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In this paper, the authors introduce lattice valued neutrosophic sets and study their properties. A decomposition theorem for lattice valued neutrosophic sets is obtained. Lattice valued neutrosophic mappings are defined and verified that its properties are consistent with their crisp counterparts. Finally, a topology of lattice valued neutrosophic sets is introduced.
Book Synopsis Lattice Valued Neutrosophic Sets by : Jose James
Download or read book Lattice Valued Neutrosophic Sets written by Jose James and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the authors introduce lattice valued neutrosophic sets and study their properties. A decomposition theorem for lattice valued neutrosophic sets is obtained. Lattice valued neutrosophic mappings are defined and verified that its properties are consistent with their crisp counterparts. Finally, a topology of lattice valued neutrosophic sets is introduced.
The main purpose of this paper is to study the inclusion relations of neutrosophic sets and some applications in multiple attribute decision making.
Book Synopsis New inclusion relation of neutrosophic sets with applications and related lattice structure by : Florentin Smarandache
Download or read book New inclusion relation of neutrosophic sets with applications and related lattice structure written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this paper is to study the inclusion relations of neutrosophic sets and some applications in multiple attribute decision making.
In recent year, the mathematics of three-way fuzzy concept lattice is introduced to characterize the attributes based on its acceptation, rejection and uncertain part. One of the suitable example is descriptive analysis of opinion of people in a democratic country. This became complex for the country like India where opinion (i.e. vote) of people to choose the particular leader is based on 29 independent states and their distinct issues. Adequate analysis of these type of 29-valued data based on its acceptation, rejection and uncertain part is major issue for the government and private agencies. To resolve this issue current paper introduces n-valued neutrosophic context and its graphical structure visualization for descriptive analysis. In the same time an another method is proposed to some of the similar three-way n-valued concepts. To zoom in and zoom out the n-valued neutrosophic context at user required information granules with an illustrative example.
Book Synopsis Three-way n-valued neutrosophic concept lattice at different granulation by : Prem Kumar Singh
Download or read book Three-way n-valued neutrosophic concept lattice at different granulation written by Prem Kumar Singh and published by Infinite Study. This book was released on with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent year, the mathematics of three-way fuzzy concept lattice is introduced to characterize the attributes based on its acceptation, rejection and uncertain part. One of the suitable example is descriptive analysis of opinion of people in a democratic country. This became complex for the country like India where opinion (i.e. vote) of people to choose the particular leader is based on 29 independent states and their distinct issues. Adequate analysis of these type of 29-valued data based on its acceptation, rejection and uncertain part is major issue for the government and private agencies. To resolve this issue current paper introduces n-valued neutrosophic context and its graphical structure visualization for descriptive analysis. In the same time an another method is proposed to some of the similar three-way n-valued concepts. To zoom in and zoom out the n-valued neutrosophic context at user required information granules with an illustrative example.
This book presents the advancements and applications of neutrosophics, which are generalizations of fuzzy logic, fuzzy set, and imprecise probability. The neutrosophic logic, neutrosophic set, neutrosophic probability, and neutrosophic statistics are increasingly used in engineering applications (especially for software and information fusion), medicine, military, cybernetics, physics.In the last chapter a soft semantic Web Services agent framework is proposed to facilitate 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.
Book Synopsis Interval Neutrosophic Sets and Logic: Theory and Applications in Computing by : Haibin Wang
Download or read book Interval Neutrosophic Sets and Logic: Theory and Applications in Computing written by Haibin Wang and published by Infinite Study. This book was released on 2005 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the advancements and applications of neutrosophics, which are generalizations of fuzzy logic, fuzzy set, and imprecise probability. The neutrosophic logic, neutrosophic set, neutrosophic probability, and neutrosophic statistics are increasingly used in engineering applications (especially for software and information fusion), medicine, military, cybernetics, physics.In the last chapter a soft semantic Web Services agent framework is proposed to facilitate 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.
In this paper, we examine the relationship between rough fuzzy neutrosophic sets and lattice theory. We introduce the notion of Rough fuzzy neutrosophic set and Rough fuzzy neutrosophic lattice (resp Rough fuzzy neutrosophic ideals).
Book Synopsis Rough neutrosophic set in a lattice by : I Arockiarani
Download or read book Rough neutrosophic set in a lattice written by I Arockiarani and published by Infinite Study. This book was released on with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we examine the relationship between rough fuzzy neutrosophic sets and lattice theory. We introduce the notion of Rough fuzzy neutrosophic set and Rough fuzzy neutrosophic lattice (resp Rough fuzzy neutrosophic ideals).
In this paper, we present the lattice structures of neutrosophic theories. We prove that Zhang-Zhang’s YinYang bipolar fuzzy set is a subclass of the Single-Valued bipolar neutrosophic set. Then we show that the pair structure is a particular case of refined neutrosophy, and the number of types of neutralities (sub-indeterminacies) may be any finite or infinite number.
