Neutro Algebra and Neutro Group

Abstract

This chapter improves and extends several definitions, properties, and applications of neutro-algebras. In classical algebraic structures, the laws of compositions on a given set are well-defined. In fuzzy algebraic structures, the laws of compositions on a given set are not well-defined exactly but with a membership value. This chapter examines those structures which have huge applications or strong potential for applications outside of mathematics, namely computer science or engineering. The study emphasizes that the nature of neutro-algebra and anti-neutro algebra differs from that of the classical algebra and fuzzy algebra. This chapter presents Venn diagram for neutro-function and establishes some relations between the partial algebra and neutro-algebra. The main contribution of the chapter is the introduction of the notion of neutro-group.