Dominance-based rough set introduced by Greco et al. is an extension of Pawlak’s classical rough set theory by using dominance relations in place of equivalence relations for approximating sets of preference ordered decision classes satisfying upward and downward union properties. This paper introduces the concept of indexed blocks for representing dominance-based approximation spaces. Indexed ...

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...

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