Creating Generalized and Hybrid Set and Library with Neutrosophy and Quad-Stage Method

Creating Generalized and Hybrid Set and Library with Neutrosophy and Quad-Stage Method

Yuhua Fu (CNOOC Research Institute, China)
DOI: 10.4018/978-1-4666-9798-0.ch015
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Abstract

Generalized and hybrid set can be created with neutrosophy and quad-stage method. Firstly the generalized and hybrid neutrosophic set is discussed. Secondly the combination or synthetical body of generalized and hybrid sets is named as “library” (various generalized and hybrid sets can be put into the related “library”); such as “mathematics library”, “physics library”, and the like. As for the constitution of “library”, the concept and methodology of a special “Four-library” are proposed. Neutrosophy and quad-stage method can also be used to solve many actual problems within the framework of “set” and “library”; for example, based on the analyses of one “Four-library”, jointly solving problem of advance of planet's perihelion with partial results of law of gravity and general relativity; and jointly expanding “uncertainty principle” to “certainty-uncertainty principle set”. Finally, we introduce the concepts of “variational principle of set” and “variational principle of library”, and establish a kind of “partial and temporary unified theory of mathematics so far”.
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Introduction

At present, the concept of “set” has failed to meet the need to solve many practical problems, therefore it should be expanded into generalized and hybrid set. There are many ways to create generalized and hybrid set. This paper discusses the application of neutrosophy and quad-stage method to create generalized and hybrid set, and focuses on generalized and hybrid neutrosophic set. On this basis, some new concepts and methods related to generalized and hybrid set are presented.

Basic Contents of Neutrosophy

Neutrosophy is proposed by Prof. Florentin Smarandache in 1995.

Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra.

This theory considers every notion or idea <A> together with its opposite or negation <Anti-A> and the spectrum of “neutralities” <Neut-A> (i.e. notions or ideas located between the two extremes, supporting neither <A> nor <Anti-A>). The <Neut-A> and <Anti-A> ideas together are referred to as <Non-A>.

Neutrosophy is the base of neutrosophic logic, neutrosophic set, neutrosophic probability and statistics used in engineering applications (especially for software and information fusion), medicine, military, cybernetics, and physics.

Neutrosophic Logic is a general framework for unification of many existing logics, such as fuzzy logic (especially intuitionistic fuzzy logic), paraconsistent logic, intuitionistic logic, etc. The main idea of NL is to characterize each logical statement in a 3D Neutrosophic Space, where each dimension of the space represents respectively the truth (T), the falsehood (F), and the indeterminacy (I) of the statement under consideration, where T, I, F are standard or non-standard real subsets of ]-0, 1+[ without necessarily connection between them.

More information about Neutrosophy can be found in references (Smarandache, 2003; Fu, 2013a).

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