Parameterized simplification logic I: reasoning with implications and classes of closure operators

Enciso, Manuel; Mora, Ángel; Vychodil, Vilém

doi:10.1080/03081079.2020.1831484

Cited by 14 publications

(3 citation statements)

References 35 publications

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“…They are key elements in both pure and applied mathematics, and also in computer science [6]. Fuzzy closure operators [7,8] appear in several areas of fuzzy logic, just to list a few we mention: fuzzy mathematical morphology [9,10], fuzzy relational equations [11], approximate reasoning [12,13] and fuzzy logic in narrow sense [14]. But also its applications such as fuzzy logic programming [15] or formal concept analysis of data with fuzzy attributes [16].…”

Section: Introductionmentioning

confidence: 99%

Characterizing closure systems in the graded setting - CMMSE

Ojeda-Hernandez,

Cabrera,

Cordero

et al. 2024

Preprint

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Closure systems play a major role in both pure and applied mathematics. This paperpresents an extension of the notion of closure system, which is done adapting theidea of meet-subsemilattice to a complete fuzzy lattice. This extension is carried outon two levels, first as crisp sets and then as fuzzy sets. In both cases, the one-to-onerelations between closure operators and closure systems that hold in the classicalcase are extended properly to this framework. Furthermore, a novel characterizationfor a closure system is established.

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Section: Introductionmentioning

confidence: 99%

Characterizing closure systems in the graded setting - CMMSE

Ojeda-Hernandez,

Cabrera,

Cordero

et al. 2024

Preprint

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“…This mathematical theory was original developed in the 1980s by R. Wille and B. Ganter [1], and it has intensively been studied from a theoretical and applied point of view [2][3][4][5][6][7][8][9][10][11][12]. Two important features of FCA, in which the notion of Galois connection is fundamental [13][14][15][16], is that the information contained in a relational dataset can be described in a hierarchic manner by means of a complete lattice [17] and that dependencies between attributes can be determined [18][19][20][21], which is fundamental to applications. In both features, the removal of redundant data has a great impact.…”

Section: Introductionmentioning

confidence: 99%

Identifying Non-Sublattice Equivalence Classes Induced by an Attribute Reduction in FCA

2021

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The detection of redundant or irrelevant variables (attributes) in datasets becomes essential in different frameworks, such as in Formal Concept Analysis (FCA). However, removing such variables can have some impact on the concept lattice, which is closely related to the algebraic structure of the obtained quotient set and their classes. This paper studies the algebraic structure of the induced equivalence classes and characterizes those classes that are convex sublattices of the original concept lattice. Particular attention is given to the reductions removing FCA’s unnecessary attributes. The obtained results will be useful to other complementary reduction techniques, such as the recently introduced procedure based on local congruences.

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“…Closure operators have an important role in pure, applied mathematics and computer science [10]. Fuzzy closure operators [1,4] appear in several areas of fuzzy logic and its applications, including fuzzy mathematical morphology [13,18], fuzzy relational equations [12], approximate reasoning [6,11] and fuzzy logic in narrow sense [15], and its applications such as fuzzy logic programming [17] or formal concept analysis of data with fuzzy attributes [20].…”

Section: Introductionmentioning

confidence: 99%

Closure Systems as a Fuzzy Extension of Meet-subsemilattices

Ojeda-Hernández¹,

Cabrera²,

Muñoz‐Velasco³

2021

Atlantis Studies in Uncertainty Modelling

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An extension of the notion of closure system is studied adapting the idea of meetsubsemilattice to a complete fuzzy lattice. Results relating closure operators and closure systems in the classical case are extended properly to this framework. This definition is proved to be equivalent to the most used definition given by Bělohlávek on the fuzzy powerset lattice. A definition of fuzzy closure system is presented and related to closure systems. Atlantis Studies in Uncertainty Modelling, volume 3Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)

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Parameterized simplification logic I: reasoning with implications and classes of closure operators

Cited by 14 publications

References 35 publications

Characterizing closure systems in the graded setting - CMMSE

Characterizing closure systems in the graded setting - CMMSE

Identifying Non-Sublattice Equivalence Classes Induced by an Attribute Reduction in FCA

Closure Systems as a Fuzzy Extension of Meet-subsemilattices

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