In this paper, we build upon previous work defining explanatory relations based on mathematical morphology operators on logical formulas in propositional logics. We propose to extend such relations to the case where the set of models of a formula is fuzzy, as a first step towards morphological fuzzy abduction. The membership degrees may represent degrees of satisfaction of the formula, preferen...

This article introduces interior and closure operators with inclusion degree considered within a crisp or fuzzy topological framework. First, inclusion degree is introduced in an extension of the interior and closure operators in crisp topology. This idea is then introduced in fuzzy topology by incorporating a relaxed version of fuzzy subsethood. The introduction of inclusion degree leads to a ...

In this paper we use concepts from the lattice-based theory of morphological operators and fuzzy sets to develop generalized lattice image operators that can be expressed as nonlinear convolutions that are suprema or infima of fuzzy intersection or union norms. Our emphasis (and differences with previous works) is the construction of pairs of fuzzy dilation and erosion operators that form latti...

In this paper we use concepts from the lattice-based theory of morphological operators and fuzzy sets to develop generalized lattice image operators that are nonlinear convolutions that can be expressed as supremum (resp. infimum) of fuzzy intersection (resp. union) norms. Our emphasis and differences with many previous works is the construction of pairs of fuzzy dilation (sup of fuzzy intersec...

The goal of this work is to prove a link between the Fuzzy Mathematical Morphology and the L-fuzzy Concept Analysis when we are using structuring relations which represent the effect that we want to produce over an initial fuzzy image or signal. In this case, we prove that the problem of obtaining the Lfuzzy concepts of an L-fuzzy context is equivalent to the problem of finding fuzzy images or ...

Diabetic Retinopathy is the damage to the retina caused by complication and the most common cause of blindness in Thailand. Retinal image is essential for expert ophthalmologists to diagnose diseases. Several of method can achieve good performance on retinal feature are clearly visible. Unfortunately, the color retinal image in Thailand are low-resolution images. The existing method cannot iden...

In this work, decision tree learning algorithms and fuzzy inferencing systems are applied for galaxy morphology classification. In particular, the CART, the C4.5, the Random Forest and fuzzy logic algorithms are studied and reliable classifiers are developed to distinguish between spiral galaxies, elliptical galaxies or star/unknown galactic objects. Morphology information for the training and ...

In this paper we extend some previously established links between the derivation operators used in formal concept analysis and some mathematical morphology operators to fuzzy concept analysis. We also propose to use mathematical morphology to navigate in a fuzzy concept lattice and perform operations on it. Links with other lattice-based formalisms such as rough sets and F-transforms are also e...

Based on the observation that rough sets and mathematical morphology are both using dual operators sharing similar properties, we investigate more closely the links existing between both the domains. We establish the equivalence between some morphological operators and rough sets de"ned from either a relation, or a pair of dual operators or a neighborhood system. Then we suggest some extensions...