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Interval Neutrosophic Sets and Logic : Theory and Applications in Computing

By Smarandache, Florentin

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Book Id: WPLBN0002828372
Format Type: PDF (eBook)
File Size: 1.73 mb
Reproduction Date: 7/29/2013

Title: Interval Neutrosophic Sets and Logic : Theory and Applications in Computing  
Author: Smarandache, Florentin
Volume:
Language: English
Subject: Non Fiction, Technology, Neutrosophic Systems
Collections: Mathematics, Logic, Algebra, Authors Community, Technology, Engineering, Math, Sociolinguistics, Philosophy, Most Popular Books in China, Fine Arts, Literature, Language
Historic
Publication Date:
2013
Publisher: World Public Library
Member Page: Florentin Smarandache

Citation

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Smarandache, F., & Wang, H. (2013). Interval Neutrosophic Sets and Logic : Theory and Applications in Computing. Retrieved from http://worldlibrary.in/


Description
Chapter 1 first introduces the interval neutrosophic sets which is an instance of neutrosophic sets. In this chapter, the definition of interval neutrosophic sets and set-theoretic operators are given and various properties of interval neutrosophic set are proved. Chapter 2 defines the interval neutrosophic logic based on interval neutrosophic sets including the syntax and semantics of first order interval neutrosophic propositional logic and first order interval neutrosophic predicate logic. The interval neutrosophic logic can reason and model fuzzy, incomplete and inconsistent information. In this chapter, we also design an interval neutrosophic inference system based on first order interval neutrosophic predicate logic. The interval neutrosophic inference system can be applied to decision making. Chapter 3 gives one application of interval neutrosophic sets and logic in the field of relational databases. Neutrosophic data model is the generalization of fuzzy data model and paraconsistent data model. Here, we generalize various set-theoretic and relation-theoretic operations of fuzzy data model to neutrosophic data model. Chapter 4 gives another application of interval neutrosophic logic. A soft semantic Web Services agent framework is proposed to faciliate the registration and discovery of high quality semantic Web Services agent. The intelligent inference engine module of soft Semantic Web Services agent is implemented using interval neutrosophic logic.

Summary
This book presents the advancements and applications of neutrosophics.

Excerpt
The neutrosophic set generalizes the above mentioned sets from philosophical point of view. From scientific or engineering point of view, the neutrosophic set and set-theoretic operators need to be specified. Otherwise, it will be difficult to apply in the real applications. In this chapter, we de_ne the set theoretic operators on an instance of neutrosophic set called Interval Neutrosophic Set (INS). We call it as “interval" because it is subclass of neutrosophic set, that is we only consider the subunitary interval of [0; 1].

Table of Contents
Preface iii 1 Interval Neutrosophic Sets 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Neutrosophic Set . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Interval Neutrosophic Set . . . . . . . . . . . . . . . . . . . . . 6 1.4 Properties of Set-theoretic Operators . . . . . . . . . . . . . . . . . . 14 1.5 Convexity of Interval Neutrosophic Set . . . . . . . . . . . . . . . . . . 15 1.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2 Interval Neutrosophic Logic 21 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 Interval Neutrosophic Propositional Calculus . . . . . . . . . . . . . . . 23 2.2.1 Syntax of Interval Neutrosophic Propositional Calculus . . . . . . . . . 23 2.2.2 Semantics of Interval Neutrosophic Propositional Calculus . . . . . . . . . 24 2.2.3 Proof Theory of Interval Neutrosophic Propositional Calculus . . . . . . . . 25 2.3 Interval Neutrosophic Predicate Calculus . . . . . . . . . . . . . . . . 27 2.3.1 Syntax of Interval Neutrosophic Predicate Calculus . . . . . . . . . . . . 27 2.3.2 Semantics of Interval Neutrosophic Predicate Calculus . . . . . . . . . . 29 2.3.3 Proof Theory of Interval Neutrosophic Predicate Calculus . . . . . . . . . 30 2.4 An Application of Interval Neutrosophic Logic . . . . . . . . . . . . . . . 32 2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3 Neutrosophic Relational Data Model 39 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.2 Fuzzy Relations and Operations . . . . . . . . . . . . . . . . . . . . 42 3.2.1 Set-theoretic operations on Fuzzy relations . . . . . . . . . . . . . . 42 3.2.2 Relation-theoretic operations on Fuzzy relations . . . . . . . . . . . . 43 3.3 Neutrosophic Relations . . . . . . . . . . . . . . . . . . . . . . . 43 3.4 Generalized Algebra on Neutrosophic Relations . . . . . . . . . . . . . . . 47 3.5 An Application . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.6 An In_nite-Valued Tuple Relational Calculus . . . . . . . . . . . . . . . 54 3.6.1 An Example . . . . . . . . . . . . . . . . . . . . . . . 57 3.7 A Generalized SQL Query Construct for Neutrosophic Relations . . . . . . . . . 58 3.7.1 In_nite-Valued Conditions . . . . . . . . . . . . . . . . . . . 59 3.7.2 An Example . . . . . . . . . . . . . . . . . . . . . . . 62 3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4 Soft Semantic Web Services Agent 65 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.2.1 Traditional Web services . . . . . . . . . . . . . . . . . . . . 67 4.2.2 Semantic Web . . . . . . . . . . . . . . . . . . . . . . . 68 4.2.3 Semantic Web Services . . . . . . . . . . . . . . . . . . . . . 68 4.2.4 Soft Computing Methodology . . . . . . . . . . . . . . . . . . 68 4.2.5 QoS Model . . . . . . . . . . . . . . . . . . . . . . . . 69 4.3 Architecture of Extensible Soft SWS Agent . . . . . . . . . . . . . . . . 69 4.3.1 Registries Crawler . . . . . . . . . . . . . . . . . . . . . 70 4.3.2 SWS Repository . . . . . . . . . . . . . . . . . . . . . . 71 4.3.3 Inquiry Server . . . . . . . . . . . . . . . . . . . . . . . 72 4.3.4 Publish Server . . . . . . . . . . . . . . . . . . . . . . . 73 4.3.5 Agent Communication Server . . . . . . . . . . . . . . . . . . 74 4.3.6 Intelligent Inference Engine . . . . . . . . . . . . . . . . . . 74 4.3.7 Design of Intelligent Inference Engine . . . . . . . . . . . . . . . 75 4.3.8 Input neutrosophic sets . . . . . . . . . . . . . . . . . . . . 76 4.3.9 Neutrosophic rule bases . . . . . . . . . . . . . . . . . . . . 76 4.3.10 Design of deneutrosophication . . . . . . . . . . . . . . . . . . 76 4.3.11 Genetic algorithms . . . . . . . . . . . . . . . . . . . . . 76 4.3.12 Simulations . . . . . . . . . . . . . . . . . . . . . . . . 78 4.4 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 79

 

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