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...

This paper is a reply to Laviolette and Seaman’s critical discussion of fuzzy set theory. Rather than questioning the interest of the Bayesian approach to uncertainty, some reasons why Bayesian find the idea of a fuzzy set not palatable are laid bare. Some links between fuzzy sets and probability that Laviolette and Seaman seem not to be aware of are pointed out. These links suggest that, contr...

In this paper a self-learning classification method, able to deal with both qualitative and quantitative data, will be presented. This technique presents important advantages with respect to classical approaches, both numerical and symbolical ones : it is faster, less memory demanding, performs a sequential treatment and can carry out both supervised (non-iterative) and unsupervised learning . ...

The problem of deriving membership functions as a means for describing linguistic variables (for some control process) and the choice of fuzzy inference operators and connectives is at the heart of developing fuzzy control systems. Over the years con-nectionist systems have obtained prominence as a means to solve complicated learning tasks. More recently a surge in interest for applying neural ...

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.

In Gödel fuzzy propositional logic, neither conjunction nor implication is expressible (definable) in terms of the remaining three logical connectives. In classical propositional logic, propositions are associated with two truth values 1 (truth) and 0 (falsity). In fuzzy logics further (intermediate) truth values lying between 0 and 1 are possible. Usually the truth values are linearly ordered ...

In this paper, we further investigate the constructions of fuzzy connectives on a complete lattice. We firstly illustrate the concepts of left (right) semi-uninorms and implications satisfying the order property by means of some examples. Then we give out the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation.

Among various approaches to fuzzy logics, we have chosen two of them, which are built up in a similar way. Although starting from diierent basic logical connectives, they both use interpretations based on Frank t-norms. Diierent interpretations of the implication lead to diierent axiomatizations, but most logics studied here are complete. We compare the properties, advantages and disadvantages ...