Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are s...

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...

In ring and module theory, the concept of an exact sequence is commonly employed. The generalized into U-exact V-coexact sequence. Rough set theory has also been applied to a variety algebraic structures, including groups, rings, modules, others. this study, we investigated characteristics rough in groups

This paper discusses the relationship between probability and fuzziness based on the process of perception. As a generalization of crisp set, fuzzy set is used to model fuzzy event as proposed by Zadeh. Similarly, we may consider rough set to represent rough event in terms of probability measure. Special attention will be given to conditional probability of fuzzy event as well as conditional pr...

Similarity rough set model for document clustering (SRSM) uses a generalized rough set model based on similarity relation and term co-occurrence to group documents in the collection into clusters. The model is extended from tolerance rough set model (TRSM) (Ho and Funakoshi, 1997). The SRSM methods have been evaluated and the results showed that it perform better than TRSM. However, in document...

  For efficiency evaluation of some of the Decision Making Units that have uncertain information, Rough Data Envelopment Analysis technique is used, which is derived from rough set theorem and Data Envelopment Analysis (DEA). In some situations rough data alter nonradially. To this end, this paper proposes additive rough–DEA model and illustrates the proposed model by a numerical example.

location selection is one of the most important activities in establishment of bank branches. choosing a suitable location have a direct impact on the performance of banks and also facilitating the achievement of other objectives. there are a lot of influential factors on the location selection which are complicated and therefore the traditional methods cannot be used. so we need to have a suit...

we consider the fundamental relation  on a semihypergroup  to interpret the lower and upper approximations as subsets of the fundamental semigroup  and we give some results in this connection. also, we introduce the notion of a bi-hyperideal to study the relationship between approximations and bi-hyperideals.