The axiomatic characterizations on<i>L</i>-fuzzy covering-based approximation operators

Li, Lingqiang; Jin, Qiu; Hu, Kai; Zhao, Fang Fang

doi:10.1080/03081079.2017.1308360

Cited by 47 publications

(10 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let µ, ν be L-fuzzy sets in X. The subsethood degree [37][38][39][40] of µ, ν, denoted by S X (µ, ν), is defined by…”

Section: Preliminariesmentioning

confidence: 99%

p-Topologicalness—A Relative Topologicalness in ⊤-Convergence Spaces

Li¹

2019

Mathematics

View full text Add to dashboard Cite

In this paper, p-topologicalness (a relative topologicalness) in ⊤-convergence spaces are studied through two equivalent approaches. One approach generalizes the Fischer’s diagonal condition, the other approach extends the Gähler’s neighborhood condition. Then the relationships between p-topologicalness in ⊤-convergence spaces and p-topologicalness in stratified L-generalized convergence spaces are established. Furthermore, the lower and upper p-topological modifications in ⊤-convergence spaces are also defined and discussed. In particular, it is proved that the lower (resp., upper) p-topological modification behaves reasonably well relative to final (resp., initial) structures.

show abstract

“…Let µ, ν be L-fuzzy sets in X. The subsethood degree [37][38][39][40] of µ, ν, denoted by S X (µ, ν), is defined by…”

Section: Preliminariesmentioning

confidence: 99%

p-Topologicalness—A Relative Topologicalness in ⊤-Convergence Spaces

Li¹

2019

Mathematics

View full text Add to dashboard Cite

show abstract

“…In 1936, Birkhoff and von Neumann [20] considered the orthomodular lattice as quantum logic for studying the algebraic structure of quantum mechanics. There are many extensions of Pawlak's rough set, such as fuzzy rough sets [21,22], covering based rough sets [23][24][25], probabilistic rough sets [26,27], soft rough sets [28][29][30][31], Diophantine fuzzy rough sets [32][33][34][35], multi-granulation rough sets [36][37][38], hesitant fuzzy rough set [39] and so on. However, as far as I know, there is only a little literature addressing the rough sets and quantum logics together.…”

Section: Introductionmentioning

confidence: 99%

Rough Approximation Operators on a Complete Orthomodular Lattice

Dai

2021

Axioms

View full text Add to dashboard Cite

This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the distributive law. Furthermore, we study the relationship among the distributive law, rough approximation and orthomodular lattice-valued relation.

show abstract

“…(Fuzzy) rough sets are closely related to (fuzzy) topology [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. e well-known result may be that there is a one-toone correspondence between reflexive and transitive (fuzzy) approximation spaces and quasidiscrete (fuzzy) topological spaces [26,37,38].…”

Section: Introductionmentioning

confidence: 99%

A New Single-Valued Neutrosophic Rough Sets and Related Topology

Jin

et al. 2021

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

(Fuzzy) rough sets are closely related to (fuzzy) topologies. Neutrosophic rough sets and neutrosophic topologies are extensions of (fuzzy) rough sets and (fuzzy) topologies, respectively. In this paper, a new type of neutrosophic rough sets is presented, and the basic properties and the relationships to neutrosophic topology are discussed. The main results include the following: (1) For a single-valued neutrosophic approximation space U , R , a pair of approximation operators called the upper and lower ordinary single-valued neutrosophic approximation operators are defined and their properties are discussed. Then the further properties of the proposed approximation operators corresponding to reflexive (transitive) single-valued neutrosophic approximation space are explored. (2) It is verified that the single-valued neutrosophic approximation spaces and the ordinary single-valued neutrosophic topological spaces can be interrelated to each other through our defined lower approximation operator. Particularly, there is a one-to-one correspondence between reflexive, transitive single-valued neutrosophic approximation spaces and quasidiscrete ordinary single-valued neutrosophic topological spaces.

show abstract

The axiomatic characterizations onL-fuzzy covering-based approximation operators

Cited by 47 publications

References 55 publications

p-Topologicalness—A Relative Topologicalness in ⊤-Convergence Spaces

p-Topologicalness—A Relative Topologicalness in ⊤-Convergence Spaces

Rough Approximation Operators on a Complete Orthomodular Lattice

A New Single-Valued Neutrosophic Rough Sets and Related Topology

Contact Info

Product

Resources

About