Refined Literal Indeterminacy and the Multiplication Law of Sub-Indeterminacies

• Main Author: Florentin Smarandache
• Format: Article
• Language: English
• Published: University of New Mexico 2015-09-01
• Series: Neutrosophic Sets and Systems
• Subjects: neutrosophic set; elementary neutrosophic algebraic structures; neutrosophic numerical components; neutrosophic literal components; neutrosophic numbers; refined neutrosophic set; refined elementary neutrosophic algebraic structures; refined neutrosophic numerical components; refined neutrosophic literal components
• Online Access: http://fs.gallup.unm.edu/NSS/Refined%20Literal%20Indeterminacy.pdf

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 into literal sub-indeterminacies, and to define a multiplication law of these literal sub-indeterminacies in order to be able to build refined neutrosophic algebraic structures. Also, examples of splitting the numerical indeterminacy into numerical sub-indeterminacies, and examples of splitting neutrosophic numerical components into neutrosophic numerical sub-components are given.