This paper continues our study in fuzzy interval logic based on the Checklist Paradigm(CP) semantics of Bandler and Kohout. We investigate the fuzzy interval system of negation which was defined by the Sheffer(NAND), the Nicod(NOR) and the implication connectives of m1 interval system in depth. The top-bottom(TOPBOT) pair of fuzzy negation interval shows non-involutive property; however, it sho...

Information to be stored in databases is often fuzzy. Two important issues in research in this field are the representation of fuzzy information in a database and the provision of flexibility in database querying, especially via including linguistic terms in human-oriented queries and returning results with matching degrees. Fuzzy linguistic logic programming (FLLP), where truth values are ling...

Fuzzy logic programming is a growing declarative paradigm aiming to integrate fuzzy logic into logic programming. One of the most di cult tasks when specifying a fuzzy logic program is determining the right weights for each rule, as well as the most appropriate fuzzy connectives and operators. In this paper, we introduce a symbolic extension of fuzzy logic programs in which some of these parame...

This paper develops a category-theoretic approach to uncertainty and decision-making problems. It is based on appropriate rst order fuzzy logic in which not only logical connectives but also quantiiers have fuzzy interpretation. It is shown that all fundamental concepts of probability and statistics such as joint distribution, conditional distribution, etc., have meaningful analogs in new conte...

Fuzzy logic programming is a growing declarative paradigm aiming to integrate fuzzy logic into logic programming. One of the most difficult tasks when specifying a fuzzy logic program is determining the right weights for each rule, as well as the most appropriate fuzzy connectives and operators. In this paper, we introduce a symbolic extension of fuzzy logic programs in which some of these para...

Fuzzy implications are one of the most important fuzzy logic connectives. In this work, we conduct a systematic algebraic study on the set I of all fuzzy implications. To this end, we propose a binary operation, denoted by ~, which makes (I,~) a non-idempotent monoid. While this operation does not give a group structure, we determine the largest subgroup S of this monoid and using their represe...

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...

The starting point of this paper are the works of Hájek and Vychodil on the axiomatization of truthstressing and -depressing hedges as expansions of Hájek’s BL logic by new unary connectives. They showed that their logics are chain-complete, but standard completeness was only proved for the expansions over Gödel logic. We propose weaker axiomatizations over an arbitrary core fuzzy logic which h...

The study of linearly compensated hybrid connectives H = λC +(1−λ)C̄, where C is a t-norm and C̄ represents the dual connective of C, to define aggregation operators for fuzzy classifications is a key point not only in fuzzy sets theory but also in learning processes. Although these operators are not associative, the fact that they can be decomposed into associative functions easily gives rise to...

The starting point of this paper are the works of Hájek and Vychodil on the axiomatization of truth-stressing and depressing hedges as expansions of Hájek's BL logic by new unary connectives. They showed that their logics are chain-complete, but standard completeness was only proved for the expansions over Gödel logic. We propose weaker axiomatizations over an arbitrary core fuzzy logic which h...