scholarly journals Systematic Review of Decision Making Algorithms in Extended Neutrosophic Sets

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 314 ◽  
Author(s):  
Mohsin Khan ◽  
Le Hoang Son ◽  
Mumtaz Ali ◽  
Hoang Thi Minh Chau ◽  
Nguyen Thi Nhu Na ◽  
...  
Keyword(s):  
Systematic Review ◽  
Decision Making ◽  
Fuzzy Number ◽  
Daily Life ◽  
Triangular Fuzzy Number ◽  
Neutrosophic Set ◽  
Neutrosophic Sets ◽  
Inconsistent Information ◽  
Mathematical Properties ◽  
Interval Neutrosophic Sets

The Neutrosophic set (NS) has grasped concentration by its ability for handling indeterminate, uncertain, incomplete, and inconsistent information encountered in daily life. Recently, there have been various extensions of the NS, such as single valued neutrosophic sets (SVNSs), Interval neutrosophic sets (INSs), bipolar neutrosophic sets (BNSs), Refined Neutrosophic Sets (RNSs), and triangular fuzzy number neutrosophic set (TFNNs). This paper contains an extended overview of the concept of NS as well as several instances and extensions of this model that have been introduced in the last decade, and have had a significant impact in literature. Theoretical and mathematical properties of NS and their counterparts are discussed in this paper as well. Neutrosophic-set-driven decision making algorithms are also overviewed in detail.

scholarly journals Multi-Attribute Decision Making Based on Interval Neutrosophic Trapezoid Linguistic Aggregation Operators

2016 ◽  
pp. 344-365
Author(s):  
Broumi Said ◽  
Florentin Smarandache
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Neutrosophic Sets ◽  
Numerical Example ◽  
Inconsistent Information ◽  
Weighted Arithmetic ◽  
Multi Attribute Decision Making ◽  
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.

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

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 370 ◽  
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.

scholarly journals Multi-attribute group decision-making method based on weighted partitioned Maclaurin symmetric mean operator and a novel score function under neutrosophic cubic environment

2021 ◽  
Author(s):  
Jianping Fan ◽  
Shanshan Zhai ◽  
Meiqin Wu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Score Function ◽  
Neutrosophic Set ◽  
Neutrosophic Sets ◽  
Score Functions ◽  
Complex Information ◽  
Maclaurin Symmetric Mean ◽  
Interval Neutrosophic Sets

Abstract Neutrosophic cubic set (NCS) is the generalized version of neutrosophic sets and interval neutrosophic sets. It can deal with the complex information by combining the neutrosophic set (NS) and cubic set (CS). The partitioned Maclaurin symmetric mean (PMSM) operator can reflect the interrelationships among attributes where there are interrelationships among attributes in the same partition, but the attributes in different partitions are irrelevant. To effectively gather neutrosophic cubic information, we extend the PMSM operator to neutrosophic cubic environment and define the neutrosophic cubic partitioned Maclaurin symmetric mean (NCPMSM) operator and neutrosophic cubic weighted partitioned Maclaurin symmetric mean (NCWPMSM) operator. Later, we define a novel score function of NCS which overcome the drawbacks of the existing score functions. Next, based on NCWPMSM operator and the novel score function, we develop a multi-attribute group decision-making method. Finally, we give an example of supplier selection to illustrate the usefulness of the proposed multi-attribute group decision-making (MAGDM) method. At the same time, a comparative analysis is to show the effectiveness and advantages of the proposed method compared with the existing methods

scholarly journals Neutrosophic Cubic Einstein Geometric Aggregation Operators with Application to Multi-Criteria Decision Making Method

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 247 ◽  
Author(s):  
Majid Khan ◽  
Muhammad Gulistan ◽  
Naveed Yaqoob ◽  
Madad Khan ◽  
Florentin Smarandache
Keyword(s):  
Decision Making ◽  
Daily Life ◽  
Aggregation Operators ◽  
Scalar Multiplication ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Vague Data ◽  
Multiplication Score ◽  
Geometric Operator ◽  
Interval Neutrosophic Sets

Neutrosophic cubic sets (NCs) are amore generalized version of neutrosophic sets(Ns) and interval neutrosophic sets (INs). Neutrosophic cubic setsare better placed to express consistent, indeterminate and inconsistent information, which provides a better platform to deal with incomplete, inconsistent and vague data. Aggregation operators play a key role in daily life, and in relation to science and engineering problems. In this paper we defined the algebraic and Einstein sum, multiplication and scalar multiplication, score and accuracy functions. Using these operations we defined geometric aggregation operators and Einstein geometric aggregation operators. First, we defined the algebraic and Einstein operators of addition, multiplication and scalar multiplication. We defined score and accuracy function to compare neutrosophic cubic values. Then we definedthe neutrosophic cubic weighted geometric operator (NCWG), neutrosophic cubic ordered weighted geometric operator (NCOWG), neutrosophic cubic Einstein weighted geometric operator (NCEWG), and neutrosophic cubic Einstein ordered weighted geometric operator (NCEOWG) over neutrosophic cubic sets. A multi-criteria decision making method is developed as an application to these operators. This method is then applied to a daily life problem.

