Similarity Measure: An Intuitionistic Fuzzy Rough Set Approach

Subject Areas : Transactions on Fuzzy Sets and Systems

Jaydip  Bhattacharya ¹ (Department of Mathematics, Bir Bikram Memorial College, Agartala, Tripura, India.)

Received: 2023-02-02 Accepted : 2023-10-24 Published : 2023-11-07

Keywords: Similarity measure, Intuitionistic fuzzy set, Rough set,

Abstract :

In fuzzy set theory, the concept of a non-membership function and the hesitation margin were not considered while these two concepts have been included along with the membership function for intuitionistic fuzzy sets. It is also to be noted that the intuitionistic fuzzy set is reflected as an extension of the fuzzy set accommodating both membership and non-membership functions together with a hesitation margin. In the intuitionistic fuzzy set theory, the sum of the membership function and the non-membership function is a value between 0 and 1. In recent times, intuitionistic fuzzy rough set theory has emerged as a powerful tool for dealing with imprecision and uncertain information in relational database theory. Measures of similarity between fuzzy rough sets as well as intuitionistic fuzzy rough sets provide wide applications in real-life problems and that is why many researchers paid more attention to this concept. Intuitionistic fuzzy rough set theory behaves like an excellent tool to tackle impreciseness or uncertainties. In this paper, we propose a new approach of similarity measure on an intuitionistic fuzzy rough set based on a set-theoretic approach. The proposed measure is able to give an exact result. In the application part, we consider a real-life problem for selecting a fair play award-winning team in a cricket tournament and describe the algorithm.

References:

 Atanassov KT. (1983). Intuitionistic fuzzy sets. VII ITKRs Session, Sofia, 20-23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: International Journal of Bioautomation, 2016, 20(S1), S1-S6.

[2] Atanassov KT. Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 1986; 20(1): 87-96. DOI: https://doi.org/10.1016/S0165-0114(86)80034-3
[3] Atanassov KT. Intuitionistic fuzzy sets. In: Theory and Applications, Physica-Verlag, Heidelberg; 1999. p.1-137. DOI: https://doi.org/10.1007/978-3-7908-1870-3-1
[4] Atanasova L. On intuitionistic fuzzy versions of L. Zadeh’s extension principle. Notes on Intuitionistic Fuzzy Sets. 2007; 13(3): 33-36. http://ifigenia.org/wiki/issue:nifs/13/3/33-36
[5] Chen SM, Yeh MS, Hsiao PY. A comparison of similarity measures of fuzzy values. Fuzzy Sets and Systems. 1995; 72(1): 79-89. DOI: https://doi.org/10.1016/0165-0114(94)00284-E
[6] Chengyi Z, Pingan D, Haiyan F. On measures of similarity between fuzzy rough sets. International Journal of Pure and Applied Mathematics. 2004; 10(4), 451-458.
[7] Coker D. Fuzzy rough sets are intuitionistic L-fuzzy sets. Fuzzy Sets and System. 1998; 96(3): 381-383. DOI: https://doi.org/10.1016/S0165-0114(97)00249-2
[8] Das TK, Acharjya DP, Patra MR. Multi-criteria decision making using intuitionistic Fuzzy rough set on two universal sets. International Journal of Intelligent Systems and Applications. 2015; 7(4): 26-33. DOI: https://doi.org/10.5815/ijisa.2015.04.04
[9] Dubois D, Prade H. Rough fuzzy sets and fuzzy rough sets. International Journal of General System. 1990; 17(2-3): 191-209. DOI: https://doi.org/10.1080/03081079008935107
[10] Gangwal C, Bhaumik RN. Functional dependences in intuitionistic fuzzy rough relational databases, In: S.Bhattacharya Halder (ed.), Rough sets, Fuzzy sets and Soft Computing. 2015; 111-120.
[11] Nanda S, Majumdar S. Fuzzy rough sets. Fuzzy sets and System. 1992; 45(2): 157-160. DOI:
https://doi.org/10.1016/0165-0114(92)90114-J
[12] Pappis CP, Karacapilidis NI. A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets and Systems. 1993; 56(2): 171-174. DOI: https://doi.org/10.1016/0165-0114(93)90141-4
[13] Pawlak Z. Rough sets. International Journal of Computer and Information Sciences. 1982; 11: 341-356. DOI: https://doi.org/10.1007/BF01001956
[14] Pawlak Z. Rough Sets: Theoretical Aspects of Reasoning about Data. Netherlands: Kluwer Academic Publishers, Dordrecht; 1991. DOI: https://doi.org/10.1007/978-94-011-3534-4
[15] Sharma O, Rani A, Gupta P. Some similarity and distance measures on fuzzy rough sets and it’s applications. International Journal of Engineering, Science and Mathematics. 2017; 6(5): 85-105.
[16] Yun SM, Lee SJ. New approach to intuitionistic fuzzy rough sets. International Journal of Fuzzy Logic and Intelligent Systems. 2020; 20(2): 129-137. DOI: https://doi.org/10.5391/IJFIS.2020.20.2.129
[17] Zadeh LA. Fuzzy sets. Information and Control. 1965; 8(3): 338-353. DOI: https://doi.org/10.1016/S0019-9958(65)90241-X
[18] Zhou L, Wu WZ. On generalized intuitionistic fuzzy rough approximation operators. Information Sciences. 2008; 178(11): 2448-2465. DOI: https://doi.org/10.1080/03081070802187723
[19] Zhou L, Wu WZ, Zhang WX. On intuitionistic fuzzy rough sets and their topological structures. International Journal General Systems. 2009; 38 (6): 589-616.
[20] Zwick R, Carlstein E, Budescu DV. Measures of similarity among fuzzy concepts: A comparative analysis. International Journal of Approximate Reasoning. 1987; 1(2): 221-242. DOI: https://doi.org/10.1016/0888-613X(87)90015-6