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Neutrosophic set (NS) was originally proposed by Smarandache to handle indeterminate and inconsistent information.
Book Synopsis Generalized Interval Neutrosophic Rough Sets and its Application in Multi-Attribute Decision Making by : Hai-Long Yang
Download or read book Generalized Interval Neutrosophic Rough Sets and its Application in Multi-Attribute Decision Making written by Hai-Long Yang and published by Infinite Study. This book was released on with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic set (NS) was originally proposed by Smarandache to handle indeterminate and inconsistent information.
Neutrosophic set (NS) was originally proposed by Smarandache to handle indeterminate and inconsistent information. It is a generalization of fuzzy sets and intuitionistic fuzzy sets. Wang and Smarandache proposed interval neutrosophic sets (INS) which is a special case of NSs and would be extensively applied to resolve practical issues. In this paper, we put forward generalized interval neutrosophic rough sets based on interval neutrosophic relations by combining interval neutrosophic sets with rough sets. We explore the hybrid model through constructive approach as well as axiomatic approach. On one hand, we define generalized interval neutrosophic lower and upper approximation operators through constructive approach. Moreover, we investigate the relevance between generalized interval neutrosophic lower (upper) approximation operators and particular interval neutrosophic relations. On the other hand, we study axiomatic characterizations of generalized interval neutrosophic approximation operators, and also show that different axiom sets of theoretical interval neutrosophic operators make sure the existence of different classes of INRs that yield the same interval neutrosophic approximation operators. Finally, we introduce generalized interval neutrosophic rough sets on two universes and a universal algorithm of multi-attribute decision making based on generalized interval neutrosophic rough sets on two universes. Besides, an example is given to demonstrate the validity of the new rough set model.
Book Synopsis Generalized Interval Neutrosophic Rough Sets and its Application in Multi-Attribute Decision Making by : Hai-Long Yang
Download or read book Generalized Interval Neutrosophic Rough Sets and its Application in Multi-Attribute Decision Making written by Hai-Long Yang and published by Infinite Study. This book was released on with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic set (NS) was originally proposed by Smarandache to handle indeterminate and inconsistent information. It is a generalization of fuzzy sets and intuitionistic fuzzy sets. Wang and Smarandache proposed interval neutrosophic sets (INS) which is a special case of NSs and would be extensively applied to resolve practical issues. In this paper, we put forward generalized interval neutrosophic rough sets based on interval neutrosophic relations by combining interval neutrosophic sets with rough sets. We explore the hybrid model through constructive approach as well as axiomatic approach. On one hand, we define generalized interval neutrosophic lower and upper approximation operators through constructive approach. Moreover, we investigate the relevance between generalized interval neutrosophic lower (upper) approximation operators and particular interval neutrosophic relations. On the other hand, we study axiomatic characterizations of generalized interval neutrosophic approximation operators, and also show that different axiom sets of theoretical interval neutrosophic operators make sure the existence of different classes of INRs that yield the same interval neutrosophic approximation operators. Finally, we introduce generalized interval neutrosophic rough sets on two universes and a universal algorithm of multi-attribute decision making based on generalized interval neutrosophic rough sets on two universes. Besides, an example is given to demonstrate the validity of the new rough set model.
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.
Covering rough set is a classical generalization of rough set. As covering rough set is a mathematical tool to deal with incomplete and incomplete data, it has been widely used in various fields. The aim of this paper is to extend the covering rough sets to interval neutrosophic sets, which can make multi-attribute decision making problem more tractable. Interval neutrosophic covering rough sets can be viewed as the bridge connecting Interval neutrosophic sets and covering rough sets. Firstly, the paper introduces the definition of interval neutrosophic sets and covering rough sets, where the covering rough set is defined by neighborhood. Secondly, Some basic properties and operation rules of interval neutrosophic sets and covering rough sets are discussed. Thirdly, the definition of interval neutrosophic covering rough sets are proposed. Then, some theorems are put forward and their proofs of interval neutrosophic covering rough sets also be gived. Lastly, this paper gives a numerical example to apply the interval neutrosophic covering rough sets.
