16 research outputs found
On the existence of right adjoints for surjective mappings between fuzzy structures0
En este trabajo los autores continúan su estudio de la caracterización de la existencia de adjunciones (conexiones de Galois isótonas) cuyo codominio no está dotado de estructura en principio. En este artículo se considera el caso difuso en el que se tiene un orden difuso R definido en un conjunto A y una aplicación sobreyectiva f:A-> B compatible respecto de dos relaciones de similaridad definidas en el dominio A y en el condominio B, respectivamente. Concretamente, el problema es encontrar un orden difuso S en B y una aplicación g:B-> A compatible también con las correspondientes similaridades definidas en A y en B, de tal forma que el par (f,g) constituya un adjunción
Parameterizing the semantics of fuzzy attribute implications by systems of isotone Galois connections
We study the semantics of fuzzy if-then rules called fuzzy attribute
implications parameterized by systems of isotone Galois connections. The rules
express dependencies between fuzzy attributes in object-attribute incidence
data. The proposed parameterizations are general and include as special cases
the parameterizations by linguistic hedges used in earlier approaches. We
formalize the general parameterizations, propose bivalent and graded notions of
semantic entailment of fuzzy attribute implications, show their
characterization in terms of least models and complete axiomatization, and
provide characterization of bases of fuzzy attribute implications derived from
data
On the Existence of Right Adjoints for Surjective Mappings between Fuzzy Structures
Abstract. We continue our study of the characterization of existence of adjunctions (isotone Galois connections) whose codomain is insufficiently structured. This paper focuses on the fuzzy case in which we have a fuzzy ordering ρA on A and a surjective mapping f : A, ≈A → B, ≈B compatible with respect to the fuzzy equivalences ≈A and ≈B. Specifically, the problem is to find a fuzzy ordering ρB and a compatible mapping g : B, ≈B → A, ≈A such that the pair (f, g) is a fuzzy adjunction
Heterogeneous environment on examples
We propose a running example for heterogeneous approach based on new type of fuzzification that diversifies fuzziness of every object, fuzziness of every attribute and fuzziness of every table value in a formal context. Moreover we suggest another working examples on heterogeneous environment and provide additional utilization and illustration of this new model that allows to use Formal Concept Analysis also for heterogenenous data. An interpretation of heterogeneous formal concepts and the resulting concept lattice is included
Heterogeneous environment on examples
We propose a running example for heterogeneous approach based on new type of fuzzification that diversifies fuzziness of every object, fuzziness of every attribute and fuzziness of every table value in a formal context. Moreover we suggest another working examples on heterogeneous environment and provide additional utilization and illustration of this new model that allows to use Formal Concept Analysis also for heterogenenous data. An interpretation of heterogeneous formal concepts and the resulting concept lattice is included
The f -index of inclusion as optimal adjoint pair for fuzzy modus ponens
We continue studying the properties of the f -index of inclusion and show that, given a fixed pair of fuzzy sets, their f -index
of inclusion can be linked to a fuzzy conjunction which is part of an adjoint pair. We also show that, when this pair is used as
the underlying structure to provide a fuzzy interpretation of the modus ponens inference rule, it provides the maximum possible
truth-value in the conclusion among all those values obtained by fuzzy modus ponens using any other possible adjoint pair.Partially supported by the Spanish Ministry of Science, Innovation and Universities (MCIU), State Agency of Research (AEI), Junta de Andalucía (JA), Universidad de Málaga (UMA) and European Regional Development Fund (FEDER) through the projects PGC2018-095869-B-I00 (MCIU/AEI/FEDER) and UMA2018-FEDERJA-001 (JA/UMA/FEDER).
Funding for open access charge: Universidad de Málaga / CBU
Attribute implications with unknown information based on weak Heyting algebras
Simplification logic, a logic for attribute implications, was originally defined for Boolean sets. It was extended to distributive fuzzy sets by using a complete dual Heyting algebra. In this paper, we weaken this restriction in the sense that we prove that it is possible to define a simplification logic on fuzzy sets in which the membership value structure is not necessarily distributive. For this purpose, we replace the structure of the complete dual Heyting algebra by the so-called weak complete dual Heyting algebra. We demonstrate the soundness and completeness of this simplification logic, and provide a characterisation of the operations defining weak complete dual Heyting algebras.Funding for open access charge: Universidad de Málaga/CBU