On the relation between fuzzy closing morphological operators, fuzzy consequence operators induced by fuzzy preorders and fuzzy closure and co-closure systems

Elorza, Jorge; Fuentes-González, Ramón; Bragard, J.; Burillo, P.

doi:10.1016/j.fss.2012.08.010

Cited by 17 publications

(8 citation statements)

References 33 publications

(38 reference statements)

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“…Con la composición de los operadores antes definidos es posible crear operadores que nos brinden mayor exactitud en el reconocimiento de detalles específicos de una imagen [9], uno de ellos es el operador apertura el cual consta de la composición del operador erosión seguido del operador dilatación, i.e. α R (µ) = R • (R op µ); dicho operador es usado especialmente para eliminar regiones pequeñas y protuberancias.…”

Section: Algunos Operadores Morfológicos Difusosunclassified

Del Operador Apertura en la Matemática Morfológica Difusa

Baquero

Castillo

2017

Ing.

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Contexto: Las propiedades que posee un operador de interior se pueden trasladar a la determinación de características específicas de imágenes, las cuales, desde la matemática morfológica difusa pueden llegar a ser analizadas por medio del operador erosión y apertura, al conjugar estas ideas es pertinente indagar en torno a la naturaleza de estos operadores. Método: Gracias a las propiedades reticulares que posee el análisis matemático de una imagen por medio de matemática morfológica difusa, se busca dotar de restricciones al elemento estructural con el cual se desea filtrar la imagen para así obtener caracterizaciones del operador apertura y erosión. Resultados: Se demuestre que si la relación estructural es reflexiva o * -antitransitiva el operador apertura es interior; en caso que la relación cumpla ambas, la erosión es un operador interior. Conclusiones: Los operadores morfológicos difusos permiten obtener información relevante sin alterar la estructural global de la imagen; arrojando mayor calidad que los métodos clásicos, en especial si se emplea el operador apertura difuso con una relación estructural adecuada. Palabras clave: Apertura, erosión, interior, matemática morfológica, operador.Interior operators have interesting properties that can be used in detecting relevant features in digital images. In this respect, it is pertinent to study the behaviour of the opening and erosion operators from the perspective of fuzzy morphological mathematics. Method: Bearing in mind the reticular properties inherent to the mathematical anaysis of an image by fuzzy morphological mathematics we seek to find restrictions on the structural element intended to filter the image so as to obtain characterizations of the opening and erosion operators. Results: We prove that if the structural relationship is reflexive or * -antitransitive the opening operator is interior. On the other hand, we found that if the relationship meets both erosion is a interior operator. Conclusions: The fuzzy morphological operators can give us more information than the classical methods when we filter an image, especially if we implement the opening operator with a right structural element.

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Section: Algunos Operadores Morfológicos Difusosunclassified

Del Operador Apertura en la Matemática Morfológica Difusa

Baquero

Castillo

2017

Ing.

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“…In fuzzy mathematical morphology, both kinds of operators act as morphological filters for image processing [14,15]. They have been extensively studied in several contexts [5,23,29] and they have been used to transfer results from the field of approximate reasoning to the field of fuzzy mathematical morphology [19].…”

Section: Preliminariesmentioning

confidence: 99%

“…In fuzzy mathematical morphology, fuzzy consequence operators and fuzzy interior operators are called fuzzy closings and openings respectively and they act as morphological filters used for image processing [6,7,14,15]. Operators induced by fuzzy relations appear in this context as a generalization of morphological filters defined in sets were an additive operation does not necessarily exist [19,21]. In these cases, the fuzzy relation plays the role of structuring element.…”

Section: Introductionmentioning

confidence: 99%

Permutable fuzzy consequence and interior operators and their connection with fuzzy relations

Carmona

Elorza

Recasens

et al. 2015

Information Sciences

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Fuzzy operators are an essential tool in many fields and the operation of composition is often needed. In general, composition is not a commutative operation. However, it is very useful to have operators for which the order of composition does not affect the result. In this paper, we analyze when permutability appears. That is, when the order of application of the operators does not change the outcome. We characterize permutability in the case of the composition of fuzzy consequence operators and the dual case of fuzzy interior operators. We prove that for these cases, permutability is completely connected to the preservation of the operator type.We also study the particular case of fuzzy operators induced by fuzzy relations through Zadeh's compositional rule and the inf-→ composition. For this cases, we connect permutability of the fuzzy relations (using the sup- * composition) with permutability of the induced operators. Special attention is paid to the cases of operators induced by fuzzy preorders and similarities. Finally, we use these results to relate the operator induced by the transitive closure of the composition of two reflexive fuzzy relations with the closure of the operator this composition induces.

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“…Min-subgroups can be identified as indistinguishability operators that are invariant by translations (see [8]). This type of indistinguishability operator plays a fundamental role in some applications, notably in mathematical morphology (see [8][9][10][11]).…”

Section: Introductionmentioning

confidence: 99%

On Self-Aggregations of Min-Subgroups

Bejines

Ardanza-Trevijano

Elorza

2021

Axioms

Self Cite

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Preservation of structures under aggregation functions is an active area of research with applications in many fields. Among such structures, min-subgroups play an important role, for instance, in mathematical morphology, where they can be used to model translation invariance. Aggregation of min-subgroups has only been studied for binary aggregation functions . However, results concerning preservation of the min-subgroup structure under binary aggregations do not generalize to aggregation functions with arbitrary input size since they are not associative. In this article, we prove that arbitrary self-aggregation functions preserve the min-subgroup structure. Moreover, we show that whenever the aggregation function is strictly increasing on its diagonal, a min-subgroup and its self-aggregation have the same level sets.

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On the relation between fuzzy closing morphological operators, fuzzy consequence operators induced by fuzzy preorders and fuzzy closure and co-closure systems

Cited by 17 publications

References 33 publications

Del Operador Apertura en la Matemática Morfológica Difusa

Del Operador Apertura en la Matemática Morfológica Difusa

Permutable fuzzy consequence and interior operators and their connection with fuzzy relations

On Self-Aggregations of Min-Subgroups

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