Fuzzy and Bipolar Mathematical Morphology, Applications in Spatial Reasoning

Bloch, Isabelle

doi:10.1007/978-3-642-02906-6_1

Cited by 2 publications

(1 citation statement)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Generalizations of fuzzy mathematical morphology from different perspectives and interesting applications have been recently proposed (see for instance [7,8,16,43,46]). …”

Section: Introductionmentioning

confidence: 99%

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

Elorza

Fuentes-González

Bragard

et al. 2013

Fuzzy Sets and Systems

View full text Add to dashboard Cite

In a previous paper, Elorza and Burillo explored the coherence property in fuzzy consequence operators. In this paper we show that fuzzy closing operators of mathematical morphology are always coherent operators. We also show that the coherence property is the key to link the four following families: fuzzy closing morphological operators, fuzzy consequence operators, fuzzy preorders and fuzzy closure and co-closure systems. This will allow to translate important well-known properties from the field of approximate reasoning to the field of image processing.

show abstract

“…Generalizations of fuzzy mathematical morphology from different perspectives and interesting applications have been recently proposed (see for instance [7,8,16,43,46]). …”

Section: Introductionmentioning

confidence: 99%

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

Elorza

Fuentes-González

Bragard

et al. 2013

Fuzzy Sets and Systems

View full text Add to dashboard Cite

show abstract

Handling bipolar knowledge with imprecise probabilities

Destercke

2011

Int. J. Intell. Syst.

View full text Add to dashboard Cite

Information is said to be bipolar when it has a positive and a negative part. The problem of representing and processing such bipolar information has recently received a lot of attention in uncertainty theories. In this paper, we are concerned with the representation of asymmetric bipolarity, i.e., with situations where positive and negative information are unrelated and processed in parallel. In this latter case, positive information consists of observations of experiment results, showing what values are possible, whereas negative information consists of constraints (e.g., provided by an expert), restricting the range of possible variable values. Up to now, there are no proposition as to how such bipolar information can be treated in the framework of imprecise probability theory, i.e., when information is represented by convex sets of probabilities. In this paper, we propose the basis of such a framework and provide some illustrative examples. C 2011 Wiley Periodicals, Inc.

show abstract

Fuzzy and Bipolar Mathematical Morphology, Applications in Spatial Reasoning

Cited by 2 publications

References 44 publications

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

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

Handling bipolar knowledge with imprecise probabilities

Contact Info

Product

Resources

About