A novel divergence measure and its based TOPSIS method for multi criteria decision-making under single-valued neutrosophic environment
A novel divergence measure and its based TOPSIS method for multi criteria decision-making under single-valued neutrosophic environment

Author: Nancy

Publisher: Infinite Study

Published:

Total Pages: 15

ISBN-13:

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The theme of this work is to present an axiomatic definition of divergence measure for single-valued neutrosophic sets (SVNSs). The properties of the proposed divergence measure have been studied. Further, we develop a novel technique for order preference by similarity to ideal solution (TOPSIS) method for solving single-valued neutrosophic multi-criteria decision-making with incomplete weight information. Finally, a numerical example is presented to verify the proposed approach and to present its effectiveness and practicality.

A novel divergence measure and its based TOPSIS method for multi criteria decision-making under single-valued neutrosophic environment
A novel divergence measure and its based TOPSIS method for multi criteria decision-making under single-valued neutrosophic environment

Author: Nancy

Publisher: Infinite Study

Published:

Total Pages: 15

ISBN-13:

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The theme of this work is to present an axiomatic definition of divergence measure for single-valued neutrosophic sets (SVNSs). The properties of the proposed divergence measure have been studied. Further, we develop a novel technique for order preference by similarity to ideal solution (TOPSIS) method for solving single-valued neutrosophic multi-criteria decision-making with incomplete weight information. Finally, a numerical example is presented to verify the proposed approach and to present its effectiveness and practicality.

Algorithms for single-valued neutrosophic decision making based on TOPSIS and clustering methods with new distance measure
Algorithms for single-valued neutrosophic decision making based on TOPSIS and clustering methods with new distance measure

Author: Harish Garg

Publisher: Infinite Study

Published:

Total Pages: 23

ISBN-13:

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Single-valued neutrosophic set (SVNS) is an important contrivance for directing the decision-making queries with unknown and indeterminant data by employing a degree of “acceptance”, “indeterminacy”, and “non-acceptance” in quantitative terms. Under this set, the objective of this paper is to propose some new distance measures to find discrimination between the SVNSs. The basic axioms of the measures have been highlighted and examined their properties. Furthermore, to examine the relevance of proposed measures, an extended TOPSIS (“technique for order preference by similarity to ideal solution”) method is introduced to solve the group decision-making problems. Additionally, a new clustering technique is proposed based on the stated measures to classify the objects. The advantages, comparative analysis as well as superiority analysis is given to shows its influence over existing approaches.

Hausdorff Distance and Similarity Measures for Single-Valued Neutrosophic Sets with Application in Multi-Criteria Decision Making
Hausdorff Distance and Similarity Measures for Single-Valued Neutrosophic Sets with Application in Multi-Criteria Decision Making

Author: Mehboob Ali

Publisher: Infinite Study

Published: 2022-01-01

Total Pages: 17

ISBN-13:

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Hausdorff distance is one of the important distance measures to study the degree of dissimilarity between two sets that had been used in various fields under fuzzy environments. Among those, the framework of single-valued neutrosophic sets (SVNSs) is the one that has more potential to explain uncertain, inconsistent and indeterminate information in a comprehensive way. And so, Hausdorff distance for SVNSs is important. Thus, we propose two novel schemes to calculate the Hausdorff distance and its corresponding similarity measures (SMs) for SVNSs. In doing so, we firstly develop the two forms of Hausdorff distance between SVNSs based on the definition of Hausdorff metric between two sets. We then use these new distance measures to construct several SMs for SVNSs. Some mathematical theorems regarding the proposed Hausdorff distances for SVNSs are also proven to strengthen its theoretical properties. In order to show the exact calculation behavior and distance measurement mechanism of our proposed methods in accordance with the decorum of Hausdorff metric, we utilize an intuitive numerical example that demonstrate the novelty and practicality of our proposed measures. Furthermore, we develop a multi-criteria decision making (MCDM) method under single-valued neutrosophic environment using the proposed SMs based on our defined Hausdorff distance measures, called as a single-valued neutrosophic MCDM (SVN-MCDM) method. In this connection, we employ our proposed SMs to compute the degree of similarity of each option with the ideal choice to identify the best alternative as well as to perform an overall ranking of the alternatives under study. We then apply our proposed SVN-MCDM scheme to solve two real world problems of MCDM under single-valued neutrosophic environment to show its effectiveness and application.

New distance and similarity measures of single value neutrosophic sets with application in multi-criteria decision-making
New distance and similarity measures of single value neutrosophic sets with application in multi-criteria decision-making

Author: Yameng Wang

Publisher: Infinite Study

Published:

Total Pages: 16

ISBN-13:

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The processing of uncertainty information has gradually became one of the hot issues in arti cial intelligence eld, and the infor- mation measures of uncertainty information processing are of importance. Single value neutrosophic sets (SVNSs) provide us a exible mathematical framework to process uncertainty information. In this paper, we mainly consider the measures of SVNSs. The existing information measures mostly are constructed based on the two typical inclusion relations about single value neutrosopgic sets. However, there exist some practical problems that do not apply to the two typical inclusion relations. Therefore, there exists another inclusion relation which is called the type-3 inclusion relation about SVNSs.

