Set-valued mapping and Rough Probability

In 1982, the theory of rough sets proposed by Pawlak and in 2013, Luay concerned a rough probability by using the notion of Topology. In this paper, we study the rough probability in the stochastic approximation spaces by using set-valued mapping and obtain results on rough expectation, and rough variance.Comment: 9 page

Some Properties of Rough Ideals on Rough Rings

The concept of rough set was first introduced by Pawlak in 1982. The basic concepts in set theory such as intersections, unions, differences, and complements still apply to rough sets. Furthermore, researchers in the field of mathematics and informatics who study rough sets can relate the concept of rough sets to algebraic structures so that a concept called rough algebraic structures is obtained. Some concepts on rough algebraic structures are rough groups, rough rings, and rough modules. In this paper, the properties related to the ideal of roughness will be given to the rough ring.Konsep himpunan kasar pertama kali diperkenalkan oleh Pawlak pada tahun 1982. Konsep dasar pada teori himpunan seperti irisan, gabungan, selisih, dan komplemen masih berlaku pada himpunan kasar. Selanjutnya, para peneliti bidang matematika dan informatika yang mendalami himpunan kasar dapat mengaitkan konsep himpunan kasar dengan struktur aljabar sehingga diperoleh konsep yang dinamakan struktur aljabar kasar. Beberapa konsep pada struktur aljabar kasar adalah grup kasar, ring kasar, dan modul kasar. Pada paper ini, akan diberikan sifat-sifat terkait ideal kasar pada dari ring kasar

Roughness in Anti Semigroup

In this paper, we present the concepts of the upper and lower approximations of Anti-rough subgroups, Anti-rough subsemigroups, and homeomorphisms of Anti-Rough anti-semigroups in approximation spaces. Specify the concepts of rough in Finite anti-groups of types(4) are studies. Moreover, some properties of approximations and these algebraic structures are introduced. In addition, we give the definition of homomorphism anti-group

Sub-exact sequence of rough groups

Rough Set Theory (RST) is an essential mathematical tool to deal with imprecise, inconsistent, incomplete information and knowledge Rough Some algebra structures, such as groups, rings, and modules, have been presented on rough set theory. The sub-exact sequence is a generalization of the exact sequence. In this paper, we introduce the notion of a sub-exact sequence of groups. Furthermore, we give some properties of the rough group and rough sub-exact sequence of groups.

The Implementation of Rough Set on A Group Structure

Let  be a non-empty set and  an equivalence relation on . Then,  is called an approximation space. The equivalence relation on  forms disjoint equivalence classes. If , then we can form a lower approximation and an upper approximation of . If X⊆U, then we can form a lower approximation and an upper approximation of X. In this research, rough group and rough subgroups are constructed in the approximation space  for commutative and non-commutative binary operations

Rough sets applied in sublattices and ideals of lattices

The purpose of this paper is the study of rough hyperlattice. In this regards we introduce rough sublattice and rough ideals of lattices. We will proceed by obtaining lower and upper approximations in these lattices

Himpunan Fuzzy dan Rough Sets

The concept of a fuzzy set was introduced by Zadeh in 1965. Fuzzy set is a mathematical model of vague qualitative or quantitative data, frequently generated by means of the natural language. The model is based on the generalization of the classical concepts of set and its characteristic function. Intuitionistic fuzzy sets are sets whose elements have degrees of membership and non-membership. Intuitionistic fuzzy sets have been introduced by Atanassov in 1983 as an extension fuzzy sets. On the other hand, the concept of rough set was proposed by Pawlak 1982. Since then the subject has been investigated in many papers. The overall aim of this paper is to present an introduction to some of main concepts related to fuzzy sets, intuitionistic fuzzy sets and rough sets. We investigate Crisp sets and characteristic functions, fuzzy sets, intuitionistic fuzzy sets, rough sets and probabilistic rough sets