A Novel Method of Decision-making Based on Intuitionistic Fuzzy Set Theory
Keywords: Intuitionistic fuzzy sets, Modal operators, Measure of similarity, Decision making, Optimal solution. ,
Abstract :
Atanassov's intuitionistic fuzzy set is more adept at representing and managing uncertainty. Within intuitionistic fuzzy set theory, intuitionistic fuzzy measure is a significant field of study. In order to address decision making, we present a novel similarity metric between intuitionistic fuzzy sets in this study. First, based on the minimum and maximum levels of similarity, we suggest a new similarity metric between intuitionistic fuzzy values. It is capable of overcoming the limitations of current approaches to gauging the degree of resemblance between fuzzy intuitionistic sets. It is also possible to show some aspects of the suggested similarity measure between intuitionistic fuzzy sets by taking into account the modal operators and their different extensions. Finally, we apply the proposed similarity measure between intuitionistic fuzzy sets to deal with a real life problem. The suggested action can provide a precise outcome. The application section examines a real-world issue of choosing the best course of action among n options based on m criteria. A fictitious case study is created along with the method's algorithm.
[1] Anum MT, Zhang H, Ejegwa PA, Feng Y. Tendency coefficient-based weighted distance measure for intuitionistic fuzzy sets with applications. In: 2024 12th Int. Conf. on Intelligent Control and Information Processing (ICICIP). 2024. p.54-61. DOI: https://10.1109/ICICIP60808.2024.10477789
[2] Atanassov KT. Intuitionistic fuzzy sets. Int. J. Bioautomation, 2016, 20(S1), S1-S6.
[3] 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
[4] Atanassov KT. New operations defined over Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 1994; 61(2): 137-142. DOI: https://doi.org/10.1016/0165-0114(94)90229-1
[5] Atanassov KT. Some operators in Intuitionistic fuzzy sets. First Int. Conf. on IFS, Sofia, NIFS. 1997; 3(4): 28-33. http://ifigenia.org/wiki/issue:nifs/3/4/28-33
[6] Atanassov KT. Type-1 fuzzy sets and intuitionistic fuzzy sets. Algorithms. 2017; 10(3): 106. DOI: https://doi.org/10.3390/a10030106
[7] Bhattacharya J. A few more on Intuitionistic fuzzy set. Journal of Fuzzy set Valued Analysis. 2016; 3: 214-222. DOI: https://doi:10.5899/2016/jfsva-00322
[8] Bhattacharya J. Some special operations and related results on Intuitionistic fuzzy sets. International Journal of Scientific Research in Mathematical and Statistical Sciences. 2021; 8(4): 10-13. DOI: https://doi.org/10.26438/ijsrmss/v8i4.1013
[9] Bhattacharya J. Some results on certain properties of Intuitionistic fuzzy sets. Journal of Fuzzy Extension and Applications. 2021; 2(4): 377-387. DOI: https://doi.org/10.22105/jfea.2021.290202.1155
[10] Chen SM. A new approach to handling fuzzy decision making problems. IEEE Transactions on Systems, Man, and Cybernetics. 1988; 18(6): 1012-1016. DOI: https://doi.org/10.1109/21.23100
[11] Citil M, Tugrul F. Some new equalities on the intuitionistic fuzzy modal operators. Sakarya University Journal of Science. 2018; 22(6): 1524-1531. DOI: https://doi.org/10.16984/saufenbilder.338899
[12] De SK, Biswas R, Roy AR. Multicriteria decision making using intuitionistic fuzzy set theory. The Journal of Fuzzy Mathematics. 1998; 6(4): 837-842.
[13] Dencheva K. Extension of intuitionistic fuzzy modal operators ⊞ and ⊠. Proceedings of the Second Int. IEEE Symposium: Intelligent Systems, Varna. 2004; (3): 21-22. DOI: http://dx.doi.org/10.1109/IS.2004.1344843
[14] Dengfeng L, Chuntian C. New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recognition Letters. 2002; 23(1-3): 221225. DOI: https://doi.org/10.1016/S0167- 8655(01)00110-6
[15] Ejegwa PA, Akowe SO, Otene PM, Ikyule JM. An overview on intuitionistic fuzzy sets. Int. Journal of Scientific and Technology Research. 2014; 3(3): 142-145.
[16] Ejegwa PA, Anum MT, Isife KI. A new method of distance measure between intuitionistic fuzzy sets and its applications in admission procedure. Journal of Uncertain Systems. 2024; 17(2): 2440005. DOI: https://doi.org/10.1142/S1752890924400051
[17] Ejegwa PA, Kausar N, Agba JA, Ugwuh F, Ozbilge E, Ozbilge E. Determination of medical emergency via new intuitionistic fuzzy correlation measures based on Spearman’s correlation coefficient. AIMS Mathematics. 2024; 9(6): 15639-15670. DOI: https://doi.org/10.3934/math.2024755
[18] Ejegwa PA, Onyeke IC. Medical diagnostic analysis on some selected patients based on modified Thao et. al.’s correlation coefficient of intuitionistic fuzzy sets via an algorithmic approach. Journal of Fuzzy Extension and Applications. 2020; 1(2): 122-132. DOI: https://doi.org/10.22105/jfea.2020.250108.1014
[19] Eker E, Tagrul F, Citil M. New equalities on the intuitionistic fuzzy operators and operations. Notes on Intuitionistic Fuzzy Sets. 2015; 21(4): 124-128.
[20] Grzegorzewski P. Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets and Systems. 2004; 148(2): 319-328. DOI: https://doi.org/10.1016/j.fss.2003.08.005
[21] Hung WL, Yang MS. Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recognition Letters. 2004; 25(14): 1603-1611. DOI: https://doi.org/10.1016/j.patrec.2004.06.006
[22] Kozae AM, Elshenawy A, Omran M. Intuitionistic fuzzy set and its Application in selecting specialization: a case study for engineering students. Int. Journal of Mathematical Analysis and Applications. 2015; 2(6): 74-78.
[23] Li J, Deng G, Li H, Zeng W. The relationship between similarity measure and entropy of intuitionistic fuzzy sets. Information Sciences. 2012; 188: 314-321. DOI: https://doi.org/10.1016/j.ins.2011.11.021
[24] Nwokoro CO, Inyang UG, Eyoh IJ, Ejegwa PA. Intuitionistic fuzzy approach for predicting maternal outcomes. Fuzzy Optimization, Decision-making and Operations Research. 2023; 399-421. DOI:
http://dx.doi.org/10.1007/978-3-031-35668-1-18
[25] Song Y, Wang X, Lei L, Xue A. A new similarity measure between intuitionistic fuzzy sets and its application to pattern recognition. Abstract and Applied Analysis. 2014; 2014(1):1-11. DOI: https://doi.org/10.1155/2014/384241
[26] Szmidt E, Kacprzyk J. Intuitionistic fuzzy sets in group decision making. Notes on Intuitionistic Fuzzy Sets. 1996; 2(1): 11-14.
[27] Szmidt E, Kacprzyk J. Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems. 2000; 114(3): 505-518. DOI: https://doi.org/10.1016/S0165-0114(98)00244-9
[28] Tarsuslu S, Citil M, Dimirbas E, Aydin M. Some modal operators with intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets. 2017; 23(5): 20-28.
[29] Xia M, Xu Z. Some new similarity measures for intuitionistic fuzzy values and their application in group decision making. Journal of Systems Science and Systems Engineering. 2010; 19(4): 430-452. DOI:
https://doi.org/10.1007/s11518-010-5151-9
[30] Xu ZS, Chen J. An overview of distance and similarity measures of intuitionistic fuzzy sets. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems. 2008; 16(04): 529-555. DOI: https://doi.org/10.1142/S0218488508005406
[31] Xu ZS, Yager RR. Intuitionistic and interval-valued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optimization and Decision Making. 2009; 8: 123-139. DOI: https://doi.org/10.1007/s10700-009-9056-3
[32] Ye J. Cosine similarity measures for intuitionistic fuzzy sets and their applications. Mathematical and Computer Modelling. 2011; 53(1-2): 91-97. DOI: https://doi.org/10.1016/j.mcm.2010.07.022
[33] Zadeh LA. Fuzzy sets . Information and Control. 2018; 8: 338-353. DOI: https://doi.org/10.1016/S0019- 9958(65)90241-X
[34] Zeng W, Guo P. Normalized distance, similarity measure, inclusion measure and entropy of intervalvalued fuzzy sets and their relationship. Information Sciences. 2008; 178(5): 1334-1342. DOI: https://doi.org/10.1016/j.ins.2007.10.007
[35] Zhang H, Yu L. New distance measures between intuitionistic fuzzy sets and interval-valued fuzzy sets. Information Sciences. 2013; 245: 181-196. DOI: https://doi.org/10.1016/j.ins.2013.04.040
[36] Zhou Y, Ejegwa PA, Johney SE. Generalized similarity operator for intuitionistic fuzzy sets and its applications based on recognition principle and multiple criteria decision making technique. International Journal of Computational Intelligence Systems. 2023; 16(1): 85. DOI: https://doi.org/10.1007/s44196- 023-00245-2
