The validation set of a formula in a fuzzy logic is the set of all truth values which this formula may achieve. We summarize characterizations of validation sets of -fuzzy logics and extend them to the case of -fuzzy logics.
The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized...
In this article I show how to obtain a powerful and truthful explanation of the failure of sorites arguments combining an adaptation of the Wide Set Theory formulated by Formato and Gerla and the concept of deep many valuedness established by Marraud. It is shown that if the premises of a sorites argument are conceived as a succession of indexed consequence operators (where indices express the accuracy of the inferences) prefixing sentences, the argument fails because the transitive property for...
Recently, Yager in the article “On some new classes of implication operators and their role in approximate reasoning” [Yager2004] has introduced two new classes of fuzzy implications called the -generated and -generated implications. Along similar lines, one of us has proposed another class of fuzzy implications called the -generated implications. In this article we discuss in detail some properties of the above mentioned classes of fuzzy implications and we describe their relationships amongst...