The notion of a rough set, developed by Pawlak [10], is an important tool to describe situation of incomplete or partially unknown information. In this article, which is essentially the continuation of [6], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in t...

The classical rough set theory based on complete information systems stems from the observation that objects with the same characteristics are indiscernible according to available information. With respect to upper-approximation and lower-approximation defined on an indiscernibility relation it classifies objects into different equivalent classes. But in some cases such a rigid indiscernibility...

This study describes application of some approximate reasoning methods to analysis of hydrocyclone performance. In this manner, using a combining of Self Organizing Map (SOM), Neuro-Fuzzy Inference System (NFIS)-SONFISand Rough Set Theory (RST)-SORST-crisp and fuzzy granules are obtained. Balancing of crisp granules and non-crisp granules can be implemented in close-open iteration. Using differ...

Rough set theory is a useful and effective tool to cope with granularity and vagueness in information system and has been used in many fields. However, it is hard to get the reduct of a covering in rough sets. This paper attempts to get the reduct of a covering at a high speed in theory. It defines upset and downset based on a poset in a covering, studies the relationship between reducible elem...

Forestry ecological projects have a huge impact on the living standard of forest farmers. Thus, information channels forest farmers choose to know about the information of these projects have great importance. The purpose of this study is to find out the main factors that influencing the adoption of these information channels of forest farmers in Western China. Rough set theory is used to solve...

This work focuses on lattice-theoretical foundations of rough set theory. It consists of the following sections: 1: Introduction 2: Basic Notions and Notation, 3: Orders and Lattices, 4: Distributive, Boolean, and Stone Lattices, 5: Closure Systems and Topologies, 6: Fixpoints and Closure Operators on Ordered Sets, 7: Galois Connections and Their Fixpoints, 8: Information Systems, 9: Rough Set ...

Dependability of software, a major concern in many computer applications, can be improved through several means. But systematic approaches for its evaluation do not exist, which is the prerequisite for dependability control and improvement. Software dependability evaluation is an urgent problem to be solved. There is some subjectivity about weighting coefficient when applying fuzzy comprehensiv...

We present a hierarchical scheme for synthesis of concept approximations based on given data and domain knowledge. We also propose a solution, founded on rough set theory, to the problem of constructing the approximation of higher level concepts by composing the approximation of lower level concepts. We examine the effectiveness of the layered learning approach by comparing it with the standard...

In rough set theory, the approximation quality γ is the traditional measure to evaluate the classification success of attributes in terms of a numerical evaluation of the dependency properties generated by these attributes. In this paper we re-interpret the classical γ in terms of a classic measure based on sets, the Marczewski–Steinhaus metric, and also in terms of “proportional reduction of e...

Relations between rough sets and algebraic structures have been already considered by many mathematicians. Motivated by studying the properties of rough (m,n) bi-Γ -hyperideals in Γ -semihypergroups, we now introduced the notion of prime (m,n) biΓ -hyperideals in Γ -semihypergroups and investigated several properties of these prime (m,n) bi-Γ -hyperideals. Also we applied the rough set theory t...