We are interested in generalizations of the concepts of t-norm and t-conorm. In a companion chapter in this volume [14] we have presented a family of hypert-norms ∧q and a family of hyper-t-conorms ∨p. The prefix hyper is used to indicate multi-valued operations, also known as hyperoperations (see [5, 14]), i.e. operations which map pairs of elements to sets of elements. See [14] for the constr...

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 ...

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 process one considers the Leibniz relation of indiscernible formulae. Such approach has resulted in a classification of logics partly based on generalizations of equivalence connectives: the Leibniz hierarchy. This paper p...

Abstract This paper provides the first cross-linguistic study on non-exhaustive connectives. After defining non-exhaustivity and briefly exploring range of linguistic strategies encoding it across languages, methodology underlying will be discussed. Based analysis 35 for which at least one connective was found, argued that connectives exhibit quite homogenous distributional properties derive fr...

Interpretation of outputs of fuzzy systems often involves the use of linguistic approximation that assigns a linguistic label to a fuzzy set based on the predefined primary terms, linguistic modifiers and linguistic connectives. More formally linguistic approximation can be considered in the terms of retranslation rules that correspond to the translation rules in explicitation in computing with...

Over the last decade or so, significant advances have been made in two distinct technological areas: fuzzy logic and computational neutral networks. The theory of fuzzy logic provides a mathematical framework to capture the uncertainties associated with human cognitive processes, such as thinking and reasoning. Also, it provides a mathematical morphology to emulate certain perceptual and lingui...

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...

Keywords: mathematical fuzzy logic, basic fuzzy logic, monoidal t-norm logic, hoop logic, non-commutative fuzzy logic. This paper is a companion to my [12]. The latter is a rather technical paper developing a generalized (mathematical) fuzzy logic. Main definitions and results of [12] are reproduced here without any proofs; but this is preceded by a survey on the basic proposi-tional fuzzy logi...

The paper introduces fuzzy linguistic logic programming, which is a combination of fuzzy logic programming, introduced by P. Vojtáš, and hedge algebras in order to facilitate the representation and reasoning on human knowledge expressed in natural languages. In fuzzy linguistic logic programming, truth values are linguistic ones, e.g., VeryTrue, VeryProbablyTrue, and LittleFalse, taken from a h...