The role of opposition in rough set theory is laid bare. There are two sources which generate oppositions in rough sets: approximations and relations. In the former case, we outline a hexagon and a cube of oppositions. In the second case, we define a classical square of oppositions and also a tetrahedron when considering the standpoint of two agents.

Information granulation and concept approximation are some of the fundamental issues of granular computing. Granulation of a universe involves grouping of similar elements into granules to form coarse-grained views of the universe. Approximation of concepts, represented by subsets of the universe, deals with the descriptions of concepts using granules. In the context of rough set theory, this p...

This paper researches on potential relations of dependency space, closure system and rough set theory, and mainly focuses on solving some essential problems of rough set theory based on dependency space and closure system respectively. Firstly, we pretreat an information system into a relatively simple derivative system, in which dependency space and closure system are generated; Secondly, by m...

In this paper, we discuss some basic properties of rough intuitionistic fuzzy set in semigroup. Intuitionistic fuzzy analogues of some results concerning rough semiprime (semiprimary) ideals in semigroup are obtained. 2010 AMS Classification: 03E72, 03F55, 06B10.

Supplier performance management and continuous improvement play an important role for organizational and supply chain development. Many broad-based empirical studies have provided insights into the relationships of supplier development practices to supplier performance. Yet, specific tools available for organizations to internally evaluate such relationships are limited. To help further the res...

The paradigm of granular rough computing has risen quite recently — was initiated by Professor Lotfi Zadeh in 1979. This paradigm is strictly connected with the Rough Set Theory, which was proposed by Professor Zdzisław Pawlak in 1982. Granular rough computing is a paradigm in which one deals with granules that are aggregates of objects connected together by some form of similarity. In the roug...

This paper presents some roughness bounds for rough set operations. The results show that a bound of the set operation can be determined from their operand’s roughnesses. We prove also that this bound is not determined under some special operations.

This paper deals with rough set approach on lattice theory. We represent the lattices for rough sets determined by an equivalence relation. Without any loss of generality, we have defined the rough set as a pair of sets (lower approximation set, upper approximation set) and then we showed that the collection of all rough sets of an approximations by an equivalence relation form a lattice by som...

Multisets alias bags are similar to fuzzy sets but essentially different in basic concepts and operations. We overview multisets together with basics of fuzzy sets in order to observe differences between the two. We then introduce fuzzy multisets and the combination of the both concepts. There is another concept of real-valued multisets as a generalization of multisets. Rough approximations of ...