Immediate consequences operator on generalized quantifiers

The semantics of a multi-adjoint logic program is usually defined through the immediate consequences operator TP. However, the definition of the immediate consequences operator as the supremum of a set of values can provide some problem when imprecise datasets are considered, due to the strict feature of the supremum operator. Hence, based on the flexibility of generalized quantifiers to weaken the existential feature of the supremum operator, this paper presents a generalization of the immediate consequences operator with interesting properties for solving the aforementioned problem. © 2022 The Author(s

Rough sets based on Galois connections

Rough set theory is an important tool to extract knowledge from relational databases. The original definitions of approximation operators are based on an indiscernibility relation, which is an equivalence one. Lately. different papers have motivated the possibility of considering arbitrary relations. Nevertheless, when those are taken into account, the original definitions given by Pawlak may lose fundamental properties. This paper proposes a possible solution to the arising problems by presenting an alternative definition of approximation operators based on the closure and interior operators obtained from an isotone Galois connection. We prove that the proposed definition satisfies interesting properties and that it also improves object classification tasks

A neural implementation of multi-adjoint logic programs via sf-homogenization

A generalization of the homogenization process needed for the neural im- plementation of multi-adjoint logic programming (a unifying theory to deal with uncertainty, imprecise data or incomplete information) is presented here. The idea is to allow to represent a more general family of adjoint pairs, but maintaining the advantage of the existing implementation recently introduced in [6]. The soundness of the transformation is proved and its complexity is analysed. In addition, the corresponding generalization of the neural-like implementation of the fixed point semantics of multi-adjoint is presented

Impact of local congruences in variable selection from datasets

Formal concept analysis (FCA) is a useful mathematical tool for obtaining information from relational datasets. One of the most interesting research goals in FCA is the selection of the most representative variables of the dataset, which is called attribute reduction. Recently, the attribute reduction mechanism has been complemented with the use of local congruences in order to obtain robust clusters of concepts, which form convex sublattices of the original concept lattice. Since the application of such local congruences modifies the quotient set associated with the attribute reduction, it is fundamental to know how the original context (attributes, objects and relationship) has been modified in order to understand the impact of the application of the local congruence in the attribute reduction.Partially supported by the the 2014-2020 ERDF Operational Programme in collaboration with the State Research Agency (AEI) in project 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

δ-information reducts and bireducts

Attribute reduction is an important step in order to decrease the computational complexity to derive information from databases. In this paper, we extend the notions of reducts and bireducts introduced in rough set theory for attribute reduction purposes and let them work with similarity relations defined on attribute values. Hence, the related mathematical concepts will be introduced and the characterizations of the new reducts and bireducts will be given in terms of the corresponding generalizations of the discernibility function.La reducción en atributos es un paso importante para disminuir la complejidad computacional para obtener información de una base de datos. En este trabajo, extendemos la noción de reductos y birredcutos introducidos en Teoría de Conjuntos Rugosos para reducción de atributos y trabajamos con relaciones de similaridad definidas en los valores de los atributos. Luego, los conceptos matemáticos relacionados se introducirán junto con las caracterizaciones de los nuevos reductos y birreductos en términos de la función de discernibilidad

Identifying Non-Sublattice Equivalence Classes Induced by an Attribute Reduction in FCA

The detection of redundant or irrelevant variables (attributes) in datasets becomes essential in different frameworks, such as in Formal Concept Analysis (FCA). However, removing such variables can have some impact on the concept lattice, which is closely related to the algebraic structure of the obtained quotient set and their classes. This paper studies the algebraic structure of the induced equivalence classes and characterizes those classes that are convex sublattices of the original concept lattice. Particular attention is given to the reductions removing FCA's unnecessary attributes. The obtained results will be useful to other complementary reduction techniques, such as the recently introduced procedure based on local congruences

Influence of Variety and Storage Time of Fresh Garlic on the Physicochemical and Antioxidant Properties of Black Garlic

Black garlic is made from the fresh kind, submitting it to a controlled temperature (~65 C) and humidity (>85 C) for a prolonged period of time. The aim of this study was to assess the di erences in the process and in the final product as a result of employing three garlic varieties (Spanish Roja, Chinese Spring and California White), and to check the influence of the storage time on fresh garlic in the quality of the final product by using garlic obtained in two di erent agricultural seasons, that of the current year (2014) and of the previous one (2013). The results revealed some di erences in the parameters analysed during the manufacturing of the black garlic from the three varieties used, and even according to the harvest in question. However, when comparing initial and final values of the samples, a very similar evolution in their acidity, reducing sugars, Brix, pH, polyphenol content, and antioxidant capacity was note

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

Relating Multi-Adjoint Normal Logic Programs to Core Fuzzy Answer Set Programs from a Semantical Approach

This paper relates two interesting paradigms in fuzzy logic programming from a semantical approach: core fuzzy answer set programming and multi-adjoint normal logic programming. Specifically, it is shown how core fuzzy answer set programs can be translated into multi-adjoint normal logic programs and vice versa, preserving the semantics of the starting program. This translation allows us to combine the expressiveness of multi-adjoint normal logic programming with the compactness and simplicity of the core fuzzy answer set programming language. As a consequence, theoretical properties and results which relate the answer sets to the stable models of the respective logic programming frameworks are obtained. Among others, this study enables the application of the existence theorem of stable models developed for multi-adjoint normal logic programs to ensure the existence of answer sets in core fuzzy answer set programs

Solving Generalized Equations with Bounded Variables and Multiple Residuated Operators

This paper studies the resolution of sup-inequalities and sup-equations with bounded variables such that the sup-composition is defined by using different residuated operators of a given distributive biresiduated multi-adjoint lattice. Specifically, this study has analytically determined the whole set of solutions of such sup-inequalities and sup-equations. Since the solvability of these equations depends on the character of the independent term, the resolution problem has been split into three parts distinguishing among the bottom element, join-irreducible elements and join-decomposable elements