Volume 5 , Issue 1 , PP: 52-58, 2023 | Cite this article as | XML | Html | PDF | Full Length Article
Pritpal Singh 1 *
Doi: https://doi.org/10.54216/JNFS.050106
Recently, precise measurement of uncertainty of data with fuzzy attributes is considered as one of the main problems. For this purpose, fuzzy sets, intuitionistic fuzzy sets, and neutrosophic set theory are extensively introduced. The problem arises in computing the complement of true or false membership values in the case of indeterminacy. Instead of indeterminacy as discussed in neutrosophic set theory, it can be completely true, partially true, or partially false. To deal with this, the theory of ambiguous sets has recently been introduced. A real-time example of dealing with unconsciousness and ambiguousness in relation to human perception is discussed, illustrating the motivation of the ambiguous set theory. Finally, this study focuses on the definition of the ambiguous set, its mathematical representation, and the associated concepts.
Fuzzy set , intuitionistic fuzzy set , neutrosophic set , turiyam set , ambiguous set , unconsciousness , uncertainty.
[1] Zadeh, L. A., Fuzzy sets. Information and Control 8(3), 338–353, 1965.
[2] Atanassov, K. T., Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20, 87–96, 1986.
[3] Smarandache, F., A unifying field in logics. Neutrosophy: neutrosophic probability, set and logic. American Research Press, Rehoboth, 1999.
[4] Singh, P, Huang, Y. P., & Lee, T. T., A novel ambiguous set theory to represent uncertainty and its application to brain MR image segmentation. In: Proc. of IEEE Int. Conf. on Systems, Man and Cybernetics (SMC), Bari, Italy, 2460–2465, 2019.
[5] Singh, P., & Bose, S. S., Ambiguous D-means fusion clustering algorithm based on the ambiguous set theory: Special application in clustering of CT scan images of COVID -19. Knowledge-Based Systems, 231, 107432, 2021.
[6] Singh, P., & and Huang, Y.-P., Membership functions, set-theoretic operations, distance measurement methods based on ambiguous set theory: A solution to a decision-making problem in selecting the appropriate colleges. International Journal of Fuzzy Systems, In Press, 2023.
[7] Singh, P. K., Data with turiyam set for fourth dimension quantum information processing. Journal of Neutrosophic and Fuzzy Systems, 1, 9–23, 2021.
[8] Singh, P. K., Quaternion set for dealing fluctuation in quantum turiyam cognition. Journal of Neutrosophic and Fuzzy Systems, 4(02), 57–64, 2022.
[9] Singh, P. K., Four-way turiyam set-based human quantum cognition analysis. Journal of Artificial Intelligence and Technology, 2(4), 144–151, 2022.
[10] Smarandache, F., Introduction to the symbolic plithogenic algebraic structures (revisited). Neutrosophic Set and System, 53, 653–665, 2023.
