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A Unified Definition of Consistent Functions

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Zhu P. , Xie H. , Wen Q.

tom Vol. 135, nr 3

331--340

In recent years, homomorphisms have been exploited to compare the structures and properties of two generalized information systems. Some of these homomorphisms are based on consistent functions, which are a class of special mappings between universal sets. The purpose of this paper is to unify and extend the consistent functions in the literature into the framework of neighborhood systems. After introducing the notion of consistent functions with respect to neighborhood systems, we explore some important properties of the extended consistent functions such as preserving the inverse images and the intersections of neighborhoods. Our results provide a sound basis for further investigating neighborhood systems via homomorphisms.

Neighborhood Systems : Rough Set Approximations and Definability

100%

Syau Y.-R. , Lin E.-B. , Liau C.-J.

2018

tom Vol. 159, nr 4

429--450

The notions of approximation and definability in classical rough set theory and their generalizations have received much attention. In this paper, we study such generalizations from the perspective of neighborhood systems. We introduce four different types of definability, called interior definability, closure definability, interior-closure (IC) definability, and weak IC definability respectively. We also point out the relationship between IC definability and other types of definability for some special kinds of neighborhood systems. Several examples are presented to illustrate the concepts introduced in this paper.

Neighborhood Systems and Variable Precision Generalized Rough Sets

100%

Syau Y.-R. , Lin E.-B. , Liau C.-J.

Fundamenta Informaticae

2017

tom Vol. 153, nr 3

271--290

In this paper, we present the connection between the concepts of Variable Precision Generalized Rough Set model (VPGRS-model) and Neighborhood Systems through binary relations. We provide characterizations of lower and upper approximations for VPGRS-model by introducing minimal neighborhood systems. Furthermore, we explore generalizations by investigating variable parameters which are limited by variable precision. We also prove some properties of lower and upper approximations for VPGRS-model.