Book Synopsis Interval neutrosophic covering rough sets based on neighborhoods by : Dongsheng Xu
Download or read book Interval neutrosophic covering rough sets based on neighborhoods written by Dongsheng Xu and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering rough set is a classical generalization of rough set. As covering rough set is a mathematical tool to deal with incomplete and incomplete data, it has been widely used in various fields. The aim of this paper is to extend the covering rough sets to interval neutrosophic sets, which can make multi-attribute decision making problem more tractable. Interval neutrosophic covering rough sets can be viewed as the bridge connecting Interval neutrosophic sets and covering rough sets. Firstly, the paper introduces the definition of interval neutrosophic sets and covering rough sets, where the covering rough set is defined by neighborhood. Secondly, Some basic properties and operation rules of interval neutrosophic sets and covering rough sets are discussed. Thirdly, the definition of interval neutrosophic covering rough sets are proposed. Then, some theorems are put forward and their proofs of interval neutrosophic covering rough sets also be gived. Lastly, this paper gives a numerical example to apply the interval neutrosophic covering rough sets.
Multi-attribute decision-making (MADM) is a part of management decision-making and an important branch of the modern decision theory and method. MADM focuses on the decision problem of discrete and finite decision schemes. Uncertain MADM is an extension and development of classical multi-attribute decision making theory. When the attribute value of MADM is shown by neutrosophic number, that is, the attribute value is complex data and needs three values to express, it is called the MADM problem in which the attribute values are neutrosophic numbers. However, in practical MADM problems, to minimize errors in individual decision making, we need to consider the ideas of many people and synthesize their opinions.
Book Synopsis Non-Dual Multi-Granulation Neutrosophic Rough Set with Applications by : Chunxin Bo
Download or read book Non-Dual Multi-Granulation Neutrosophic Rough Set with Applications written by Chunxin Bo and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-attribute decision-making (MADM) is a part of management decision-making and an important branch of the modern decision theory and method. MADM focuses on the decision problem of discrete and finite decision schemes. Uncertain MADM is an extension and development of classical multi-attribute decision making theory. When the attribute value of MADM is shown by neutrosophic number, that is, the attribute value is complex data and needs three values to express, it is called the MADM problem in which the attribute values are neutrosophic numbers. However, in practical MADM problems, to minimize errors in individual decision making, we need to consider the ideas of many people and synthesize their opinions.
In this paper, we extend the rough set model on two different universes in intuitionistic fuzzy approximation spaces to a single-valued neutrosophic environment.
Book Synopsis A Novel Rough Set Model in Generalized Single Valued Neutrosophic Approximation Spaces and Its Application by : Zhi-Lian Guo
Download or read book A Novel Rough Set Model in Generalized Single Valued Neutrosophic Approximation Spaces and Its Application written by Zhi-Lian Guo and published by Infinite Study. This book was released on with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we extend the rough set model on two different universes in intuitionistic fuzzy approximation spaces to a single-valued neutrosophic environment.
In the present study we aim to introduce novel concepts of m-polar neutrosophic set (MPNS) and m-polar neutrosophic topology. For this aim, we first investigate several characterizations of the notion of m-polar neutrosophic set and discuss its fundamental properties. We establish some operations on m-polar neutrosophic set. We propose score functions for the comparison of m-polar neutrosophic numbers (MPNNs). Then we introduce m-polar neutrosophic topology and define interior, closure, exterior and frontier for m-polar neutrosophic sets (MPNSs) with illustrative examples. We discuss some results which holds for classical set theory but do not hold for m-polar neutrosophic set theory. We introduce cosine similarity measure and set theoretic similarity measures for MPNSs. Furthermore, we present two algorithms for multi-criteria decision-making (MCDM) in medical diagnosis by using m-polar neutrosophic set (MPNS) and m-polar neutrosophic topology.
Book Synopsis m-polar Neutrosophic Topology and its Application to Medical Diagnosis by : Muhammad Riaz
Download or read book m-polar Neutrosophic Topology and its Application to Medical Diagnosis written by Muhammad Riaz and published by Infinite Study. This book was released on with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present study we aim to introduce novel concepts of m-polar neutrosophic set (MPNS) and m-polar neutrosophic topology. For this aim, we first investigate several characterizations of the notion of m-polar neutrosophic set and discuss its fundamental properties. We establish some operations on m-polar neutrosophic set. We propose score functions for the comparison of m-polar neutrosophic numbers (MPNNs). Then we introduce m-polar neutrosophic topology and define interior, closure, exterior and frontier for m-polar neutrosophic sets (MPNSs) with illustrative examples. We discuss some results which holds for classical set theory but do not hold for m-polar neutrosophic set theory. We introduce cosine similarity measure and set theoretic similarity measures for MPNSs. Furthermore, we present two algorithms for multi-criteria decision-making (MCDM) in medical diagnosis by using m-polar neutrosophic set (MPNS) and m-polar neutrosophic topology.
