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New Operators on Interval Valued Neutrosophic Sets

Author: Abhijit Saha

Publisher: Infinite Study

Published:

Total Pages: 10

ISBN-13:

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As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed by F. Smarandache to represent imprecise, incomplete and inconsistent information existing in the real world. A neutrosophic set is characterized by a truth-membership function, an indeterminacy membership function, and a falsity-membership function. An interval neutrosophic set is an instance of a neutrosophic set, which can be used in real scientific and engineering applications. In this paper we have defined some new operators on interval valued neutrosophic sets and studied their properties. In addition, we give numerical examples to illustrate the defined operations.

Book Synopsis New Operators on Interval Valued Neutrosophic Sets by : Abhijit Saha

Download or read book New Operators on Interval Valued Neutrosophic Sets written by Abhijit Saha and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed by F. Smarandache to represent imprecise, incomplete and inconsistent information existing in the real world. A neutrosophic set is characterized by a truth-membership function, an indeterminacy membership function, and a falsity-membership function. An interval neutrosophic set is an instance of a neutrosophic set, which can be used in real scientific and engineering applications. In this paper we have defined some new operators on interval valued neutrosophic sets and studied their properties. In addition, we give numerical examples to illustrate the defined operations.

Arithmetic Operations of Neutrosophic Sets, Interval Neutrosophic Sets and Rough Neutrosophic Sets

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 18

ISBN-13:

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In approximation theory, neutrosophic set and logic show an important role. They are generalizations of intuitionistic fuzzy set and logic respectively. Based on neutrosophy, which is a new branch of philosophy, every idea X, has an opposite denoted as anti (X) and their neutral which is denoted as neut (X). These are the main features of neutrosophic set and logic. This chapter is based on the basic concepts of neutrosophic set as well as some of their hybrid structures. In this chapter, we define and study the notion of neutrosophic set and their basic properties. Moreover, interval-valued neutrosophic set are studied with some of their properties. Finally, we define rough neutrosophic sets.

Book Synopsis Arithmetic Operations of Neutrosophic Sets, Interval Neutrosophic Sets and Rough Neutrosophic Sets by : Florentin Smarandache

Download or read book Arithmetic Operations of Neutrosophic Sets, Interval Neutrosophic Sets and Rough Neutrosophic Sets written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In approximation theory, neutrosophic set and logic show an important role. They are generalizations of intuitionistic fuzzy set and logic respectively. Based on neutrosophy, which is a new branch of philosophy, every idea X, has an opposite denoted as anti (X) and their neutral which is denoted as neut (X). These are the main features of neutrosophic set and logic. This chapter is based on the basic concepts of neutrosophic set as well as some of their hybrid structures. In this chapter, we define and study the notion of neutrosophic set and their basic properties. Moreover, interval-valued neutrosophic set are studied with some of their properties. Finally, we define rough neutrosophic sets.

Some New Operations of (a, β, g) Interval Cut Set of Interval Valued Neutrosophic Sets

Author: Mehmet Şahin

Publisher: Infinite Study

Published:

Total Pages: 18

ISBN-13:

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In this paper, we define the disjunctive sum, difference and Cartesian product of two interval valued neutrosophic sets and study their basic properties. The notions of the (a, β, g) interval cut set of interval valued neutrosophic sets and the (a, β, g) strong interval cut set of interval valued neutrosophic sets are put forward. Some related properties have been established with proof, examples and counter examples.

Book Synopsis Some New Operations of (a, β, g) Interval Cut Set of Interval Valued Neutrosophic Sets by : Mehmet Şahin

Download or read book Some New Operations of (a, β, g) Interval Cut Set of Interval Valued Neutrosophic Sets written by Mehmet Şahin and published by Infinite Study. This book was released on with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we define the disjunctive sum, difference and Cartesian product of two interval valued neutrosophic sets and study their basic properties. The notions of the (a, β, g) interval cut set of interval valued neutrosophic sets and the (a, β, g) strong interval cut set of interval valued neutrosophic sets are put forward. Some related properties have been established with proof, examples and counter examples.