Multicriteria Decision Making Using Double Refined Indeterminacy Neutrosophic Cross Entropy and Indeterminacy Based Cross Entropy

2016 ◽  
Vol 859 ◽  
pp. 129-143 ◽  
Author(s):  
Ilanthenral Kandasamy ◽  
Florentin Smarandache
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multicriteria Decision Making ◽  
Cross Entropy ◽  
Neutrosophic Set ◽  
Neutrosophic Sets ◽  
Multicriteria Decision ◽  
Inconsistent Information ◽  
Decision Making Problem ◽  
The Cross

Double Refined Indeterminacy Neutrosophic Set (DRINS) is an inclusive case of the refined neutrosophic set, defined by Smarandache (2013), which provides the additional possibility to represent with sensitivity and accuracy the uncertain, imprecise, incomplete, and inconsistent information which are available in real world. More precision is provided in handling indeterminacy; by classifying indeterminacy (I) into two, based on membership; as indeterminacy leaning towards truth membership (IT) and indeterminacy leaning towards false membership (IF). This kind of classification of indeterminacy is not feasible with the existing Single Valued Neutrosophic Set (SVNS), but it is a particular case of the refined neutrosophic set (where each T, I, F can be refined into T1, T2, ...; I1, I2, ...; F1, F2, ...). DRINS is better equipped at dealing indeterminate and inconsistent information, with more accuracy than SVNS, which fuzzy sets and Intuitionistic Fuzzy Sets (IFS) are incapable of. Based on the cross entropy of neutrosophic sets, the cross entropy of DRINSs, known as Double Refined Indeterminacy neutrosophic cross entropy, is proposed in this paper. This proposed cross entropy is used for a multicriteria decision-making problem, where the criteria values for alternatives are considered under a DRINS environment. Similarly, an indeterminacy based cross entropy using DRINS is also proposed. The double valued neutrosophic weighted cross entropy and indeterminacy based cross entropy between the ideal alternative and an alternative is obtained and utilized to rank the alternatives corresponding to the cross entropy values. The most desirable one(s) in decision making process is selected. An illustrative example is provided to demonstrate the application of the proposed method. A brief comparison of the proposed method with the existing methods is carried out.

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

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 444 ◽  
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.

scholarly journals A Neutrosophic Multi-Criteria Decision Making Method

2014 ◽  
Vol 10 (02) ◽  
pp. 143-162 ◽  
Author(s):  
Athar Kharal
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Neutrosophic Set ◽  
University Faculty ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Mathematical Properties ◽  
Faculty Selection

This work presents a method of multi-criteria decision making (MCDM) using neutrosophic sets. Besides studying some interesting mathematical properties of the method, algorithm viz neut-MCDM is presented. The work also furnishes the fundamentals of neutrosophic set theory succinctly, to provide a first introduction of neutrosophic sets for the MCDM community. To illustrate the computational details, neut-MCDM has been applied to the problem of university faculty selection against a given set of criteria.

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

2015 ◽  
Vol 15 (4) ◽  
pp. 13-26 ◽  
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.

Neutrosophic Soft Block Matrices And Some Of Its Properties

2020 ◽  
pp. 39-49
Author(s):  
admin admin ◽  
Keyword(s):  
Decision Making ◽  
Crucial Role ◽  
Real Life ◽  
Decision Making Process ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Neutrosophic Sets ◽  
Block Matrices ◽  
Inconsistent Information

In real life situations, there are many issues in which there are uncertainties, vagueness, complexities and unpredictability. Neutrosophic sets are a mathematical tool to address some issues which cannot be met using the existing methods. Neutrosophic soft matrices play a crucial role in handling indeterminant and inconsistent information during decision making process. The main focus of this article is to discuss the concept of neutrosophic sets, neutrosophic soft sets, neutrosophic soft matrices theory and finally to discuss about neutrosophic soft block matrics which are very useful and applicable in various situations involving uncertainties and imprecisions. In this article, neutrosophic soft block matrices, various types of neutrosophic soft block matrices, some operations on it along with some properties associated with it are discussed in details.

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