In this paper, we give some properties of fuzzy Riesz homomorphism on fuzzy Riesz space. We give definitions of fuzzy quotient spaces, and some characterizations of fuzzy Archimedean quotient spaces. We prove the properties which fuzzy Riesz homomorphism is fuzzy order continuous, and study the extension of fuzzy lattice homomorphism and the extension of fuzzy order continuous lattice homomorphism. Finally, we investigate the factorization by fuzzy Riesz homomorphisms.

Fuzzy Riesz homomorphism on fuzzy Riesz space.

This paper uses the concept of mapping as a basic tool to study the communication between fuzzy information systems. We firstly define the concept of a compatible mapping with respect to fuzzy sets and study their basic properties. Then, we introduce the concepts of fuzzy covering information system and its homomorphism, and examine some invariant properties of fuzzy covering information systems under homomorphism. We find out that the attribute reductions of the original system and image system are equivalent to each other in fuzzy information systems.

A mapping between fuzzy covering information systems

In order to compare the structures and properties of two generalized information systems, a class of special mappings, called consistent functions in some literature, have been extensively studied over the past years. Most recently, consistent functions have been unified and extended into the framework of neighborhood systems which have general binary relations, dominance relations, and coverings as instances. In this paper, we further extend and investigate the notion of consistent functions for fuzzy neighborhood systems. After introducing the definition of extended consistent functions and showing their relationships with related functions, we present some basic properties of the new consistent functions with respect to set-theoretic operations and fuzzy neighborhoods, respectively. As an application, we consider the attribute reduction based on consistent functions. In doing so, we contribute to a unified view of consistent functions and attempt to develop a general theory for investigating the invariant properties of fuzzy neighborhood systems under consistent functions.

A unified view of consistent functions

Set-valued information systems are important generalizations of single-valued information systems. In this paper, three relations are proposed for attribute reduction of set-valued information systems. Then, we convert a large-scale set-valued information system into a smaller relation information system. An incremental algorithm is designed to compress dynamic set-valued information systems. Concretely, we mainly address the compression updating from three aspects: variations of attribute set, immigration and emigration of objects and alterations of attribute values. Finally, several illustrative examples are employed to demonstrate that attribute reduction of dynamic set-valued information systems are simplified significantly by our proposed approaches.

An incremental approach to attribute reduction of dynamic set-valued information systems

Relationships between information systems are very important topics in the field of artificial intelligence. The concept of homomorphisms is an effective mathematical tool to study relationships between information systems. A knowledge base is a special relation information system. This paper investigates invariant characteristics of knowledge bases under the homomorphism. The fact that knowledge bases themselves are invariant and inverse invariant under the homomorphism is firstly proved. Next, some invariant characteristics and inverse invariant characteristics under the homomorphism, such as the dependency of knowledge bases, knowledge reductions, coordinate families and necessary relations, are obtained based on this fact. Finally, lattice characteristics of the dependency of knowledge bases are given. These results will be significant for establishing a framework of granular computing in knowledge bases.

Relationships between knowledge bases and related results

An information system is one of the very important mathematical models in the field of artificial intelligence. The notion of information system's homomorphism as a kind of tools to study the relation between two information systems was introduced by Grzymala-Busse (1986). In this paper, some invariant characteristics of an information system under a homomorphism are discussed.

Invariant characteristics of information systems under some homomorphisms. I

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Invariant characteristics of information systems under some homomorphisms. I