single-jc.php

JACIII Vol.22 No.1 pp. 147-155
doi: 10.20965/jaciii.2018.p0147
(2018)

Paper:

Entropy Analysis on Intuitionistic Fuzzy Sets and Interval-Valued Intuitionistic Fuzzy Sets and its Applications in Mode Assessment on Open Communities

Hang Tian*, Jiaru Li*, Fangwei Zhang*,†, Yujuan Xu**, Caihong Cui**, Yajun Deng*, and Shujun Xiao***

*College of Transport, Communications, Shanghai Maritime University
1550 Haigang Avenue, Shanghai 201306, China

**College of Economics and Management, Shanghai Maritime University
1550 Haigang Avenue, Shanghai 201306, China

***Logistics Engineering College, Shanghai Maritime University
1550 Haigang Avenue, Shanghai 201306, China

Corresponding author

Received:
May 25, 2017
Accepted:
November 14, 2017
Published:
January 20, 2018
Keywords:
intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, entropy, uncertainty, open community
Abstract

This paper identifies four variables to reveal the internal mechanisms of the entropy measures on intuitionistic fuzzy sets (IFSs) and interval-valued intuitionistic fuzzy sets (IVIFSs). First, four variables are used to propose a pair of generalized entropy measures on IFSs and IVIFSs. Second, three specific entropy measures are put forward to illustrate the effectiveness of the generalized entropy measure functions. Third, a novel multiple attribute decision-making approach under an intuitionistic fuzzy environment is proposed. The superiority of the decision-making approach is that the weight values of the attributes are obtained by their related entropy measures. Finally, the performance of the proposed entropy regulations on IFSs and IVIFSs is illustrated through a mode assessment example on open communities.

References
  1. [1] K. T. Atanassov and P. Rangasamy, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, Vol.20, No.1, pp. 87-96, 1986.
  2. [2] K. Hu and J. Li, “The entropy and similarity measure of interval valued intuitionistic fuzzy sets and their relationship,” Int. J. of Fuzzy Systems, Vol.15, No.3, pp. 279-288, 2013.
  3. [3] F. Meng and X. Chen, “Entropy and similarity measure of Atanassov’s intuitionistic fuzzy sets and their application to pattern recognition based on fuzzy measures,” Pattern Analysis and Applications, Vol.19, No.1, pp. 11-20, 2016.
  4. [4] A. D. Luca and S. Termini, “A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory,” Information and Control, Vol.20, No.4, pp. 301-312, 1972.
  5. [5] E. Szmidt and J. Kacprzyk, “Entropy for intuitionistic fuzzy sets,” Fuzzy Sets and Systems, Vol.118, No.3, pp. 467-477, 2001.
  6. [6] G. Deschrijver, “Implication Functions in Interval-Valued Fuzzy Set Theory,” Advances in Fuzzy Implication Functions, Springer Berlin Heidelberg, Vol.300, pp. 73-99, 2013.
  7. [7] J. Ye, “Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment,” Int. Conf. on Computer-Aided Industrial Design and Conceptual Design, Vol.205, No.1, pp. 2057-2060, 2009.
  8. [8] J. Ye, “Two effective measures of intuitionistic fuzzy entropy,” Computing, Vol.87, No.1, pp. 55-62, 2010.
  9. [9] J. Ye, “Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets,” Mathematical Modelling, Vol.34, No.12, pp. 3864-3870, 2010.
  10. [10] H. Nguyen, “A new interval-valued knowledge measure for interval-valued intuitionistic fuzzy sets and application in decision making,” Expert Systems with Applications An Int. J., Vol.56, Issue C, pp. 143-155, 2016.
  11. [11] Q. Zhang, H. Xing, F. Liu, J. Ye, and P. Tang, “Some new entropy measures for interval-valued intuitionistic fuzzy sets based on distances and their relationships with similarity and inclusion measures,” Information Sciences, Vol.283, pp. 55-69, 2014.
  12. [12] N. Zhao and X. Zeshui, “Entropy measures for interval-valued intuitionistic fuzzy information from a comparative perspective and their application to decision making,” Informatica, Vol.27, No.1, pp. 203-229, 2015.
  13. [13] H. Zhao, You J. X., and H. C. Liu, “Failure mode and effect analysis using multimoora method with continuous weighted entropy under interval-valued intuitionistic fuzzy environment,” Soft Computing, pp. 1-13, 2016.
  14. [14] R. Joshi and S. Kumar, “Parametric (r, s) (R, S) math container loading mathjaxnorm entropy on intuitionistic fuzzy sets with a new approach in multiple attribute decision making,” Fuzzy Information & Engineering, Vol.9, No.2, pp. 181-203, 2017.
  15. [15] C. Duan, “Intuitionistic fuzzy multiple attribute decision making based on interval numbers,” J. of Zhejiang University, Vol.44, Issue 2, 2017.
  16. [16] K. T. Atanassov, “More on intuitionistic fuzzy sets,” Fuzzy Sets and Systems, Vol.33, No.1, pp. 37-45, 1989.
  17. [17] K. T. Atanassov, “New operations defined over the intuitionistic fuzzy sets,” Fuzzy Sets and Systems, Vol.61, No.2, pp. 137-142, 1994.
  18. [18] Z. Xu and R. R. Yager, “Some geometric aggregation operators based on intuitionistic fuzzy sets,” Int. J. Gen. Syst., Vol.35, No.4, pp. 417-433, 2006.
  19. [19] Z. S. Xu, “Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making,” Control Decis, Vol.22, No.2, pp. 215-219, 2007.
  20. [20] F. W. Zhang, “Several kinds of uncertain multi-attribute decision-making methods and their application in transportation management,” People’s Communication Press, 2016.
  21. [21] X. Chen, L. Yang, P. Wang, and W. Yue, “An effective interval-valued intuitionistic fuzzy entropy to evaluate entrepreneurship orientation of online p2p lending platforms,” Advances in Mathematical Physics, Vol.2013, No.4, pp. 594-603, 2013.
  22. [22] X. K. Lv, Y. B. Zhang, X. X. Yan, and W. Ma, “Study on the influence caused by opening different types of community on surrounding traffic,” Engineering Management Research, Vol.6, No.1, pp. 1927-7318, 2016.
  23. [23] F. Meng and X. Chen, “Entropy and similarity measure for Atannasov’s interval-valued intuitionistic fuzzy sets and their application,” Kluwer Academic Publishers, 2016.
  24. [24] I. K. Vlachos and G. D. Sergiadis, “Subsethood, entropy, and cardinality for interval-valued fuzzy sets-an algebraic derivation,” Fuzzy Sets and Systems, Vol.158, No.12, pp. 1384-1396, 2007.
  25. [25] F. W. Zhang and S. H. Xu, “Multiple attribute group decision making method based on utility theory under interval-valued intuitionistic fuzzy environment,” Group Decision and Negotiation, Vol.25, No.6, pp. 1261-1275, 2016.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, IE9,10,11, Opera.

Last updated on Feb. 20, 2018