Eloy Renedo

AN OVERVIEW ON THE CONSTRUCTION OF FUZZY SET THEORIES

This paper analyzes the main issues involved in the construction of Fuzzy Set Theories. It reviews both standard solutions (based on the well-known triangular norms and conorms) as well as less the conventional proposals that provide alternative views on, for example, the definition of fuzzy connectives or the study of their properties.

On Fuzzy Set Theories

This paper analyzes some of the main issues involved in the construction of fuzzy set theories. It reviews both standard solutions (based on the well-known t-norms and t-conorms), as well as less conventional proposals that provide alternative views on, e.g. the definition of fuzzy connectives and the study of their properties.

On the law (a·b')'=b+a'·b' in de Morgan algebras and orthomodular lattices

This papers goal is to prove that the only de Morgan algebras and the only orthomodular lattices in which the law (a·b′)′=b+a′·b′, posed by Charles Elkan in [1] holds, are those that are boolean algebras. That is, that among both families of de Morgan algebras and orthomodular lattices, Elkans formula is only characteristic of boolean algebras.

On a new theory of fuzzy sets with just one self-contradiction

To avoid self-contradictions in fuzzy set theory, it is needed to consider only fuzzy sets that are not self-contradictory and whose complements are also not self-contradictory. This paper deals with a subset F/sub nc/(E) in [0,1]/sup E/, where the above conditions are satisfied. A particular fuzzy set theory is defined in F/sub nc/(E) with adequate logical connectives. Finally, which classical properties hold in the new theory is studied.

ON SOME SCHEMES OF REASONING IN FUZZY LOGIC

This paper deals with the validity in fuzzy logic of some classical schemes of reasoning, namely, with those of disjunctive reasoning, resolution, reductio ad absurdum, and the so-called constructive dilemma.

A First Inquiry on Semantic-Based Models of And

Language is basically the system used by humans for communication and covers a wide range of their activities. It is a social phenomenon resulting in an evolving system of great complexity. Language is inextricably linked to knowledge communication and representation, and is viewed here as a complex reality to be mathematically represented step by step, in a incremental fashion.

Studying Fuzzy Modus Ponens

This paper investigates the relations between implication functions, modus ponens and conjunctions. For that purpose, a review of fuzzy modus ponens is done, that takes into account the different worlds involved in the inference. This leads to consider two new modalities of that rule, the modus intusconiugando ponens and the modus forisconjugando ponens from which internal and external conjunctive conditional relations respectively follows. In addition, given such formulation, the modus ponens inequalities can be studied

Classes of T-conditionals and fuzzy inference

This paper deals with some properties of the functions Jthetav = thetav-1 middot J middot (thetav times thetav) introduces in (M. Baczynski and J. Drewniak, 1999), with thetav an order-automorphism of the unit interval, and J either a T-conditional or implication functions

Fuzzy Sets Versus Language

This paper just tries to stimulate some reflection to extend the current theories of fuzzy sets to wider areas of language, with the objective of reaching a better knowledge of the links between language and its representation by means of fuzzy sets, when possible. This for the progress of computing with words that, sooner or later, will pose the theoretically challenging, and practically important, problem of the linguistic credit, or soundness in language, of the theories of fuzzy sets. A problem that fuzzy logic cannot avoid to become a basic representation’s tool for computing with words. To this end, the strategy of reconsidering the current knowledge of fuzzy sets theories does not seem far from scope.