Authors:
Zahid Hussain,Sahar Abbas ,Shahid Hussain,Zaigham Ali,Gul Jabeen,DOI NO:
https://doi.org/10.26782/jmcms.2021.06.00006Keywords:
Divergence measure,Intuitionistic fuzzy set (IFS),Pythagorean fuzzy set (PFS),Pattern recognition,similarity measure,multicriteria decision making,Abstract
The construction of divergence measures between two Pythagorean fuzzy sets (PFSs) is significant as it has a variety of applications in different areas such as multicriteria decision making, pattern recognition and image processing. The main purpose of this study to introduce an information-theoretic divergence so-called Pythagorean fuzzy Jensen-Rényi divergence (PFJRD) between two PFSs. The strength and characterization of the proposed Jensen-Rényi divergence between Pythagorean fuzzy sets lie in its practical applications which are very closed to real life. The proposed divergence measure is utilized to induce some useful similarity measures between PFSs. We apply them in pattern recognition, characterization of the similarity between linguistic variables and in multiple criteria decision making. To demonstrate the practical utility and applicability, we present some numerical examples related to daily life with the construction of Pythagorean fuzzy TOPSIS (Techniques of preference similar to ideal solution). Which is utilized to rank the Belt and Road initiative (BRI) projects. Our numerical simulation results show that the suggested measures are well suitable in pattern recognition, characterization of linguistic variables and multi-criteria decision-making environment.Refference:
I. Abbas, S. E. (2005). On intuitionistic fuzzy compactness. Information Sciences, 173(1-3), 75-91.
II. Atanassov, K. T. (2000). Two theorems for intuitionistic fuzzy sets. Fuzzy sets and systems, 110(2), 267-269.
III. Atanassov K, (1999). Intuitionistic Fuzzy Sets, Theory and Applications, Heidelberg: Physica-Verlag, New York.
IV. Atanassov K,(1994a). New operations defined over the intuitionistic fuzzy sets. Fuzzy SetsSyst, 61,137–142.
V. Atanassov K, (1989). More on intuitionistic fuzzy sets. Fuzzy Sets Syst, 33,37–46.
VI. Atanassov K, & Gargov G,(1989). Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst,31,343–349.
VII. Atanassov K,(1986). Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20:87–96.
VIII. Bouchon-Meunier, B., Rifqi, M., & Bothorel, S. (1996). Towards general measures of comparison of objects. Fuzzy sets and systems, 84(2), 143-153.
IX. Candan, K. S., Li, W. S., & Priya, M. L. (2000). Similarity-based ranking and query processing in multimedia databases. Data & Knowledge Engineering, 35(3), 259-298.
X. Garg, H. (2016). A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. International Journal of Intelligent Systems, 31(9), 886-920.
XI. Gou, X., Xu, Z., & Ren, P. (2016). The properties of continuous Pythagorean fuzzy information. International Journal of Intelligent Systems, 31(5), 401-424.
XII. Hussian, Z., & Yang, M. S. (2019). Distance and similarity measures of Pythagorean fuzzy sets based on the Hausdorff metric with application to fuzzy TOPSIS. International Journal of Intelligent Systems, 34(10), 2633-2654.
XIII. Hwang, C. M., & Yang, M. S. (2016). Belief and plausibility functions on intuitionistic fuzzy sets. International Journal of Intelligent Systems, 31(6), 556-568.
XIV. He, Y., Hamza, A. B., & Krim, H. (2003). A generalized divergence measure for robust image registration. IEEE Transactions on Signal Processing, 51(5), 1211-1220.
XV. Kacprzyk, J., & Ziolkowski, A. (1986). Database queries with fuzzy linguistic quantifiers. IEEE transactions on systems, man, and cybernetics, 16(3), 474-479.
XVI. Lin, J. (1991). Divergence measures based on the Shannon entropy. IEEE Transactions on Information theory, 37(1), 145-151.
XVII. Hwang, C. M., Yang, M. S., & Hung, W. L. (2018). New similarity measures of intuitionistic fuzzy sets based on the Jaccard index with its application to clustering. International Journal of Intelligent Systems, 33(8), 1672-1688.
XVIII. Mitchell, H. B. (2003). On the Dengfeng–Chuntian similarity measure and its application to pattern recognition. Pattern Recognition Letters, 24(16), 3101-3104.
XIX. Montes S, Couso I, Gil P, &Bertoluzza C,(2002). Divergence between fuzzy sets. Int. J. of Approx. Reasoning, 31,91–105.
XX. Peng, X., & Garg, H. (2019). Multiparametric similarity measures on Pythagorean fuzzy sets with applications to pattern recognition. Applied Intelligence, 49(12), 4058-4096.
