Interval Neutrosophic Sets and Logic: Theory and Applications in Computing

By Haibin Wang, Florentin Smarandache, Yanqing Zhang, Rajshekhar Sunderraman. arXiv.org, 2005

744 citations recorded by the source corpus.

This book presents the advancements and applications of neutrosophics. 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.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/3482e5e305abced9f8fffe9b0d903cac046ced1b

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Florentin Smarandache

Citations in the corpus

Neutrosophic Game Theoretic Approach to Indo-Pak Conflict over Jammu-Kashmir (2013, methodology): “We hope that the concept of the interval neutrosophic set [88] can be used to formulate interval neutrosophic game theoretic model of the Indo-Pak conflict in more general way.”
Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean (2014, background): “[15] defined interval neutrosophic sets (INSs) in which the truth-membership, indeterminacy-membership, and false-membership were extended to interval numbers and proved various properties of INSs.”
Relations on Interval Valued Neutrosophic Soft Sets (2014, background): “[40] Let X be a space of points (objects) with generic elements in X denoted by x.”
Correlation Coefficient of Interval Neutrosophic Set (2013, background): “It is a branch of philosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra [2].”
Neutrosophic Sets: An Overview (2018, background): “…valued neutrosophic set A (SVNS ) is characterized by truth-membership function ( ) A T x ) x , and a falsity-membership function ( ) x A SVNS A can be written as 3 Interval valued neutrosophic sets (Wang et al., 2005) Let 𝜉 be a space of points (objects) with generic elements in X denoted by x.”
Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems (2014, background): “Definition 6 (see [31]).”
Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making (2014, neutral): “Section introduces the some concepts of neutrosophic ] and INSs [5].”
Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses (2015, neutral): “For two INSs A = {x, T A (x), I A (x), F A (x)| x ∈ X} and B = {x, T B (x), I B (x), F B (x)| x ∈ X}, there are the following relations [12]: (1) Complement: A c = { x, [inf F A (x), sup F A (x)], [1 − sup I A (x), 1 − inf I A (x)], [inf T A (x), sup T A (x) |x ∈ X}; (2) Inclusion: A ⊆ B if and…”
Neutrosophic Precalculus and Neutrosophic Calculus (2015, background): “93 <5, 5, 1>, <5, 5, 3>, <5, 5, 5>, <5, 5, 7>, <5, 5, 9>, so four anti(5)'s = 1, 3, 5, 7, 9; <6, 6, 1>, <6, 6, 6>, so two anti(6)'s = 1, 6; <8, 6, 2>, <8, 6, 7>, so two anti(8)'s = 2, 7.”