Book Synopsis Refined Neutrosophy and Lattices vs. Pair Structures and YinYang Bipolar Fuzzy Set by : Florentin Smarandache
Download or read book Refined Neutrosophy and Lattices vs. Pair Structures and YinYang Bipolar Fuzzy Set written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we present the lattice structures of neutrosophic theories. We prove that Zhang-Zhang’s YinYang bipolar fuzzy set is a subclass of the Single-Valued bipolar neutrosophic set. Then we show that the pair structure is a particular case of refined neutrosophy, and the number of types of neutralities (sub-indeterminacies) may be any finite or infinite number.
Neutrosophic set is a part of neutrosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic set is a powerful general formal framework that has been recently proposed. However, neutrosophic set needs to be specified from a technical point of view. To this effect, we define the settheoretic operators on an instance of neutrosophic set, we call it single valued neutrosophic set (SVNS). We provide various properties of SVNS, which are connected to the operations and relations over SVNS.
Book Synopsis Single Valued Neutrosophic Sets by : Haibin Wang
Download or read book Single Valued Neutrosophic Sets written by Haibin Wang and published by Infinite Study. This book was released on 2010-01-01 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic set is a part of neutrosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic set is a powerful general formal framework that has been recently proposed. However, neutrosophic set needs to be specified from a technical point of view. To this effect, we define the settheoretic operators on an instance of neutrosophic set, we call it single valued neutrosophic set (SVNS). We provide various properties of SVNS, which are connected to the operations and relations over SVNS.
Neutrosophic triangular norms (t-norms) and their residuated lattices are not only the main research object of neutrosophic set theory, but also the core content of neutrosophic logic. Neutrosophic implications are important operators of neutrosophic logic. Neutrosophic residual implications based on neutrosophic t-norms can be applied to the fields of neutrosophic inference and neutrosophic control. In this paper, neutrosophic t-norms, neutrosophic residual implications, and the residuated lattices derived from neutrosophic t-norms are investigated deeply. First of all, the lattice and its corresponding system are proved to be a complete lattice and a De Morgan algebra, respectively. Second, the notions of neutrosophic t-norms are introduced on the complete lattice discussed earlier. The basic concepts and typical examples of representable and non-representable neutrosophic t-norms are obtained. Naturally, De Morgan neutrosophic triples are defined for the duality of neutrosophic t-norms and neutrosophic t-conorms with respect to neutrosophic negators. Third, neutrosophic residual implications generated from neutrosophic t-norms and their basic properties are investigated. Furthermore, residual neutrosophic t-norms are proved to be infinitely -distributive, and then some important properties possessed by neutrosophic residual implications are given. Finally, a method for producing neutrosophic t-norms from neutrosophic implications is presented, and the residuated lattices are constructed on the basis of neutrosophic t-norms and neutrosophic residual implications.
Book Synopsis Neutrosophic Triangular Norms and Their Derived Residuated Lattices by : Qingqing Hu
Download or read book Neutrosophic Triangular Norms and Their Derived Residuated Lattices written by Qingqing Hu and published by Infinite Study. This book was released on with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic triangular norms (t-norms) and their residuated lattices are not only the main research object of neutrosophic set theory, but also the core content of neutrosophic logic. Neutrosophic implications are important operators of neutrosophic logic. Neutrosophic residual implications based on neutrosophic t-norms can be applied to the fields of neutrosophic inference and neutrosophic control. In this paper, neutrosophic t-norms, neutrosophic residual implications, and the residuated lattices derived from neutrosophic t-norms are investigated deeply. First of all, the lattice and its corresponding system are proved to be a complete lattice and a De Morgan algebra, respectively. Second, the notions of neutrosophic t-norms are introduced on the complete lattice discussed earlier. The basic concepts and typical examples of representable and non-representable neutrosophic t-norms are obtained. Naturally, De Morgan neutrosophic triples are defined for the duality of neutrosophic t-norms and neutrosophic t-conorms with respect to neutrosophic negators. Third, neutrosophic residual implications generated from neutrosophic t-norms and their basic properties are investigated. Furthermore, residual neutrosophic t-norms are proved to be infinitely -distributive, and then some important properties possessed by neutrosophic residual implications are given. Finally, a method for producing neutrosophic t-norms from neutrosophic implications is presented, and the residuated lattices are constructed on the basis of neutrosophic t-norms and neutrosophic residual implications.
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.
Book Synopsis Neutrosophic Sets and Systems, Vol. 31, 2020 by : Florentin Smarandache
Download or read book Neutrosophic Sets and Systems, Vol. 31, 2020 written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.
In the current year, the precise measurement of uncertainty and fluctuation exists in a complex fuzzy at- tributes is addressed as computationally and mathematically expensive tasks with regard to its graphical analytics.
Book Synopsis Complex neutrosophic concept lattice and its applications to air quality analysis by : Prem Kumar Singh
Download or read book Complex neutrosophic concept lattice and its applications to air quality analysis written by Prem Kumar Singh and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the current year, the precise measurement of uncertainty and fluctuation exists in a complex fuzzy at- tributes is addressed as computationally and mathematically expensive tasks with regard to its graphical analytics.
