part A, 2002, 32: 376–393.
  • Zeng,W. Y. , Li, H. X. , Inclusion measures, similarity measures and the fuzziness of fuzzy sets and their relations, International Journal of Intelligence Systems,2006, 21, 639-653.
  • Qi X. W. , Liang C. Y. , Zhang E. Q. , Ding Y. , Approach to interval valued intuitionistic fuzzy multiple attributes group decision making based on maximum entropy. Systems Engineering-Theory and Practice, 2011, 31(10):1940-1948.
  • Ye J. , Multiple Attribute Group Decision-Making Methods with Completely Unknown Weights in Intuitionistic Fuzzy Setting and Interval- Valued Intuitionistic Fuzzy Setting. Group Decis. Negot. , 2011, DOI 10. 1007/s 10726- 011-9255- 5.
  • D. Li, "TOPSIS-Based Nonlinear-Programming Methodology for Multi-attribute Decision Making With Interval- Valued Intuitionistic Fuzzy Sets," IEEE Transactions on Fuzzy Systems, 2010, vol. 18, no. 2, pp. 299-311.
  • Z. Xu, Intuitionistic Fuzzy Information Aggregation Theory and Application. Science Press, BeiJing, 2008.
  • F. Boran, S. Genc, M. Kurt and D. Akay, "A multi-criteria Intuitionistic fuzzy group decision making for supplier selection with TOPSIS method," Expert Systems with Applications, 2009, vol. 36, no. 8, pp. 11363-11368.