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 ...

The notion of three-way decisions was originally introduced by the needs to explain the three regions of probabilistic rough sets. Recent studies show that rough set theory is only one of possible ways to construct three regions. A more general theory of three-way decisions has been proposed, embracing ideas from rough sets, interval sets, shadowed sets, three-way approximations of fuzzy sets, ...

The paper investigates relationships between chemical structure, surface active properties and antibacterial activity of 70 bis-quaternary imidazolium chlorides. Chemical structure and properties of imidazolium chlorides were described by 7 condition attributes and antimicrobial properties were mapped by a decision attribute. Dominance-based Rough Set Approach (DRSA) was applied to discover a p...

Dominance-based Rough Set Approach (DRSA) is an extension of classical Rough Set Theory (RST). Approximation of class unions is a very important approach in DRSA. Aiming at the disadvantage of the classical method we presented a new methodology for approximation of class unions based on dominance-matrix. It only needs to calculate the dominance-matrix and does not need to consider the preferenc...