Lankun Guo

Hunan Normal University · College of Mathematics and Computer Science

This paper mainly addresses the connection between fuzzy rough sets and lattices. Based on a complete lattice equipped with a t-norm, the concepts of TL-fuzzy lower and upper rough approximation operators induced by an L-fuzzy set on a lattice are introduced, and their basic properties are investigated. Particularly, some characterizations of TL-fu...

This study considers the application of generalized pseudo-metrics to the extension of decomposable measures. We prove that the extension of a non-strict Archimedean t-conorm-based σ-decomposable measure can be formulated as the closure of a subset of a certain generalized pseudo-metric space. We show that the extension via generalized pseudo-metri...

This book contains thirteen chapters. There are (1) Preliminary, (2) Formal Context Based on Pictorial Diagram, (3) Partially-Ordered Attribute Diagram, (4) Non-matrix Knowledge Reduction Method for Fuzzy Context, (5) Interval-Set-Based Concept Lattice, (6) Axiality Concept Lattice and Its Attribute Redction, (7) Representation of Special Ordered S...

By introducing new approximation relations on posets, the notion of -doubly continuous posets is proposed and its relationship with doubly continuous posets is presented. Aslo the B-topology on posets is defined and the special properties of the B-topology on -doubly continuous posets are studied. Then, a sufficient and necessary condition for the...

In this paper, we propose the notion of L-information systems which provides a concrete representation of L-domains. In particular, we prove that the category of L-information systems with approximable mappings as morphisms is equivalent to that of L-domains with Scott continuous functions as morphisms.

In this paper, a new notion of (v-consistent) L *-closure L-system is proposed where L is a complete residuated lattice and \(*\) is a truth stresser on L. The one-to-one correspondence between (v-consistent) L *-closure L-systems and (v-consistent) L *-closure operators is established. Furthermore, the notion of v-consistent L *-closure system is...

The rough approximations on a complete completely distributive lattice L based on binary relation were introduced by Zhou and Hu (Inf Sci 269:378–387, 2014), where the binary relation was defined on the set of non-zero join-irreducible elements. This paper extends Zhou and Hu’s rough set model by defining new approximation operators via ideal. When...

In this paper, we introduce the notion of consistent F-augmented contexts by adding a special family of finite subsets into the structure of a formal context, which essentially establishes the basis of the representation of general algebraic domains. In particular, we investigate the association rule systems which are derived from the consistent F-...

Information system homomorphisms have made a substantial contribution to attribute reduction of covering information systems. However, the efforts made on homomorphisms are far from sufficient. This paper further studies homomorphisms for attribute reduction of dynamic fuzzy covering information systems. First, the concepts of neighbourhood and ind...

Fuzzy order congruences play an important role in studying the categorical properties of fuzzy posets. In this paper, the correspondence between the fuzzy order congruences and the fuzzy order-preserving maps is discussed. We focus on the characterization of fuzzy order congruences on the fuzzy poset in terms of the fuzzy preorders containing the f...

This paper is to study the rough sets within the context of lattices. We study the special properties of the rough sets which can be constructed by means of the congruences determined by ideals of lattice. Also the properties of the generalized rough sets with respect to ideals of lattice are investigated. Finally we give an example of their applic...

The notion of information system initially introduced by Scott provides an efficient approach to represent various kinds of domains. In this note, a new type of information systems named finitely derived information systems is introduced. For this notion, the requirement for the consistency predicate used in Scott's information systems is simplifie...

In this paper, we investigate the representation of algebraic domains by means of Formal Concept Analysis. For a formal context, we can define a large number of consistent sets. Associated with each consistent set, there is a set of F-approximable concepts which are selected from the well known approximable concepts. By virtue of F-approximable con...

We introduce the notion of F-augmented closure spaces by incorporating an additional structure (a family of finite subsets of the underlying set) into a given closure space in an appropriate way. We also introduce the notion of F-morphisms between F-augmented closure spaces and establish the equivalence between the category of F-augmented closure s...

In this paper, some properties of prime elements, pseudoprime elements, irreducible elements and coatoms in posets are investigated. We show that the four kinds of elements are equivalent to each other in finite Boolean posets. Furthermore, we demonstrate that every element of a finite Boolean poset can be represented by one kind of them. The examp...