Some New Operations of (𝜶, 𝜷, 𝜸) Interval Cut Set of Interval Valued Neutrosophic Sets

Author: Mehmet Şahin

Publisher: Infinite Study

Published:

Total Pages: 18

ISBN-13:

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In this paper, we define the disjunctive sum, difference and Cartesian product of two interval valued neutrosophic sets and study their basic properties.

Book Synopsis Some New Operations of (𝜶, 𝜷, 𝜸) Interval Cut Set of Interval Valued Neutrosophic Sets by : Mehmet Şahin

Download or read book Some New Operations of (𝜶, 𝜷, 𝜸) Interval Cut Set of Interval Valued Neutrosophic Sets written by Mehmet Şahin and published by Infinite Study. This book was released on with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we define the disjunctive sum, difference and Cartesian product of two interval valued neutrosophic sets and study their basic properties.

Operations on Interval Valued Neutrosophic Graphs

Author: BROUMI, S.

Publisher: Infinite Study

Published:

Total Pages: 24

ISBN-13:

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Combining the single valued neutrosophic set with graph theory, a new graph model emerges, called single valued neutrosophic graph.

Book Synopsis Operations on Interval Valued Neutrosophic Graphs by : BROUMI, S.

Download or read book Operations on Interval Valued Neutrosophic Graphs written by BROUMI, S. and published by Infinite Study. This book was released on with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining the single valued neutrosophic set with graph theory, a new graph model emerges, called single valued neutrosophic graph.

A two level interval valued neutrosophic AHP integrated TOPSIS methodology for post-earthquake fire risk assessment: An application for Istanbul

Author: Pelin Gulum

Publisher: Infinite Study

Published:

Total Pages: 17

ISBN-13:

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Earthquakes are the leading natural disasters that seriously affect human life. Furthermore, earthquakes are natural disasters that have the ability to trigger a second disaster in addition to the damages they cause. From this point of view, post-earthquake fires are defined as the one of the most dangerous secondary disasters after an earthquake and often cause even more serious dangers. For this reason, government officials and relevant decision-makers should effectively determine post-earthquake fire risks and take necessary precautions. In this study, we consider the problem of determining the fire risk after an earthquake as a multi-criteria decision problem and present a two-level framework for risk assessment. The main and sub-criteria are determined by a detailed literature review and Modified Delphi method is employed to gain and consolidate expert opinions.

Book Synopsis A two level interval valued neutrosophic AHP integrated TOPSIS methodology for post-earthquake fire risk assessment: An application for Istanbul by : Pelin Gulum

Download or read book A two level interval valued neutrosophic AHP integrated TOPSIS methodology for post-earthquake fire risk assessment: An application for Istanbul written by Pelin Gulum and published by Infinite Study. This book was released on with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: Earthquakes are the leading natural disasters that seriously affect human life. Furthermore, earthquakes are natural disasters that have the ability to trigger a second disaster in addition to the damages they cause. From this point of view, post-earthquake fires are defined as the one of the most dangerous secondary disasters after an earthquake and often cause even more serious dangers. For this reason, government officials and relevant decision-makers should effectively determine post-earthquake fire risks and take necessary precautions. In this study, we consider the problem of determining the fire risk after an earthquake as a multi-criteria decision problem and present a two-level framework for risk assessment. The main and sub-criteria are determined by a detailed literature review and Modified Delphi method is employed to gain and consolidate expert opinions.

Interval Neutrosophic Sets and Logic: Theory and Applications in Computing

Author: Haibin Wang

Publisher: Infinite Study

Published: 2005

Total Pages: 99

ISBN-13: 1931233942

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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.

