In the paper we explore the idea of describing Pawlak’s rough sets using three-valued logic, whereby the value t corresponds to the positive region of a set, the value f — to the negative region, and the undefined value u — to the border of the set. Due to the properties of the above regions in rough set theory, the semantics of the logic is described using a non-deterministic matrix (Nmatrix)....

The rough-set theory proposed by Pawlak, has been widely used in dealing with data classification problems. The original rough-set model is, however, quite sensitive to noisy data. Tzung thus proposed deals with the problem of producing a set of fuzzy certain and fuzzy possible rules from quantitative data with a predefined tolerance degree of uncertainty and misclassification. This model allow...

On the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set (SVNHFS) as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single-valued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, we introduce the basic operational relations and cosine...

The optimistic multigranulation T-fuzzy rough set model was established based on multiple granulations under T-fuzzy approximation space by Xu et al., 2012. From the reference, a natural idea is to consider pessimistic multigranulation model in T-fuzzy approximation space. So, in this paper, the main objective is to make further studies according to Xu et al., 2012. The optimistic multigranulat...

In this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. Finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.

Set-valued information systems are generalized models of single-valued information systems. In this paper, we propose two new relations for set-valued information systems. Based on these two relations, the concepts of knowledge information entropy, knowledge rough entropy, knowledge granulation and knowledge granularity measure are defined in set-valued information systems, and some properties ...

The fuzzy measure can highlight important information in analyzing component features, patterns, and trends. However, fuzzy densities and interaction effects are usually unknown or uncertain for implications thus making the fuzzy measure limited in applications. This research proposes an extended fuzzy measure to derive the conditional fuzzy densities from dominance-based rough set approach (DR...

Granular structure plays a very important role in the model construction, theoretical analysis and algorithm design of a granular computing method. The granular structures of classical rough sets and fuzzy rough sets have been proven to be clear. In classical rough set theory, equivalence classes are basic granules, and the lower and upper approximations of a set can be computed by those basic ...

Rough set theory has attracted much attention in modeling with imprecise and incomplete information. A generalized approximation space, called fuzzy probability approximation space has been proposed by introducing probability into fuzzy approximation space. The novel definition combines three types of uncertainty into a model. Information or knowledge is considered as a partition of the univers...