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

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

Level subsets and translations of QFST(G)

First, we introduce level subsets and translations of  QFST(G)  and study their properties.  Secondly,  we prove that the union and intersection of two-level subsets of QTST(G)  are subgroups of G. Also we prove that translations of  QTST(G)  are also  QFST(G).  Finally,  we define  fuzzy image and fuzzy pre-image of translations of  QFST(G)  under group homomorphisms and anti group homomorphisms and investigate properties of them

NEW CLASS OF SOFT LINEAR ALGEBRAIC CODES AND THEIR PROPERTIES USING SOFT SETS

Algebraic codes play a signiÖcant role in the minimization of data corruption which caused by defects such as inference, noise channel, crosstalk, and packet lost. In this paper, we introduced soft codes (soft linear codes) through the application of soft sets which is an approximated collection of codes. We also discussed several types of soft codes such as type-1 soft codes, complete soft codes etc. The innovative idea of soft codes is advantageous, for it can simultaneously transmit n-distinct messages to n-set of receivers. Further this new technique makes use of bi-matrices or to be more general uses the concept of n-matrices. Certainly this notion will save both time and economy. Moreover, we develop two techniques for the decoding of soft codes. At the end, we present a soft communication process and develop a model for this soft communication process. The distinctions and comparison of soft linear codes and linear codes are also presented

Cyclic Soft Groups and Their Applications on Groups

In crisp environment the notions of order of group and cyclic group are well known due to many applications. In this paper, we introduce order of the soft groups, power of the soft sets, power of the soft groups, and cyclic soft group on a group. We also investigate the relationship between cyclic soft groups and classical groups