A Relational Logic for Spatial Contact Based on Rough Set Approximation

Fuzzy sets, rough sets, and later on IF sets became useful mathematical tools for solving various decision making problems and data mining problems. Molodtsov introduced another concept soft set theory as a general frame work for reasoning about vague concepts. Since most of the data collected are either linguistic variable or consist of vague concepts so IF set and soft set help a lot in data mining problem. The aim of this paper is to introduce the concept of IF soft lower rough approximation and IF upper rough set approximation. Also, some properties of this set are studied, and also some problems of decision making are cited where this concept may help. Further research will be needed to apply this concept fully in the decision making and data mining problems.

Download Full-text

Aximatics for Rough Set Model Based on Vague Relations

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.282-283.283 ◽

2011 ◽

Vol 282-283 ◽

pp. 283-286

Author(s):

Hai Dong Zhang ◽

Yan Ping He

Keyword(s):

Rough Set ◽

Rough Sets ◽

General Framework ◽

Axiomatic Approach ◽

Constructive Approach ◽

Approximation Operators ◽

Rough Approximation ◽

Axiomatic Approaches ◽

Set Approximation

This paper presents a general framework for the study of rough set approximation operators in vague environment in which both constructive and axiomatic approaches are used. In constructive approach, by means of a vague relation defined by us, a new pair of vague rough approximation operators is ﬁrst deﬁned. Also some properties about the approximation operators are then discussed. In axiomatic approach, an operator-oriented characterization of vague rough sets is proposed, that is, vague rough approximation operators are defined by axioms.

Download Full-text

Representations of rough set approximation operators

Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium ◽

10.1109/afss.1996.583541 ◽

2002 ◽

Author(s):

Y.Y. Yao

Keyword(s):

Rough Set ◽

Approximation Operators ◽

Set Approximation

Download Full-text

Rough Set Approximation as Formal Concept

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2006.p0606 ◽

2006 ◽

Vol 10 (5) ◽

pp. 606-611 ◽

Cited By ~ 4

Author(s):

Nozomi Ytow ◽

◽

David R. Morse ◽

David McL. Roberts ◽

◽

...

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Formal Concept Analysis ◽

Rough Set Theory ◽

The Other ◽

Formal Concept ◽

Object Based ◽

Formal Concepts ◽

Set Approximation

Formal Concept Analysis (FCA) defines a formal concept as a pair of sets: objects and attributes, called extent and intent respectively. A rough set, on the other hand, approximates a concept using sets of objects only (in terms of FCA). We show that 1) a formal concept can be composed using a set of objects and its complement, 2) such object-based formal concepts are isomorphic to formal concepts based on objects and attributes, 3) upper and lower approximations of rough sets give generalization of formal concept, and 4) the pair of positive and negative sets (sensu rough set theory) are isomorphic to complemental formal concepts when the equivalence of the rough set gives positive and negative sets unique to each of the formal concepts. Implications of this are discussed.

Download Full-text