XXI. Peng, X., & Yang, Y. (2017). Algorithms for interval-valued fuzzy soft sets in stochastic multi-criteria decision making based on regret theory and prospect theory with combined weight. Applied Soft Computing, 54, 415-430.
XXII. Papageorgiou, E. I., & Iakovidis, D. K. (2012). Intuitionistic fuzzy cognitive maps. IEEE Transactions on Fuzzy Systems, 21(2), 342-354.
XXIII. Petry FE,(1996). Fuzzy Database: Principles and Applications. Kluwer, Dordrecht.
XXIV. Pal, N. R., & Pal, S. K. (1992). Some properties of the exponential entropy. Information sciences, 66(1-2), 119-137.
XXV. Pal, N. R., & Pal, S. K. (1991). Entropy: A new definition and its applications. IEEE transactions on systems, man, and cybernetics, 21(5), 1260-1270.
XXVI. R. Shashi Kumar Reddy, M.S. Teja, M. Sai Kumar, Shyamsunder Merugu, : ‘MATHEMATICAL INPUT-OUTPUT RELATIONSHIPS & ANALYSIS OF FUZZY PD CONTROLLERS’. J. Mech. Cont. & Math. Sci., Vol.-15, No.-8, August (2020) pp 330-340. DOI : 10.26782/jmcms.2020.08.00031
XXVII. Ren, P., Xu, Z., & Gou, X. (2016). Pythagorean fuzzy TODIM approach to multi-criteria decision making. Applied Soft Computing, 42, 246-259.
XXVIII. Rényi, A. (1961). On measures of entropy and information. In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics. The Regents of the University of California.
XXIX. Szmidt, E., & Kacprzyk, J. (2009, July). Analysis of Similarity Measures for Atanassov’s Intuitionistic Fuzzy Sets. In IFSA/EUSFLAT Conf. (pp. 1416-1421).
XXX. Szmidt, E., & Kacprzyk, J. (2000). Distances between intuitionistic fuzzy sets. Fuzzy sets and systems, 114(3), 505-518.
XXXI. Shannon CE, &Weaver,(1949). The Mathematical Theory of Communication. University of Illinois,Urbana, 3–91.
XXXII. Tahani, V. (1977). A conceptual framework for fuzzy query processing—a step toward very intelligent database systems. Information Processing & Management, 13(5), 289-303.
XXXIII. Wu, K. L., & Yang, M. S. (2002). Alternative c-means clustering algorithms. Pattern recognition, 35(10), 2267-2278.
XXXIV. Xiao, F., & Ding, W. (2019). Divergence measure of Pythagorean fuzzy sets and its application in medical diagnosis. Applied Soft Computing, 79, 254-267.
XXXV. Xia, M., Xu, Z., & Liao, H. (2012). Preference relations based on intuitionistic multiplicative information. IEEE Transactions on Fuzzy Systems, 21(1), 113-133.
XXXVI. Xu, Z. (2007). Intuitionistic preference relations and their application in group decision making. Information sciences, 177(11), 2363-2379.
XXXVII. Yang, M. S., & Hussain, Z. (2018). Fuzzy entropy for pythagorean fuzzy sets with application to multicriterion decision making. Complexity, 2018.
XXXVIII. Yager, R. R. (2013). Pythagorean membership grades in multicriteria decision making. IEEE Transactions on Fuzzy Systems, 22(4), 958-965.
XXXIX. Yager, R. R., & Abbasov, A. M. (2013). Pythagorean membership grades, complex numbers, and decision making. International Journal of Intelligent Systems, 28(5), 436-452.
XL. Yager, R. R. (2013, June). Pythagorean fuzzy subsets. In 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS) (pp. 57-61). IEEE.
XLI. Yang, M. S., & Wu, K. L. (2004). A similarity-based robust clustering method. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(4), 434-448.
XLII. Zhou, Q., Mo, H., & Deng, Y. (2020). A new divergence measure of pythagorean fuzzy sets based on belief function and its application in medical diagnosis. Mathematics, 8(1), 142.
XLIII. Zhang, X. (2016). A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. International Journal of Intelligent Systems, 31(6), 593-611.
XLIV. Zhang, S. F., & Liu, S. Y. (2011). A GRA-based intuitionistic fuzzy multi-criteria group decision making method for personnel selection. Expert Systems with Applications, 38(9), 11401-11405.
XLV. Zadeh, L. A. (1971). Similarity relations and fuzzy orderings. Information sciences, 3(2), 177-200.
XLVI. Zadeh LA, (1965). Fuzzy sets. Information and Control, 8,338–353.