This text is a further elaboration of the previous research report [5]. Graded properties of binary and unary connectives valued in MTL4-algebras are studied in the framework of Fuzzy Class Theory (or higher-order fuzzy logic) FCT, which serves as a tool for easy derivation of graded theorems. The properties studied include graded monotonicity, a generalized Lipschitz property, commutativity, a...

The drainage pattern of a river network is the arrangement in which a stream erodes the channels of its network of tributaries. It can reflect the geographical characteristics of a river network to a certain extent, because it depends on the topography and geology of the land. Whether in cartography or GIS, hydrography is one of the most important feature classes to generalise in order to produ...

Ever since the first hybrid fuzzy rough set model was proposed in the early 1990?s, many researchers have focused on the definition of the lower and upper approximation of a fuzzy set by means of a fuzzy relation. In this paper, we review those proposals which generalize the logical connectives and quantifiers present in the rough set approximations by means of corresponding fuzzy logic operati...

As a natural generalization of a measure space, Butnariu and Klement introduced T-tribes of fuzzy sets with T-measures. They gave a complete characterization of T-measures for a Frank triangular norm T. Here we characterize T-measures with respect to non-Frank strict triangular norms. We show the speciic roles of Frank triangular norms and a newly introduced family, nearly Frank triangular norm...

Logical connectives on fuzzy sets arise from those on the unit interval. The basic theory of these connectives is cast in an algebraic spirit with an emphasis on equivalence between the various systems that arise. Special attention is given to De Morgan systems with strict Archimedean t-norms and strong negations. A typical result is that any De Morgan system with strict t-norm and strong negat...

In Abstract Algebraic Logic the general study of propositional non-classical logics has been traditionally based on the abstraction of the Lindenbaum-Tarski process. In this kind of process one considers the Leibniz relation of indiscernible, i.e. logically equivalent, formulae. Such approach has resulted in a classification of logics partly based on generalizations of equivalence connectives: ...

Interval-valued fuzzy set theory is an increasingly popular extension of fuzzy set theory where traditional [0, 1]-valued membership degrees are replaced by intervals in [0, 1] that approximate the (unknown) membership degrees. To construct suitable graded logical connectives in this extended setting, it is both natural and appropriate to “reuse” ingredients from classical fuzzy set theory. In ...

We study some boolean-like laws with iterative variables in Fuzzy Logic. We show that beyond the classical De Morgan triplets of connectives described by t-norms, t-conorms and strong negations there are interesting models with infinite solutions and surprising situations where there are none.

While traditional algorithms concern positive associations between binary or quantitative attributes of databases, this paper focuses on mining both positive and negative fuzzy association rules. We show how, by a deliberate choice of fuzzy logic connectives, significantly increased expressivity is available at little extra cost. In particular, rule quality measures for negative rules can be co...

The problem of representing intersection and union in fuzzy set theory is considered. There are various proposals in the literature to model these concepts. The possibility of using continuous triangular norms and conorms (including min and max) are taken up in a measurement–theoretic setting. The conditions are laid out to arrive at cardinal scales on which addition and multiplication are mean...