On the relation between fuzzy closing morphological operators, fuzzy consequence operators induced by fuzzy preorders and fuzzy closure and co-closure systems
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Cited by (13)
Consequence operators, interior operators and fuzzy relations
2022, Fuzzy Sets and SystemsFuzzy closure relations
2022, Fuzzy Sets and SystemsCitation Excerpt :Originally introduced by E. H. Moore in [24], these structures seem to be ubiquitous in mathematics, together with their counterpart closure systems. In particular, fuzzy closure operators [1,5] appear in several areas of fuzzy logic such as fuzzy mathematical morphology [14,23], fuzzy relational equations [12], approximate reasoning [4,11] and fuzzy logic in narrow sense [16]. But also its applications such as fuzzy logic programming [21] or formal concept analysis of data with fuzzy attributes [26].
Fuzzy closure systems: Motivation, definition and properties
2022, International Journal of Approximate ReasoningCitation Excerpt :They are key elements in several branches of mathematics, such as algebra, topology, analysis and computer science. [11]. Fuzzy closure operators [2,6] appear in several areas of fuzzy logic, just to list a few we mention: fuzzy mathematical morphology [15,26], fuzzy relational equations [14], approximate reasoning [5,12] and fuzzy logic in narrow sense [19]. But also their applications such as fuzzy logic programming [24] or formal concept analysis of data with fuzzy attributes [31].
Permutable fuzzy consequence and interior operators and their connection with fuzzy relations
2015, Information SciencesCitation Excerpt :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 [7,8,15,16]. 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 [20,22]. In these cases, the fuzzy relation plays the role of structuring element.
Relational Extension of Closure Structures
2022, Communications in Computer and Information ScienceOn self-aggregations of min-subgroups
2021, Axioms