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...

Abstract We discuss p-variation regularity of real-valued functions defined on [0, T], based on rectangular increments. When p > 1, there are two slightly different notions of p-variation; both of which are useful in the context of Gaussian roug paths. Unfortunately, these concepts were blurred in previous works [2, 3]; the purpose of this note is to show that the afore-mentioned notions of p-v...

Article history: Received 15 September 2008 Received in revised form 24 June 2011 Accepted 5 July 2011 Available online 23 July 2011

In this paper, it is remarked that BZ lattice structures can recover several theoretical approaches to rough sets, englobing their individual richness in a unique structure. Rough sets based on a similarity relation are also considered, showing that the BZ lattice approach turns out to be even more useful, since enables one to define another rough approximation, which is better than the corresp...

Article history: Received 25 October 2011 Received in revised form 16 March 2012 Accepted 23 June 2012 Available online 2 July 2012

Dominance-based Rough Set Approach (DRSA) has been proposed to deal with multi-criteria classification problems, where data may be inconsistent with respect to the dominance principle. In this paper, we consider different measures of the quality of approximation, which is the value indicating how much inconsistent the decision table is. We begin with the classical definition, based on the relat...