L-fuzzy Rough Sets Research Articles

Granular variable precision L-fuzzy rough sets based on residuated lattices

Firstly, as for the beginning of this paper, we introduce the granular variable precision L-fuzzy rough sets based on residuated lattices with arbitrary L-fuzzy relations. And then, the equivalent expressions for the lower and upper approximation operators are given with L-fuzzy implications and L-fuzzy coimplications on arbitrary L-fuzzy relations, which can calculate the lower and upper approximation operators efficiently. Finally, some basic properties of the granular variable precision L-fuzzy rough sets on residuated lattices are investigated and the conclusions on the granular variable precision fuzzy rough sets are generalized into the situations of the truth values set becoming residuated lattices.

L -fuzzy multigranulation rough set based on residuated lattices

This paper studies L-fuzzy multigranulation rough set based on residuted lattices, which is considered as an extension of the classical L-fuzzy rough set. Two models of L-fuzzy optimistic multigrannulation rough set and L-fuzzy pessimistic multigrannulation rough set based on residuted latteices are suggested. Then, we mainly investigate some funda- mental properties of the L-fuzzy multigranulation rough set model. With regards to residuated lattices' topology, we study the topological and the lattice structure in the L-fuzzy optimistic multigranulation rough set model and L-fuzzy pessimistic multigranulation rough set model, respectively.

Some properties of L-fuzzy approximation spaces based on bounded integral residuated lattices

In this paper, we present a general framework for the study of L-fuzzy rough sets based on bounded integral residuated lattices. We introduce and discuss the notions of L-fuzzy topological spaces, left (right) lower and left (right) upper L-fuzzy approximation operators based on a complete bounded integral residuated lattice, investigate union, intersection, and composition operations of L-fuzzy approximation spaces, and study some properties of the L-fuzzy topologies generated by these L-fuzzy rough approximation operators and the L-relations induced by an L-fuzzy topology.

Fuzzy rough sets based on generalized residuated lattices

This paper is devoted to propose generalized L-fuzzy rough sets as a further generalization of the notion of L-fuzzy rough sets. A quadruple of approximation operators are defined to suit the situation when generalized residuated lattices are non-commutative. Generalized L-fuzzy rough sets are characterized from both constructive and axiomatic approaches. In the constructive approach, various classes of generalized L-fuzzy rough sets are investigated. Moreover, the relationship between generalized L-fuzzy rough sets and L-topologies on an arbitrary universe is discussed with generalized lower and upper sets. As an application of generalized L-fuzzy rough sets, fuzzy rough sets are proposed and studied on the unit interval [0,1], which are based on generalized residuated lattices induced by left-continuous pseudo-t-norms.

Topological and lattice structures of [formula omitted]-fuzzy rough sets determined by lower and upper sets

This paper builds the topological and lattice structures of L-fuzzy rough sets by introducing lower and upper sets. In particular, it is shown that when the L-relation is reflexive, the upper (resp. lower) set is equivalent to the lower (resp. upper) L-fuzzy approximation set. Then by the upper (resp. lower) set, it is indicated that an L-preorder is the equivalence condition under which the set of all the lower (resp. upper) L-fuzzy approximation sets and the Alexandrov L-topology are identical. However, associating with an L-preorder, the equivalence condition that L-interior (resp. closure) operator accords with the lower (resp. upper) L-fuzzy approximation operator is investigated. At last, it is proven that the set of all the lower (resp. upper) L-fuzzy approximation sets forms a complete lattice when the L-relation is reflexive.

The relationship between L-fuzzy rough set and L-topology

Various fuzzy generalizations of rough approximations have been proposed in the literature. This paper is devoted to the discussion of the relationship between L-fuzzy rough sets and L-topologies on an arbitrary universe. Finally, one-to-one correspondence between the set of all reflexive, transitive L-relations and the set of all Alexandrov L-topologies is obtained.

Binary Relation, Basis Algebra, Approximation Operator Form and Its Property in L-Fuzzy Rough Sets

The rough set theory usually is used in data-mining. At this time, we will suppose the approximation operator to satisfy some wonderful properties. It need us to think about the basis algebra, the binary relation and the approximation operator’s form in the rough set model. L-fuzzy rough approximation operator is a general fuzzy rough approximation operator. Comparing with the others rough approximation operator, it is more clearly for the L-fuzzy rough approximation operator that not only the binary relation and the basis algebra, but also the form of approximation operator influence its properties. To inhibit the relations between binary relation on the universe, basis algebra, the approximation operators’ properties and its form in the L-fuzzy rough set, we introduce some basis algebra (residuated lattice, MTL algebra and IMTL algebra) and some binary relations(the reflexive, symmetric, transitive, L-similar, L-indistinguish-able fuzzy binary relation) into three types L-fuzzy rough approximation operators and proof some L-fuzzy rough approximation operators’ properties as its properties. As usual, we discuss the approxima-tion operator in the constructive approach and axiomatic approach. This paper focus on the basis algebra and the form of the approximation operat-ors. As the preliminaries, we use some spaces to dis-cuss the properties of the non-classic logic algebra.

Approximation Operators, Binary Relation and Basis Algebra in L-fuzzy Rough Sets

Approximation operators play a vital role in rough set theory. Their three elements, namely, binary relation in the universe, basis algebra and properties, are fundamental in the study of approximation operators. In this paper, the interrelations among the three elements of approximation operators in L-fuzzy rough sets are discussed under the constructive approach, the axiomatic approach and the basis algebra choosing approach respectively. In the constructive approach, the properties of the approximation operators depend on the basis algebra and the binary relation. In the axiomatic approach, the induced binary relation is influenced by the axiom set and the basis algebra. In the basis algebra choosing approach, the basis algebra is constructed by properties of approximation operators and specific binary relations.

L-fuzzy roughness of n-ary polygroups

In this paper, we consider the relations among L-fuzzy sets, rough sets and n-ary polygroup theory. Some properties of (normal) TL-fuzzy n-ary subpolygroups of an n-ary polygroup are first obtained. Using the concept of L-fuzzy sets, the notion of ϑ-lower and T-upper L-fuzzy rough approximation operators with respect to an L-fuzzy set is introduced and some related properties are presented. Then a new algebraic structure called (normal) TL-fuzzy rough n-ary polygroup is defined and investigated. Also, the (strong) homomorphism of ϑ-lower and T-upper L-fuzzy rough approximation operators is studied.

Fuzzy roughness of n-ary hypergroups based on a complete residuated lattice

This paper considers the relationships among L-fuzzy sets, rough sets and n-ary hypergroup theory. Based on a complete residuated lattice, the concept of (invertible) L-fuzzy n-ary subhypergroups of a commutative n-ary hypergroup is introduced and some related properties are presented. The notions of lower and upper L-fuzzy rough approximation operators with respect to an L-fuzzy n-ary subhypergroup are introduced and studied. Then, a new algebraic structure called (invertible) L-fuzzy rough n-ary subhypergroups is defined, and the (strong) homomorphism of lower and upper L-fuzzy rough approximation operators is studied.