Implication operators generating pairs of weak negations and their algebraic structure

Negations operators have been developed and applied in many fields such as image processing, decision making, mathematical morphology, fuzzy logic, etc. One of the most effective non-monotonic operators are weak negations. This paper studies the algebraic structure and the characterization of the adjoint triples and Galois implication pairs which provides a fixed pair of weak negations. The obtained results allow the user to select the best conjunctor and implications associated with the most suitable negation to be used in the computations of the problem to be solved.Partially supported by the State Research Agency (AEI) and the European Regional Development Fund (ERDF) project TIN2016-76653-P, European Cooperation in Science & Technology (COST) Action CA17124

Algebraic structure and characterization of adjoint triples

Implications pairs, adjoint pairs and adjoint triples provide general residuated structures considered in different mathematical theories. In this paper, we carry out a deep study on the operators involved in these structures, showing how they are characterized by means of the irreducible elements of a complete lattice. Moreover, the structure of each class of these operators will be analyzed. As a consequence, the use of these operators in real problems will be more tractable, fostering their consideration as basic and useful operators for providing, for instance, preferences among attributes and objects in a given database.Partially supported by the 2014-2020 ERDF Operational Programme in collaboration with the State Research Agency (AEI) in projects TIN2016-76653-P and PID2019-108991GB-I00, and with the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia in project FEDER-UCA18-108612, and by the European Cooperation in Science & Technology (COST) Action CA17124

Rough set decision algorithms for modeling with uncertainty

The use of decision rules allows to extract information and to infer conclusions from relational databases in a reliable way, thanks to some indicators like support and certainty. Moreover, decision algorithms collect a group of decision rules that satisfies desirable properties to describe the relational system. However, when a decision table is considered within a fuzzy environment, it is necessary to extend all notions related to decision algorithms to this framework. This paper presents a generalization of these notions, highlighting the new definitions of indicators of relevance to describe decision rules and decision algorithm

Relación entre los métodos de inferencia difusa y la programación lógica multiadjunta

A lo largo de este trabajo se realiza un estudio tanto teórico como práctico de los sistemas de inferencia difusos, así como de la programación lógica multiadjunta, para terminar haciendo una comparativa de ambas teorías. A lo largo del primer capítulo, encontramos una introducción sobre el contexto histórico junto con una pequeña descripción de los campos a tratar. Tras ello, estamos en disposición de estudiar en profundidad ambas teorías para terminar con una comparación de ambas junto con las conclusiones obtenidas