This ninth volume of Collected Papers includes 87 papers comprising 982 pages on Neutrosophic Theory and its applications in Algebra, written between 2014-2022 by the author alone or in collaboration with the following 81 co-authors (alphabetically ordered) from 19 countries: E.O. Adeleke, A.A.A. Agboola, Ahmed B. Al-Nafee, Ahmed Mostafa Khalil, Akbar Rezaei, S.A. Akinleye, Ali Hassan, Mumtaz Ali, Rajab Ali Borzooei , Assia Bakali, Cenap Özel, Victor Christianto, Chunxin Bo, Rakhal Das, Bijan Davvaz, R. Dhavaseelan, B. Elavarasan, Fahad Alsharari, T. Gharibah, Hina Gulzar, Hashem Bordbar, Le Hoang Son, Emmanuel Ilojide, Tèmítópé Gbóláhàn Jaíyéolá, M. Karthika, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Huma Khan, Madad Khan, Mohsin Khan, Hee Sik Kim, Seon Jeong Kim, Valeri Kromov, R. M. Latif, Madeleine Al-Tahan, Mehmat Ali Ozturk, Minghao Hu, S. Mirvakili, Mohammad Abobala, Mohammad Hamidi, Mohammed Abdel-Sattar, Mohammed A. Al Shumrani, Mohamed Talea, Muhammad Akram, Muhammad Aslam, Muhammad Aslam Malik, Muhammad Gulistan, Muhammad Shabir, G. Muhiuddin, Memudu Olaposi Olatinwo, Osman Anis, Choonkil Park, M. Parimala, Ping Li, K. Porselvi, D. Preethi, S. Rajareega, N. Rajesh, Udhayakumar Ramalingam, Riad K. Al-Hamido, Yaser Saber, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, A.A. Salama, Ganeshsree Selvachandran, Songtao Shao, Seok-Zun Song, Tahsin Oner, M. Mohseni Takallo, Binod Chandra Tripathy, Tugce Katican, J. Vimala, Xiaohong Zhang, Xiaoyan Mao, Xiaoying Wu, Xingliang Liang, Xin Zhou, Yingcang Ma, Young Bae Jun, Juanjuan Zhang.
Book Synopsis Collected Papers. Volume IX by : Florentin Smarandache
Download or read book Collected Papers. Volume IX written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-05-10 with total page 1008 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ninth volume of Collected Papers includes 87 papers comprising 982 pages on Neutrosophic Theory and its applications in Algebra, written between 2014-2022 by the author alone or in collaboration with the following 81 co-authors (alphabetically ordered) from 19 countries: E.O. Adeleke, A.A.A. Agboola, Ahmed B. Al-Nafee, Ahmed Mostafa Khalil, Akbar Rezaei, S.A. Akinleye, Ali Hassan, Mumtaz Ali, Rajab Ali Borzooei , Assia Bakali, Cenap Özel, Victor Christianto, Chunxin Bo, Rakhal Das, Bijan Davvaz, R. Dhavaseelan, B. Elavarasan, Fahad Alsharari, T. Gharibah, Hina Gulzar, Hashem Bordbar, Le Hoang Son, Emmanuel Ilojide, Tèmítópé Gbóláhàn Jaíyéolá, M. Karthika, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Huma Khan, Madad Khan, Mohsin Khan, Hee Sik Kim, Seon Jeong Kim, Valeri Kromov, R. M. Latif, Madeleine Al-Tahan, Mehmat Ali Ozturk, Minghao Hu, S. Mirvakili, Mohammad Abobala, Mohammad Hamidi, Mohammed Abdel-Sattar, Mohammed A. Al Shumrani, Mohamed Talea, Muhammad Akram, Muhammad Aslam, Muhammad Aslam Malik, Muhammad Gulistan, Muhammad Shabir, G. Muhiuddin, Memudu Olaposi Olatinwo, Osman Anis, Choonkil Park, M. Parimala, Ping Li, K. Porselvi, D. Preethi, S. Rajareega, N. Rajesh, Udhayakumar Ramalingam, Riad K. Al-Hamido, Yaser Saber, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, A.A. Salama, Ganeshsree Selvachandran, Songtao Shao, Seok-Zun Song, Tahsin Oner, M. Mohseni Takallo, Binod Chandra Tripathy, Tugce Katican, J. Vimala, Xiaohong Zhang, Xiaoyan Mao, Xiaoying Wu, Xingliang Liang, Xin Zhou, Yingcang Ma, Young Bae Jun, Juanjuan Zhang.
“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: An International Book Series in Information Science and Engineering, vol. 20 / 2018 by : Florentin Smarandache
Download or read book Neutrosophic Sets and Systems: An International Book Series in Information Science and Engineering, vol. 20 / 2018 written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 132 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.
