Document Type : Research Paper
Authors
1 Department of Mathematical Sciences, University of Peloponnese, Graduate TEI of Western Greece, Greece.
2 University Hassan II, Casablanca, Morocco.
Abstract
The Intuitionistic Fuzzy Sets (IFSs) are generalizations of Zadeh’s fuzzy sets, in which the elements of the universe have apart from Zadeh’s membership and the degree of non-membership in [0, 1]. This paper studies applications of intuitionistic Fuzzy Sets (FS) to assessment and multi-criteria decision making, which are very useful when uncertainty characterizes the grades or parameters respectively assigned to the elements of the universal set. Applications to everyday life situations are also presented illustrating our results.
Keywords
Main Subjects
[1] Voskoglou, M. G. (2019). Methods for assessing human–machine performance under fuzzy conditions. Mathematics, 7(3). https://www.mdpi.com/2227-7390/7/3/230
[2] Berger, J. (2013). Statistical decision theory: foundations, concepts, and methods. Springer New York. https://www.google.com/books/edition/Statistical_Decision_Theory/TT_jBwAAQBAJ?hl=en&gbpv=0
[3] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353.
[4] Bellman, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management science, 17(4), 1–141. https://doi.org/10.1287/mnsc.17.4.B141
[5] Carlos R. Alcantud, J. (2017). Fuzzy techniques for decision making. Symmetry. https://www.mdpi.com/2073-8994/10/1/6/pdf
[6] Zhu, B., & Ren, P. (2022). Type-2 fuzzy numbers made simple in decision making. Fuzzy optimization and decision making, 21(2), 175–195. https://doi.org/10.1007/s10700-021-09363-y
[7] Voskoglou, M. G. (2023). An application of neutrosophic sets to decision making. https://arxiv.org/abs/2306.01746
[8] Garg, H. (2024). A new exponential-logarithm-based single-valued neutrosophic set and their applications. Expert systems with applications, 238, 121854. https://doi.org/10.1016/j.eswa.2023.121854
[9] Edalatpanah, S. A., Hassani, F. S., Smarandache, F., Sorourkhah, A., Pamucar, D., & Cui, B. (2024). A hybrid time series forecasting method based on neutrosophic logic with applications in financial issues. Engineering applications of artificial intelligence, 129. https://www.sciencedirect.com/science/article/pii/S0952197623017153
[10] Martin, N., & Edalatpanah, S. A. (2023). Application of extended fuzzy ISOCOV methodology in nanomaterial selection based on performance measures. Journal of operational and strategic analytics, 1, 55–61. https://www.researchgate.net/profile/S-A-Edalatpanah-
[11] Stanimirović, P. S., Ivanov, B., Stanujkić, D., Katsikis, V. N., Mourtas, S. D., Kazakovtsev, L. A., & Edalatpanah, S. A. (2023). Improvement of unconstrained optimization methods based on symmetry involved in neutrosophy. Symmetry, 15(1). https://www.mdpi.com/2073-8994/15/1/250
[12] Veeramani, C., Edalatpanah, S. A., & Sharanya, S. (2021). Solving the multiobjective fractional transportation problem through the neutrosophic goal programming approach. Discrete dynamics in nature and society, 2021, 7308042. https://doi.org/10.1155/2021/7308042
[13] Akram, M., Ullah, I., Allahviranloo, T., & Edalatpanah, S. A. (2021). Fully Pythagorean fuzzy linear programming problems with equality constraints. Computational and applied mathematics, 40(4), 120. https://doi.org/10.1007/s40314-021-01503-9
[14] Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy sets and systems, 20(1), 87–96.
[15] Atanassov, K. T. (1999). Intuitionistic fuzzy sets. In Intuitionistic fuzzy sets: theory and applications (pp. 1–137). Heidelberg: Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-1870-3_1
[16] Garg, H., Ünver, M., Olgun, M., & Türkarslan, E. (2023). An extended EDAS method with circular intuitionistic fuzzy value features and its application to multi-criteria decision-making process. Artificial intelligence review, 56(3), 3173–3204. https://doi.org/10.1007/s10462-023-10601-5
[17] Hussain, A., Wang, H., Garg, H., & Ullah, K. (2023). An approach to multi-attribute decision making based on intuitionistic fuzzy rough aczel-alsina aggregation operators. Journal of king saud university - science, 35(6). https://www.sciencedirect.com/science/article/pii/S1018364723002227
[18] Ali, A., Ullah, K., & Hussain, A. (2023). An approach to multi-attribute decision-making based on intuitionistic fuzzy soft information and aczel-alsina operational laws. Journal of decision analytics and intelligent computing, 3(1), 80–89. https://www.jdaic-journal.org/index.php/about/article/view/28
[19] Maji, P. K., Roy, A. R., & Biswas, R. (2002). An application of soft sets in a decision making problem. Computers & mathematics with applications, 44(8–9), 1077–1083.
[20] Molodtsov, D. (1999). Soft set theory—first results. Computers & mathematics with applications, 37(4), 19–31. https://www.sciencedirect.com/science/article/pii/S0898122199000565
[21] Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy sets and systems, 1(1), 3–28. https://www.sciencedirect.com/science/article/pii/0165011478900295
[22] Klir, G. J., & Folger, T. A. (1987). Fuzzy sets, uncertainty, and information. Prentice-Hall, Inc.
[23] Ejegwa, P. A., Akubo, A. J., & Joshua, O. M. (2014). Intuitionistic fuzzy set and its application in career determination via normalized Euclidean distance method. European scientific journal, 10(15). https://core.ac.uk/download/pdf/328024322.pdf
[24] Annamalai, C. (2022). Intuitionistic fuzzy sets: new approach and applications. https://osf.io/94y2p/download
[25] Szmidt, E., & Kacprzyk, J. (1996). Intuitionistic fuzzy sets in group decision making. Notes on IFS, 2(1). http://ifigenia.org/wiki/issue:nifs/2/1/15-32
[26] Szmidt, E., & Kacprzyk, J. (1996). Remarks on some applications of intuitionistic fuzzy sets in decision making. Note on IFS, 2. http://ifigenia.org/wiki/issue:nifs/2/3/22-31
[27] De, S. K., Biswas, R., & Roy, A. R. (2001). An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy sets and systems, 117(2), 209–213.
[28] Szmidt, E., & Kacprzyk, J. (2001). Intuitionistic fuzzy sets in some medical applications. Computational intelligence. theory and applications (pp. 148–151). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-45493-4_19
[29] Davvaz, B., & Hassani Sadrabadi, E. (2016). An application of intuitionistic fuzzy sets in medicine. International journal of biomathematics, 9(3). https://doi.org/10.1142/S1793524516500376
[30] Kozae, A. M., Shokry, M., & Omran, M. (2020). Intuitionistic fuzzy set and its application in corona covid-19. Applied and computational mathematics, 9(5), 146–154.
[31] Atanassov, K. T., & Gargov, G. (2017). Intuitionistic fuzzy logics. Springer.
[32] Atanassov, K., & Georgiev, C. (1993). Intuitionistic fuzzy prolog. Fuzzy sets and systems, 53(2), 121–128. https://www.sciencedirect.com/science/article/pii/016501149390166F
[33] Meena, K., & Thomas, K. V. (2018). An application of intuitionistic fuzzy sets in choice of discipline of study. Global journal pure applied mathemathical, 14(6), 867–871.
[34] Dubois, D., & Prade, H. (2005). Interval-valued fuzzy sets, possibility theory and imprecise probability. EUSFLAT conference (pp. 314–319). EUSFLAT - LFA.
[35] Pawlak, Z. (1991). Rough sets: theoretical aspects of reasoning about data. Springer Netherlands.
[36] Ju-Long, D. (1982). Control problems of grey systems. Systems & control letters, 1(5), 288–294.
[37] Maji, P. K., Biswas, R., & Roy, A. R. (2003). Soft set theory. Computers & mathematics with applications, 45(4), 555–562. https://www.sciencedirect.com/science/article/pii/S0898122103000166
[38] Mohammadzadeh, A., Sabzalian, M. H., & Zhang, W. (2020). An interval type-3 fuzzy system and a new online fractional-order learning algorithm: theory and practice. IEEE transactions on fuzzy systems, 28(9), 1940–1950. DOI:10.1109/TFUZZ.2019.2928509
[39] Voskoglou, M. G. (2022). Fuzziness, indeterminacy and soft sets: frontiers and perspectives. Mathematics, 10(20). https://www.mdpi.com/2227-7390/10/20/3909
[40] Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning—I. Information sciences, 8(3), 199–249. https://www.sciencedirect.com/science/article/pii/0020025575900365
[41] Mohammadzadeh, A., Zhang, C., Alattas, K. A., El-Sousy, F. F. M., & Vu, M. T. (2023). Fourier-based type-2 fuzzy neural network: Simple and effective for high dimensional problems. Neurocomputing, 547, 126316. https://doi.org/10.1016/j.neucom.2023.126316
[42] Cao, Y., Raise, A., Mohammadzadeh, A., Rathinasamy, S., Band, S. S., & Mosavi, A. (2021). Deep learned recurrent type-3 fuzzy system: application for renewable energy modeling/prediction. Energy reports, 7, 8115–8127. https://www.sciencedirect.com/science/article/pii/S2352484721004686
[43] Dan, S., Kar, M. B., Majumder, S., Roy, B., Kar, S., & Pamucar, D. (2019). Intuitionistic type-2 fuzzy set and its properties. Symmetry, 11(6). https://www.mdpi.com/2073-8994/11/6/808
[44] Castillo, O., & Melin, P. (2022). Towards interval type-3 intuitionistic fuzzy sets and systems. Mathematics, 10(21). https://www.mdpi.com/2227-7390/10/21/4091
[45] Castillo, O., Castro, J. R., & Melin, P. (2022). Interval type-3 fuzzy control for automated tuning of image quality in televisions. Axioms, 11(6). https://www.mdpi.com/2075-1680/11/6/276
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