SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2018 / Cilt: 47 - Sayı: 6

An improved cosine similarity measure for intuitionistic fuzzy sets and their applications to decision-making process

Harish GARG
Pages
1578–1594
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Numerical examples, one from the investment the money and others from the pattern recognition and medical diagnosis, have been taken to demonstrate the efficiency of the proposed approach and compared their results with the existing approaches results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present study, improved cosine similarity measure for an intuitionistic fuzzy sets (IFSs) has been proposed by considering the interaction between the pairs of the membership degrees.
📊
Key Findings & Data:Pairs of membership, non-membership are to be considered as vector representation during the formulation.
💡
Conclusion & Impact:Numerical examples, one from the investment the money and others from the pattern recognition and medical diagnosis, have been taken to demonstrate the efficiency of the proposed approach and compared their results with the existing approaches results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Cosine similarity measures · intuitionistic fuzzy set · pattern recognition

Abstract

In the present study, improved cosine similarity measure for an intuitionistic fuzzy sets (IFSs) has been proposed by considering the interaction between the pairs of the membership degrees. Pairs of membership, non-membership are to be considered as vector representation during the formulation. The shortcomings of the existing measures have been highlighted and overcome by using the proposed measure. Also, in order to deal with the situation where the elements in a set are correlative, weighted cosine similarity measure has been defined. Finally, multi-criteria decision making (MCDM) method, based on the proposed similarity measure, has been presented under intuitionistic fuzzy environment. Numerical examples, one from the investment the money and others from the pattern recognition and medical diagnosis, have been taken to demonstrate the efficiency of the proposed approach and compared their results with the existing approaches results.

🔖

Cite This Article

GARG, H. (2022). An improved cosine similarity measure for intuitionistic fuzzy sets and their applications to decision-making process. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 6, 1578–1594. https://ajindex.com/articles/530186

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. Atanassov, K. T., Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20, 87--96, 1986.
  2. Atanassov, K., Gargov, G., Interval-valued intuitionistic fuzzy sets, Fuzzy Sets Syst., 31, 343 -- 349, 1989.
  3. Bustince, H., Burillo, P., Correlation of interval-valued intuitionistic fuzzy sets,Fuzzy Sets Syst., 74, 237 -- 244, 1995.
  4. Chen, S. M., Measures of similarity between vague sets, Fuzzy Sets Syst., 74 (2), 217 -- 223, 1995.
  5. Chen, S. M., Similarity measures between vague sets and between elements, IEEE Transact. Systems Man Cybernet. 27~(1), 153 -- 158, 1997.
  6. Dengfeng, L., Chuntian, C., New similarity measure of intuitionistic fuzzy sets and application to pattern recognitions, Pattern Recognition Lett. 23, 221 -- 225, 2002.
  7. Fan, L., Zhangyan, X., Similarity measures between vague sets., J. Software 12~(6), 922 -- 927, 2001.
  8. Garg, H., Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making, Comput. Industrial Eng. 101, 53 -- 69, 2016.
  9. Garg, H., Generalized intuitionistic fuzzy multiplicative interactive geometric operators and their application to multiple criteria decision making, Int. J. Mach. Learn. Cybernet. 7~(6), 1075--1092, 2016.
  10. Garg, H., A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems, Appl. Soft Comput. 38, 988 -- 999, 2016.
  11. Garg, H., Distance and similarity measure for intuitionistic multiplicative preference relation and its application, Int. J. Uncertain. Quantif. 7~(2), 117 -- 133, 2017.
  12. Garg, H., Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application, Eng. Appli. Artif. Intell. 60, 164 -- 174, 2017.
  13. Garg, H., Agarwal, N., Choubey, A., Entropy based multi-criteria decision making method under fuzzy environment and unknown attribute weights, Global J. Technol. Optim. 6~(3), 13 -- 20, 2015.
  14. Garg, H., Agarwal, N., Tripathi, A., Generalized intuitionistic fuzzy entropy measure of order $\alpha$ and degree $\beta$ and its applications to multi-criteria decision making problem, Int. J. Fuzzy Syst. Appl. 6~(1), 86 -- 107, 2017.
  15. Garg, H., Arora, R., Distance and similarity measures for dual hesistant fuzzy soft sets and their applications in multi criteria decision-making problem, Int. J. Uncertain. Quantif., 7 (3), 229-248, 2017.
  16. Garg, H., Rani, M., Sharma, S. P., Vishwakarma, Y., Intuitionistic fuzzy optimization technique for solving multi-obj