A unifying study between modal-like operators, topologies and fuzzy sets

Järvinen, Jouni; Kortelainen, Jari

doi:10.1016/j.fss.2007.01.011

Cited by 27 publications

(7 citation statements)

References 23 publications

(34 reference statements)

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“…Note that similarly defined operators under differemt assumptions appear also in the previous researches, see e.g. (Järvinen and Kortelainen, 2007, Qin and Pai 2005, Sostak 2010, Sostak 2012 In Section 5 we define the measures of upper K (A) and lower T (A) rough approximation for an Lfuzzy subset A of a set endowed with an L-relation.…”

Section: Introductionmentioning

confidence: 87%

Measure of Roughness for Rough Approximation of Fuzzy Sets and Its Topological Interpretation

Šostak¹

2014

Proceedings of the International Conference on Fuzzy Computation Theory and Applications

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We define the measure of upper and the measure of lower rough approximation for L-fuzzy subsets of a set equipped with a reflexive transitive fuzzy relation R. In case when the relation R is also symmetric, these measures coincide and we call their value by the measure of roughness of rough approximation. Basic properties of such measures are studied. A realization of measures of rough approximation in terms of L-fuzzy topologies is presented.

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Section: Introductionmentioning

confidence: 87%

Measure of Roughness for Rough Approximation of Fuzzy Sets and Its Topological Interpretation

Šostak¹

2014

Proceedings of the International Conference on Fuzzy Computation Theory and Applications

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“…The literature, however, contains studies in which rough approximations are defined by tolerances-reflexive and symmetric binary relations-e.g., [5] and [11]. In [7] and [8], rough approximations determined by quasi-ordersreflexive and transitive binary relations-and their connection to topological spaces and fuzzy sets are studied. In [9], operators determined by frames of information relations reflecting distinguishability or indistinguishability of objects of an information system are considered.…”

Section: Rough Approximationsmentioning

confidence: 99%

Properties of Rough Approximations

Järvinen¹

2005

J. Adv. Comput. Intell. Intell. Inform.

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“…General topology has been considered the entrance to understand topology science, moreover the base of general topology is the topological space, which has been considered a representation of universal space in general, and geometric shape in special, also the mathematical analysis concepts. The concept of topology shows up naturally in almost every branch of mathematics [8,14,17,18]. This has made topology one of the great unifying ideas of mathematics.…”

Section: Introductionmentioning

confidence: 99%