Formal concept ring, an algebraic machine to equip the formal concept analysis with more constructive operations

Formal Concept Analysis (FCA) as a well-known method in data analysis, has been widely noticed by researchers in pure and applied fields. Despite the increasing development in the application area, more work needs to be done in the pure area. Designing a theoretical system based on an algebraic-analytical structure is a significant help in enhancing its power to meet the needs of researchers. Therefore, in this article, by designing a system equipped with addition and multiplication, the development of Galois lattices will be discussed as the main goal. In the shadow of such extension, we will be able to achieve a special category of partially ordered rings, by defining partial and complete approximations. Hence, some fundamental results in FCA will be developed as induced properties from ring theory intuition. \textbf{ Two significant results of this research will devote to provide the possibility of combining concepts with each other, as well as breaking the space into much distinguished components. As a result, this yields a new window in the subject of digital communication, which provides the possibility of joining concepts. The long-term prospective of this study is to assign a new observation in Big Data Analysis, based on FCA.}

کلیدواژه ها:

Approximation by ideals ، Attribute implication ، Big data ، Concept word ، Decomposable element ، Digital communication ، Formal concept ring ، Galois concept ring