Handbook of Research on the Applications of Neutrosophic Sets Theory and Their Extensions in Education
Handbook of Research on the Applications of Neutrosophic Sets Theory and Their Extensions in Education

Author: Broumi, Said

Publisher: IGI Global

Published: 2023-06-09

Total Pages: 386

ISBN-13: 1668478374

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Fuzzy sets have experienced multiple expansions since their conception to enhance their capacity to convey complex information. Intuitionistic fuzzy sets, image fuzzy sets, q-rung orthopair fuzzy sets, and neutrosophic sets are a few of these extensions. Researchers and academics have acquired a lot of information about their theories and methods for making decisions. However, only a small number of research findings discuss how neutrosophic sets theory and their extensions (NSTEs) are used in education. The Handbook of Research on the Applications of Neutrosophic Sets Theory and Their Extensions in Education implements fresh scientific approaches to enhance the quality of decisions under neutrosophic environments, particularly within education. Covering key topics such as data modeling, educational technologies, decision making, and learning management systems, this major reference work is ideal for instructional designers, researchers, academicians, scholars, practitioners, instructors, and students.

Neutrosophic Sets and Systems: An International Book Series in Information Science and Engineering, vol. 21 / 2018
Neutrosophic Sets and Systems: An International Book Series in Information Science and Engineering, vol. 21 / 2018

Author: Florentin Smarandache

Publisher: Infinite Study

Published: 2018

Total Pages: 168

ISBN-13: 1599735814

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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.

Linguistic neutrosophic power Muirhead mean operators for safety evaluation of mines
Linguistic neutrosophic power Muirhead mean operators for safety evaluation of mines

Author: Suizhi Luo

Publisher: Infinite Study

Published:

Total Pages: 21

ISBN-13:

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Safety is the fundamental guarantee for the sustainable development of mining enterprises. As the safety evaluation of mines is a complex system engineering project, consistent and inconsistent, even hesitant evaluation information may be contained simultaneously. Linguistic neutrosophic numbers (LNNs), as the extensions of linguistic terms, are effective means to entirely and qualitatively convey such evaluation information with three independent linguistic membership functions. The aim of our work is to investigate several mean operators so that the safety evaluation issues of mines are addressed under linguistic neutrosophic environment.

Type-2 neutrosophic number based multi-attributive border approximation area comparison (MABAC) approach for offshore wind farm site selection in USA
Type-2 neutrosophic number based multi-attributive border approximation area comparison (MABAC) approach for offshore wind farm site selection in USA

Author: Muhammet Deveci

Publisher: Infinite Study

Published:

Total Pages: 14

ISBN-13:

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This approach combines the advantages of neutrosophic numbers sets, which can utilize uncertain and incomplete information, with a multi-attributive border approximation area comparison that provides formulation flexibility and easy calculation. Further, this study develops and integrates a techno-economic model for OWFs in the decision-making. A case study is performed to evaluate and rank five proposed OWF sites off the coast of New Jersey. To validate the proposed model, a comparison against three alternative T2NN fuzzy based models is performed. It is demonstrated that the implemented model yields the same ranking order as the alternative approaches. Sensitivity analysis reveals that changing criteria weightings does not affect the ranking order.

A Further Study on Multiperiod Health Diagnostics Methodology under a Single-Valued Neutrosophic Set
A Further Study on Multiperiod Health Diagnostics Methodology under a Single-Valued Neutrosophic Set

Author: Jason Chih-sheng Chou

Publisher: Infinite Study

Published:

Total Pages: 11

ISBN-13:

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Employing the concept and function of tangency with similarity measures and counterpart distances for reliable medical consultations has been extensively studied in the past decades and results in lots of isomorphic measures for application. We compared the majority of such isomorphic measures proposed by various researchers and classified them into (a) maximum norm and (b) one-norm categories. Moreover, we found that previous researchers used monotonic functions to transform an identity function and resulted in complicated expressions. In this study, we provide a theoretical foundation to explain the isomorphic nature of a newer measure proposed by the following research paper against its studied existing one in deriving the same pattern recognition results. Specifically, this study initially proposes two similarity measures using maximum norm, arithmetic mean, and aggregation operators and followed by a detailed discussion on their mathematical characteristics. Subsequently, a simplified version of such measures is presented for easy application. This study completely covers two previous methods to point out that the complex approaches used were unnecessary. The findings will help physicians, patients, and their family members to obtain a proper medical diagnosis during multiple examinations.