Refined Literal Indeterminacy and the Multiplication Law of Sub-Indeterminacies

Abstract

In this paper, we make a short history about: the
neutrosophic set, neutrosophic numerical components and
neutrosophic literal components, neutrosophic numbers,
neutrosophic intervals, neutrosophic hypercomplex numbers of dimension n, and elementary neutrosophic algebraic structures. Afterwards, their generalizations to refined neutrosophic set, respectively refined neutrosophic
numerical and literal components, then refined neutrosophic numbers and refined neutrosophic algebraic structures. The aim of this paper is to construct examples of
splitting the literal indeterminacy ሺࡵሻ into literal sub-indeterminacies ሺࡵ૚, ࡵ૛,...,࢘ࡵሻ, and to define a multiplication
law of these literal sub-indeterminacies in order to be able
to build refined ࡵ െ neutrosophic algebraic structures.
Also, examples of splitting the numerical indeterminacy
ሺ࢏ሻ into numerical sub-indeterminacies, and examples of
splitting neutrosophic numerical components into neutrosophic numerical sub-components are given.