In this paper, the definition of meet-continuity on L-directed complete posets (for short, L-dcpos) is introduced. As a generalization of meetcontinuity on crisp dcpos, meet-continuity on L-dcpos, based on the generalized Scott topology, is characterized. In particular, it is shown that every continuous L-dcpo is meet-continuous and L-continuous re...

In this paper, the definition of meet-continuity on L-directed complete posets (for short, L-dcpos) is introduced. As a generalization of meet-continuity on crisp dcpos, meet-continuity on L-dcpos, based on the generalized Scott topology, is characterized. In particular, it is shown that every continuous L-dcpo is meet-continuous and L-continuous r...

Domain Theory and Rough Set Theory are relatively independent but have much close relationship worthy of further investigation. In this paper, we propose the notion of (orientated) lower concept formula (for short, lcf) of relational information systems and study the order-theoretic properties of the derived lcf systems. Particularly, we show that...

Formal concept analysis (FCA) provides an approach to restructuring important lattice structures such as complete lattices, distributive lattices and algebraic lattices. In this paper, we focus on the theoretical aspect of FCA and study the representation of algebraic domains by a special type of formal contexts. We first propose the notion of cons...

Recently, many researches have been done on attribute dependency degree models. In this work, we bring forward three attribute dependency functions for incomplete information systems and investigate their basic properties in detail. Afterward, we apply the proposed models to twelve data sets from the UCI repository of machine learning databases. Fi...

In this paper, notions of general algebraic information systems and dense abstract bases are introduced. Their relationships with algebraic dcpo's are investigated. It is shown that they both represent exactly the algebraic dcpo's. Technically, the corresponding categories of these three structures are equivalent with each other.

The covering approximation space evolves in time due to the explosion of the information, and the characteristic matrixes of coverings viewed as an effective approach to approximating the concept should update with time for knowledge discovery. This paper further investigates the construction of characteristic matrixes without running the matrix ac...

This paper provides further study on fuzzy coverings based rough sets. We first present the notions of the lower and upper approximation operators based on fuzzy coverings and derive their basic properties detailedly. Additionally, the concepts of a fuzzy subcovering, the reducible and intersectional elements, the union and intersection operations...

This paper further studies the fuzzy rough sets based on fuzzy coverings. We first present the notions of the lower and upper approximation operators based on fuzzy coverings and derive their basic properties. To facilitate the computation of fuzzy coverings for fuzzy covering rough sets, the concepts of fuzzy subcoverings, the reducible and inters...

Soft set theory, initiated by Molodtsov, can be used as a new mathematical tool for dealing with imprecise, vague, and uncertain problems. In this paper, the concepts of two types of generalised interval-valued fuzzy soft set are proposed and their basic properties are studied. The lattice structures of generalised interval-valued fuzzy soft set ar...

In this paper, we present equivalent characterizations of L-closure systems on lower bounded complete L-ordered sets and complete L-lattices, respectively. These results demonstrate the feasibility of notion of fuzzy closure system developed in our previous work (L.-K. Guo, G.-Q. Zhang, Q.-G. Li: Fuzzy closure systems on L-ordered sets. Math. Log....

We introduce a framework for the study of formal contexts and their lattices induced by the additional structure of self-relations on top of the traditional incidence relation. The induced contexts use subsets as objects and attributes, hence the name power context and power concept. Six types of new incidence relations are introduced by taking int...

In this paper, we propose a new framework for concept analysis, namely multi-conjunctor concept lattices. The motivation is to develop a more flexible and general platform of fuzzy concept analysis through an assignment of variable conjunctors into the framework of generalized concept lattices introduced by Krajči. We compare multi-conjunctor conce...

In this paper, notions of fuzzy closure system and fuzzy closure L—system on L—ordered sets are introduced from the fuzzy point of view. We first explore the fundamental properties of fuzzy closure systems. Then the correspondence between fuzzy closure systems (fuzzy closure L—systems) and fuzzy closure operators is established. Finally, we study t...

The notion of a weak approximable concept is introduced in this paper, and the lattice consisting of weak approximable concepts is investigated. It is shown that this concept lattice is a completely algebraic lattice, and each completely algebraic lattice is isomorphic to such a concept lattice.

In this paper, we first give the representation theory of completely algebraic lattice via appropriate ∩- structure named completely algebraic ∩-structure algebraic lattice. Furthermore, we define a meaningful system called completely algebraic information system, firstly create the corresponding relationship between completely algebraic ∩- structu...