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...

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. However, in real-life datasets, in the presence of noise, the notions of lower and upper approximations handling inconsistencies were found to be excessively restrictive which led to the proposal of the variable ...

Many researchers have combined rough set theory and fuzzy set theory in order to easily approach problems of imprecision and uncertainty. Covering-based rough sets are one of the important generalizations of classical rough sets. Naturally, covering-based fuzzy rough sets can be studied as a combination of covering-based rough set theory and fuzzy set theory. It is clear that Pawlak’s rough set...

A ternary semigroup is a nonempty set together with a ternary multiplication which is associative. Any semigroup can be reduced to a ternary semigroup but a ternary semigroup does not necessarily reduce to a semigroup. The notion of fuzzy sets was introduced by Zadeh in 1965 and that of rough sets by Pawlak in 1982. Applications of the fuzzy set theory and rough set theory have been found in va...