Interval valued neutrosophic sets and multi-attribute decision-making based on generalized weighted aggregation operator

Author: Zhao Aiwu

Publisher: Infinite Study

Published:

Total Pages: 11

ISBN-13:

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Neutrosophic sets are powerful logics designed to facilitate understanding of indeterminate and inconsistent information; many types of incomplete or complete information can be expressed as interval valued neutrosophic sets (IVNSs). This paper proposes improved aggregation operation rules for IVNSs, and extends the generalized weighted aggregation (GWA) operator to work congruently with IVNS data. The aggregated results are also expressed as IVNSs, which are characterized by truth membership degree, indeterminacy-membership degree, and falsity-membership degree. The proposed method is proved to be the maximum approximation to the original data, and maintains most of the information during data processing. Then, a method is proposed to determine the ranking orders for all alternatives according to their comparative advantage matrices based on their general score, degree of accuracy and degree of certainty expressed by the aggregated IVNSs. Finally, a numerical example is provided to illustrate the applicability and efficiency of the proposed approach.

Book Synopsis Interval valued neutrosophic sets and multi-attribute decision-making based on generalized weighted aggregation operator by : Zhao Aiwu

Download or read book Interval valued neutrosophic sets and multi-attribute decision-making based on generalized weighted aggregation operator written by Zhao Aiwu and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic sets are powerful logics designed to facilitate understanding of indeterminate and inconsistent information; many types of incomplete or complete information can be expressed as interval valued neutrosophic sets (IVNSs). This paper proposes improved aggregation operation rules for IVNSs, and extends the generalized weighted aggregation (GWA) operator to work congruently with IVNS data. The aggregated results are also expressed as IVNSs, which are characterized by truth membership degree, indeterminacy-membership degree, and falsity-membership degree. The proposed method is proved to be the maximum approximation to the original data, and maintains most of the information during data processing. Then, a method is proposed to determine the ranking orders for all alternatives according to their comparative advantage matrices based on their general score, degree of accuracy and degree of certainty expressed by the aggregated IVNSs. Finally, a numerical example is provided to illustrate the applicability and efficiency of the proposed approach.

Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems

Author: Hong-yu Zhang

Publisher: Infinite Study

Published:

Total Pages: 15

ISBN-13:

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As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. And interval neutrosophic sets (INSs) have been proposed exactly to address issues with a set of numbers in the real unit interval, not just a specific number.However, there are fewer reliable operations for INSs, as well as the INS aggregation operators and decisionmakingmethod. For this purpose, the operations for INSs are defined and a comparison approach is put forward based on the related research of interval valued intuitionistic fuzzy sets (IVIFSs) in this paper. On the basis of the operations and comparison approach, two interval neutrosophic number aggregation operators are developed. Then, amethod formulticriteria decisionmaking problems is explored applying the aggregation operators. In addition, an example is provided to illustrate the application of the proposed method.

Book Synopsis Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems by : Hong-yu Zhang

Download or read book Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems written by Hong-yu Zhang and published by Infinite Study. This book was released on with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. And interval neutrosophic sets (INSs) have been proposed exactly to address issues with a set of numbers in the real unit interval, not just a specific number.However, there are fewer reliable operations for INSs, as well as the INS aggregation operators and decisionmakingmethod. For this purpose, the operations for INSs are defined and a comparison approach is put forward based on the related research of interval valued intuitionistic fuzzy sets (IVIFSs) in this paper. On the basis of the operations and comparison approach, two interval neutrosophic number aggregation operators are developed. Then, amethod formulticriteria decisionmaking problems is explored applying the aggregation operators. In addition, an example is provided to illustrate the application of the proposed method.

Neutrosophic Sets and Systems, vol. 51/2022

Author: Florentin Smarandache

Publisher: Infinite Study

Published: 2022-09-01

Total Pages: 970

ISBN-13:

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“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. 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 together with its opposite or negation and with their spectrum of neutralities in between them (i.e. notions or ideas supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic).

Book Synopsis Neutrosophic Sets and Systems, vol. 51/2022 by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems, vol. 51/2022 written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-09-01 with total page 970 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. 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 together with its opposite or negation and with their spectrum of neutralities in between them (i.e. notions or ideas supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic).