The dominance–based rough set approach plays an important role in the development of the rough set theory. It can be used to express the inconsistencies coming from consideration of the preference–ordered domains of the attributes. The purpose of this paper is to further generalize the dominance–based rough set model to fuzzy environment. The constructive approach is used to define the intuitio...

Kernel methods and rough sets are two general pursuits in the domain of machine learning and intelligent systems. Kernel methods map data into a higher dimensional feature space, where the resulting structure of the classification task is linearly separable; while rough sets granulate the universe with the use of relations and employ the induced knowledge granules to approximate arbitrary conce...

Article history: Received 28 April 2016 Received in revised form 12 December 2016 Accepted 14 December 2016 Available online 23 December 2016

1 Introduction

The notion of a rough two-dimensional (convex) body is introduced, and to each rough body there is assigned a measure on T3 describing billiard scattering on the body. The main result is characterization of the set of measures generated by rough bodies. This result can be used to solve various problems of least aerodynamical resistance. Mathematics subject classifications: 37N05, 49K30, 49Q10

Article history: Received 17 May 2011 Received in revised form 3 May 2012 Accepted 24 May 2012 Available online xxxx

Article history: Available online 24 May 2012

Article history: Received 29 March 2012 Received in revised form 22 January 2013 Accepted 14 March 2013 Available online 2 April 2013

The lower and upper approximations are basic concepts in rough set theory, and the approximations will change dynamically over time. Incremental methods for updating approximations in rough set theory and its extension has been received much attention recently. This paper presents an approach for incrementally updating approximations of fuzzy rough sets in dynamic fuzzy decision systems when a ...