Abstract
There have been a few works studying metrics obtained from fuzzy logic connectives such as t-norms and copulas which are either commutative, monotonically increasing, or associative. In this work, we define a distance function generated from a non-associative, non-commutative, and non-monotonic fuzzy logic connective, viz., a fuzzy implication. We consider fuzzy implication as a relation on [0, 1] and give a way to obtain metrics from \(S_\textbf{LK}\)- transitive relations that turn out to be monometrics w.r.t. the betweenness relation obtained from the underlying total order on [0, 1]. We also give some sufficient conditions under which certain families of fuzzy implications yield a metric. Our study, on the one hand highlights the usefulness of S-transitive fuzzy relations as much as T-transitive fuzzy relations, and on the other hand, illustrates emphatically the need for fuzzy logic operations on non-linear posets.
Supported by SERB under the project MTR/2020/000506.
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Nanavati, K., Gupta, M., Jayaram, B. (2024). Metrics from Fuzzy Implications and Their Application. In: Ghosh, A., King, I., Bhattacharyya, M., Sankar Ray, S., K. Pal, S. (eds) Pattern Recognition and Machine Intelligence. PReMI 2021. Lecture Notes in Computer Science, vol 13102. Springer, Cham. https://doi.org/10.1007/978-3-031-12700-7_30
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DOI: https://doi.org/10.1007/978-3-031-12700-7_30
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