On the Relation between Fuzzy Preorders, Fuzzy Closing Morphological Operators and Fuzzy Consequence Operators
نویسندگان
چکیده
In a previous paper [10] we explored the notion of coherent fuzzy consequence operator. It is well-known that the operator induced by a fuzzy preorder through Zadeh’s compositional rule is always a coherent fuzzy consequence operator. It is also known that the relation induced by a fuzzy consequence operator is a fuzzy preorder if such operator is coherent [7]. Fuzzy closing operators of mathematical morphology can be considered as fuzzy consequence operators. In [12] we showed that they are coherent operators. The aim of this paper is to analyze the relations between both classes of operators and the class of all fuzzy preorders in order to translate well know properties from Approximate Reasoning to the one of Image Processing.
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