Group Multi-Attribute Decision Making Based on Interval Neutrosophic Sets

Multi-attribute decision making (MADM) play an important role in many applications, due to the efficiency to handle indeterminate and inconsistent information, interval neutrosophic sets is widely used to model indeterminate information. In this paper, a new MADM method based on interval neutrosophic trapezoid linguistic weighted arithmetic averaging aggregation (INTrLWAA) operator and interval neutrosophic trapezoid linguistic weighted geometric aggregation (INTrLWGA) operatoris presented. A numerical example is presented to demonstrate the application and efficiency of the proposed method.

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New Similarity and Entropy Measures of Interval Neutrosophic Sets with Applications in Multi-Attribute Decision-Making

Symmetry ◽

10.3390/sym11030370 ◽

2019 ◽

Vol 11 (3) ◽

pp. 370 ◽

Cited By ~ 4

Author(s):

Han Yang ◽

Xiaoman Wang ◽

Keyun Qin

Keyword(s):

Decision Making ◽

Hamming Distance ◽

Similarity Measures ◽

Neutrosophic Set ◽

Inclusion Relation ◽

Neutrosophic Sets ◽

Information Measures ◽

Interval Neutrosophic Set ◽

Multi Attribute Decision Making ◽

Interval Neutrosophic Sets

Information measures play an important role in the interval neutrosophic sets (INS) theory. The main purpose of this paper is to study the similarity and entropy of INS and its application in multi-attribute decision-making. We propose a new inclusion relation between interval neutrosophic sets where the importance of the three membership functions may be different. Then, we propose the axiomatic definitions of the similarity measure and entropy of the interval neutrosophic set (INS) based on the new inclusion relation. Based on the Hamming distance, cosine function and cotangent function, some new similarity measures and entropies of INS are constructed. Finally, based on the new similarity and entropy, we propose a multi-attribute decision-making method and illustrate that these new similarities and entropies are reasonable and effective.

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Neutrosophic Cubic Power Muirhead Mean Operators with Uncertain Data for Multi-Attribute Decision-Making

Symmetry ◽

10.3390/sym10100444 ◽

2018 ◽

Vol 10 (10) ◽

pp. 444 ◽

Cited By ~ 6

Author(s):

Qaisar Khan ◽

Nasruddin Hassan ◽

Tahir Mahmood

Keyword(s):

Decision Making ◽

Uncertain Data ◽

Hybrid Structure ◽

Aggregation Operators ◽

Neutrosophic Set ◽

Neutrosophic Sets ◽

Complex Decision Making ◽

Multi Attribute Decision Making ◽

Complex Decision ◽

Interval Neutrosophic Sets

The neutrosophic cubic set (NCS) is a hybrid structure, which consists of interval neutrosophic sets (INS) (associated with the undetermined part of information associated with entropy) and single-valued neutrosophic set (SVNS) (associated with the determined part of information). NCS is a better tool to handle complex decision-making (DM) problems with INS and SVNS. The main purpose of this article is to develop some new aggregation operators for cubic neutrosophic numbers (NCNs), which is a basic member of NCS. Taking the advantages of Muirhead mean (MM) operator and power average (PA) operator, the power Muirhead mean (PMM) operator is developed and is scrutinized under NC information. To manage the problems upstretched, some new NC aggregation operators, such as the NC power Muirhead mean (NCPMM) operator, weighted NC power Muirhead mean (WNCPMM) operator, NC power dual Muirhead mean (NCPMM) operator and weighted NC power dual Muirhead mean (WNCPDMM) operator are proposed and related properties of these proposed aggregation operators are conferred. The important advantage of the developed aggregation operator is that it can remove the effect of awkward data and it considers the interrelationship among aggregated values at the same time. Furthermore, a novel multi-attribute decision-making (MADM) method is established over the proposed new aggregation operators to confer the usefulness of these operators. Finally, a numerical example is given to show the effectiveness of the developed approach.

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Multi-Attribute Decision-Making Based on Preference Perspective with Interval Neutrosophic Sets in Venture Capital

Mathematics ◽

10.3390/math7030257 ◽

2019 ◽

Vol 7 (3) ◽

pp. 257 ◽

Cited By ~ 2

Author(s):

Yanran Hong ◽

Dongsheng Xu ◽

Kaili Xiang ◽

Han Qiao ◽

Xiangxiang Cui ◽

...

