Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems

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...

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Published inTheScientificWorld Vol. 2014; no. 2014; pp. 1 - 15
Main Authors Zhang, Hong-yu, Chen, Xiao-hong, Wang, Jian-Qiang
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 01.01.2014
John Wiley & Sons, Inc
Wiley
Subjects
Decision making
Decision Support Techniques
Fuzzy logic
Fuzzy sets
Hotels & motels
Models, Theoretical
Neural networks
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Abstract 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 decision making method. 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, a method for multicriteria decision making problems is explored applying the aggregation operators. In addition, an example is provided to illustrate the application of the proposed method.
AbstractList 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 decision making method. 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, a method for multicriteria decision making problems is explored applying the aggregation operators. In addition, an example is provided to illustrate the application of the proposed method.
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 decision making method. 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, a method for multicriteria decision making problems is explored applying the aggregation operators. In addition, an example is provided to illustrate the application of the proposed method.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 decision making method. 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, a method for multicriteria decision making problems is explored applying the aggregation operators. In addition, an example is provided to illustrate the application of the proposed method.
Author Zhang, Hong-yu
Chen, Xiao-hong
Wang, Jian-Qiang
AuthorAffiliation School of Business, Central South University, Changsha 410083, China
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ContentType Journal Article
Copyright Copyright © 2014 Hong-yu Zhang et al.
Copyright © 2014 Hong-yu Zhang et al. Hong-yu Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright © 2014 Hong-yu Zhang et al. 2014
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Snippet As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and...
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SubjectTerms Decision making
Decision Support Techniques
Fuzzy logic
Fuzzy sets
Hotels & motels
Models, Theoretical
Neural networks
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Title Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems
URI https://search.emarefa.net/detail/BIM-1050479
https://dx.doi.org/10.1155/2014/645953
https://www.ncbi.nlm.nih.gov/pubmed/24695916
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Volume 2014
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