Similarity measures for interval-valued intuitionistic fuzzy soft sets and its application in medical diagnosis problem.
Abstract
Similarity measure is an important topic in fuzzy set theory (L. A. Zadeh, 1965). Similarity measure of fuzzy sets is now being extensively applied in many research fields such as fuzzy clustering, image processing, fuzzy reasoning, fuzzy neural network, pattern recognition, medical diagnosis, game theory, coding theory and several problems that contain uncertainties. The aim of this paper is to introduce the concept of similarity measure for interval-valued intuitionistic fuzzy soft sets based on set theoretic approach, some examples and basic properties are also studied. Lastly an application in a medical diagnosis problem is illustrated
Keywords
Soft set intuitionistic fuzzy set interval-valued fuzzy soft set interval-valued intuitionistic fuzzy soft set Similarity Measure
References
- K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986) 87–96.
- K. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31(1989) 343–349.
- Naim Cagman, Irfan Deli, Similarity Measure of Intuitionistic Fuzzy Soft Sets and their Decision making, arXiv : 1300456vI [ math.LO] 3jan 2013.
- S. M. Chen, Measures of similarity between vague sets, Fuzzy Sets and Systems, 74(1995) 217–223.
- Kai Hu, Li Jinquan, The Entropy and Similarity Measure of Interval Valued Intuitionistic Fuzzy Sets and Their Relationship, International Journal of Fuzzy Systems, 15(3), (September 2013) 279 –288.
- Y. Jiang, Y. Tang, Q. Chen, H. Liu, J. Tung, Interval -valued intuitionistic fuzzy soft sets and their properties, Computers and Mathematics with Applications, 60(2010) 906–918.
- Hong-mei Ju, Feng-Ying Wang, A Similarity Measure for Interval-valued Fuzzy Sets and Its Application in Supporting Medical Diagnostic Reasoning, The Tenth International Symposium on Operations Research and Its Applications (ISORA) ( 2011) 251–257 .
- Zhizhen Liang, Pengfei Shi, Similarity Measures On Intuitionistic Fuzzy Sets, Pattern Recognition Letters, 24(2003) 2687– 26
- D. Molodtsov , Soft Set Theory–First Results, Computers and Mathematics with Application, 37 (1999) 19–31.
- A. Mukherjee, S. Sarkar , Similarity measures of interval-valued fuzzy soft sets, Annals of Fuzzy Mathematics and Informatics, 8(9) (2014) 447– 460.
- P. Majumdar, S. K. Samanta , Similarity Measure Of Soft Sets, New Mathematics and Natural Computation, 4(1) (2008) 1–
- P. Majumdar, S. K. Samanta , On Similarity Measures of Fuzzy Soft Sets, Int. J. Advance Soft Comput. Appl. 3(2) (July 2011) 1– 8.
- P. K. Maji, R. Biswas, A. R. Roy , Soft set theory, Computers and Mathematics with Applications, 45(4-5) (2003) 555– 5
- E. Szmidt, J. Kacprzyk, Distances Between Intuitionistic Fuzzy sets. Fuzzy Sets and System, 114(2000) 505-518.
- X. B. Yang, T. Y. Lin, J. Y. Yang, Y. Li, D. Yu, Combination of interval-valued fuzzy set and soft set, Computers and Mathematics with Applications, 58(3) (2009) 521–527.
- L. A. Zadeh, Fuzzy set, Information and Control, 8(1965) 338–353.
- L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-1, Information Sciences, 8(1975) 199−249.
Similarity measures for interval-valued intuitionistic fuzzy soft sets and its application in medical diagnosis problem
Abstract
References
- K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986) 87–96.
- K. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 31(1989) 343–349.
- Naim Cagman, Irfan Deli, Similarity Measure of Intuitionistic Fuzzy Soft Sets and their Decision making, arXiv : 1300456vI [ math.LO] 3jan 2013.
- S. M. Chen, Measures of similarity between vague sets, Fuzzy Sets and Systems, 74(1995) 217–223.
- Kai Hu, Li Jinquan, The Entropy and Similarity Measure of Interval Valued Intuitionistic Fuzzy Sets and Their Relationship, International Journal of Fuzzy Systems, 15(3), (September 2013) 279 –288.
- Y. Jiang, Y. Tang, Q. Chen, H. Liu, J. Tung, Interval -valued intuitionistic fuzzy soft sets and their properties, Computers and Mathematics with Applications, 60(2010) 906–918.
- Hong-mei Ju, Feng-Ying Wang, A Similarity Measure for Interval-valued Fuzzy Sets and Its Application in Supporting Medical Diagnostic Reasoning, The Tenth International Symposium on Operations Research and Its Applications (ISORA) ( 2011) 251–257 .
- Zhizhen Liang, Pengfei Shi, Similarity Measures On Intuitionistic Fuzzy Sets, Pattern Recognition Letters, 24(2003) 2687– 26
- D. Molodtsov , Soft Set Theory–First Results, Computers and Mathematics with Application, 37 (1999) 19–31.
- A. Mukherjee, S. Sarkar , Similarity measures of interval-valued fuzzy soft sets, Annals of Fuzzy Mathematics and Informatics, 8(9) (2014) 447– 460.
- P. Majumdar, S. K. Samanta , Similarity Measure Of Soft Sets, New Mathematics and Natural Computation, 4(1) (2008) 1–
- P. Majumdar, S. K. Samanta , On Similarity Measures of Fuzzy Soft Sets, Int. J. Advance Soft Comput. Appl. 3(2) (July 2011) 1– 8.
- P. K. Maji, R. Biswas, A. R. Roy , Soft set theory, Computers and Mathematics with Applications, 45(4-5) (2003) 555– 5
- E. Szmidt, J. Kacprzyk, Distances Between Intuitionistic Fuzzy sets. Fuzzy Sets and System, 114(2000) 505-518.
- X. B. Yang, T. Y. Lin, J. Y. Yang, Y. Li, D. Yu, Combination of interval-valued fuzzy set and soft set, Computers and Mathematics with Applications, 58(3) (2009) 521–527.
- L. A. Zadeh, Fuzzy set, Information and Control, 8(1965) 338–353.
- L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-1, Information Sciences, 8(1975) 199−249.
Details
| Journal Section | Articles |
|---|---|
| Authors | |
| Publication Date | December 1, 2014 |
| Published in Issue | Year 2014 Volume: 2 Issue: 3 |