Keyword(s):

Decision Making ◽

Venture Capital ◽

Euclidean Distance ◽

Distance Measure ◽

Distance Measures ◽

Neutrosophic Sets ◽

Todim Method ◽

Multi Attribute Decision Making ◽

Parameter Interval ◽

Interval Neutrosophic Sets

Fuzzy information in venture capital can be well expressed by neutrosophic numbers, and TODIM method is an effective tool for multi-attribute decision-making. The distance measure is an essential step in TODIM method. The keystone of this paper is to define several new distance measures, in particular the improved interval neutrosophic Euclidean distance, and these measures are applied in the TODIM method for multi-attribute decision-making. Firstly, the normalized generalized interval neutrosophic Hausdorff distance is defined and proved to be valid in this paper. Secondly, we define a weighted parameter interval neutrosophic distance and discuss whether different weight parameters affect the decision result based on TODIM method. Thirdly, considering the preference perspective of decision-makers in behavioral economics, we define the improved interval neutrosophic Euclidean distance with the known parameter of risk preference. Finally, an application example is given to compare the effects of different parameters on the result and discuss the feasibility of these two distance measures in TODIM method.

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Generalized interval neutrosophic rough sets and its application in multi-attribute decision making

Filomat ◽

10.2298/fil1801011y ◽

2018 ◽

Vol 32 (1) ◽

pp. 11-33 ◽

Cited By ~ 7

Author(s):

Hai-Long Yang ◽

Yan-Ling Bao ◽

Zhi-Lian Guo

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Rough Sets ◽

Constructive Approach ◽

Neutrosophic Sets ◽

Upper Approximation ◽

Approximation Operators ◽

Multi Attribute Decision Making ◽

Two Universes ◽

Interval Neutrosophic Sets

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.

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Correlation Coefficients of Consistency Neutrosophic Sets Regarding Neutrosophic Multi-valued Sets and Their Multi-attribute Decision-Making Method

International Journal of Fuzzy Systems ◽

10.1007/s40815-020-00983-x ◽

2020 ◽

Author(s):

Jun Ye ◽

Jiamin Song ◽

Shigui Du

Keyword(s):

Decision Making ◽

Correlation Coefficients ◽

Neutrosophic Sets ◽

Multi Attribute Decision Making

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Improved Cross Entropy Measures of Single Valued Neutrosophic Sets and Interval Neutrosophic Sets and Their Multicriteria Decision Making Methods

Cybernetics and Information Technologies ◽

10.1515/cait-2015-0051 ◽

2015 ◽

Vol 15 (4) ◽

pp. 13-26 ◽

Cited By ~ 12

Author(s):

Jun Ye

Keyword(s):

Decision Making ◽

Multicriteria Decision Making ◽

Cross Entropy ◽

Entropy Measure ◽

Neutrosophic Sets ◽

Multicriteria Decision ◽

Entropy Measures ◽

The Cross ◽

Ranking Order ◽

Interval Neutrosophic Sets

Abstract Due to some drawbacks of the cross entropy between Single Valued Neutrosophic Sets (SVNSs) in dealing with decision-making problems, the existing single valued neutrosophic cross entropy indicates an asymmetrical phenomenon or may produce an undefined (unmeaningful) phenomenon in some situations. In order to overcome these disadvantages, this paper proposes an improved cross entropy measure of SVNSs and investigates its properties, and then extends it to a cross entropy measure between interval neutrosophic sets (INSs). Furthermore, the cross entropy measures are applied to multicriteria decision making problems with single valued neutrosophic information and interval neutrosophic information. In decision making methods, through the weighted cross entropy measure between each alternative and the the ideal alternative, one can obtain the ranking order of all alternatives and the best one. The decision-making methods using the proposed cross entropy measures can efficiently deal with decision making problems with incomplete, indeterminate and inconsistent information which exist usually in real situations. Finally, two illustrative examples are provided to demonstrate the application and efficiency of the developed decision making approaches under single valued neutrosophic and interval neutrosophic environments.

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A New Multi-Attribute Decision Making Method with Single-Valued Neutrosophic Graphs

10.54216/ijns.0110202 ◽

2020 ◽

pp. 76-86

Author(s):

admin admin ◽

◽

Wenhui Bai ◽

...

Keyword(s):

Decision Making ◽

Graph Theory ◽

Comparative Analysis ◽

Fuzzy Graph ◽

Neutrosophic Sets ◽

Inconsistent Information ◽

Operational Laws ◽

Engineering Economy ◽

Multi Attribute Decision Making

In most realistic situations, the theory and method of multi-attribute decision-making have been widely used in different fields, such as engineering, economy, management, military, and others. Although many studies in some extended fuzzy contexts have been explored with multi-attribute decision-making, it is widely recognized that single-valued neutrosophic sets can describe incomplete, indeterminate and inconsistent information more easier. In this paper, aiming at addressing multi-attribute decision-making problems with single-valued neutrosophic information, related models and multi-attribute decision-making approaches based on the fuzzy graph theory are studied. In specific, the notion of single-valued neutrosophic sets and graphs is firstly introduced together with several common operational laws. Then a multi-attribute decision making method based on single-valued neutrosophic graphs is established. Finally, an illustrative example and a comparative analysis are conducted to verify the feasibility and efficiency of the proposed method.

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