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RO-implications on finite scales
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DOI：10.1016/j.ijar.2023.108921.png)
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Abstract
En 中文
Fuzzy implications, as a kind of fuzzy logical connectives, play an important role both in the theory and applications involving fuzzy sets and systems. Accordingly, the theoretical study of various fuzzy implications generated by common aggregation operators has become an attractive topic, especially on finite scales. In this paper, we analyse residual implications induced from discrete overlap functions latest proposed by the author, which belong to the category of discrete implications. Explicitly, in the beginning, we present the definition of residual implications generated by discrete overlap functions O and call them RO-implications. In the next place, we analyse a number of elementary properties of RO-implications. Most of all, it proves that RO-implications satisfy most of algebraic properties of discrete implications spontaneously, such as the left neutrality property, identity principle, ordering property, etc., which are different from the circumstance on other truth values sets. At last, via RO-implications, we reveal correlations of discrete implications and discrete quasi-overlap functions extended from discrete overlap functions.& COPY; 2023 Elsevier Inc. All rights reserved.
Keywords:
Fuzzy logic
Discrete implication
R O -implication
Discrete overlap function
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