scholarly journals Multi-Attribute Decision Making Method Based on Aggregated Neutrosophic Set

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 267 ◽  
Author(s):  
Wen Jiang ◽  
Zihan Zhang ◽  
Xinyang Deng
Keyword(s):  
Decision Making ◽  
Score Function ◽  
Point Of View ◽  
Neutrosophic Set ◽  
Expert Assessment ◽  
Ideal Solution ◽  
Decision Matrix ◽  
Neutrosophic Sets ◽  
Decision Making Problem ◽  
Multi Attribute Decision Making

Multi-attribute decision-making refers to the decision-making problem of selecting the optimal alternative or sorting the scheme when considering multiple attributes, which is widely used in engineering design, economy, management and military, etc. But in real application, the attribute information of many objects is often inaccurate or uncertain, so it is very important for us to find a useful and efficient method to solve the problem. Neutrosophic set is proposed from philosophical point of view to handle inaccurate information efficiently, and a single-valued neutrosophic set (SVNS) is a special case of neutrosophic set, which is widely used in actual application fields. In this paper, a new method based on single-valued neutrosophic sets aggregation to solve multi-attribute decision making problem is proposed. Firstly, the neutrosophic decision matrix is obtained by expert assessment, a score function of single-valued neutrosophic sets (SVNSs) is defined to obtain the positive ideal solution (PIS) and the negative ideal solution (NIS). Then all alternatives are aggregated based on TOPSIS method to make decision. Finally numerical examples are given to verify the feasibility and rationality of the method.

scholarly journals Possibility Neutrosophic Cubic Sets and Their Application to Multiple Attribute Decision Making

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 269 ◽  
Author(s):  
Huiling Xue ◽  
Xiaotong Yang ◽  
Chunfang Chen
Keyword(s):  
Decision Making ◽  
Binary Operation ◽  
Score Function ◽  
Multiple Attribute Decision Making ◽  
Membership Degree ◽  
Neutrosophic Sets ◽  
Important Indicator ◽  
Multiple Attribute ◽  
Decision Making Problem ◽  
Multi Attribute Decision Making

The neutrosophic cubic sets are an extension of the cubic sets to the neutrosophic sets. It contains three variables, which respectively represent the membership degree, non-membership degree and uncertainty of the element to the set. The score function is an important indicator in the multi-attribute decision-making problem. In this paper, we consider the possibility that an element belongs to a set and put forward the concept of possibility neutrosophic cubic sets. On this basis, we introduce some related concepts and give the binary operation of possibility neutrosophic cubic sets and use specific examples to supplement the corresponding definition. Meanwhile, a decision-making method based on the score function of possibility neutrosophic cubic sets is proposed and a numerical example is given to illustrate the effectiveness of the proposed method.

scholarly journals Bipolar quadripartitioned single valued neutrosophic sets

2020 ◽  
Vol 39 (6) ◽  
pp. 1597-1614
Author(s):  
Kalyan Sinha ◽  
Pinaki Majumdar
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Neutrosophic Set ◽  
Entropy Measure ◽  
Neutrosophic Sets ◽  
Basic Set ◽  
Decision Making Problem ◽  
Different Types ◽  
Measure Technique

The notion of simple bipolar quadripartition is presented valuable neutrosophic set. Some basic set theoretic terminologies, operations and properties of bipolar quadripartitioned single valued neutrosophic set are given here. Also different types of distances, similarity measures and entropy measure are discussed. Finally a decision making problem using the similarity measure technique of bipolar quadripartitioned single valued neutrosophic sets has been solved.

scholarly journals MCGDM Based on VIKOR and TOPSIS Methods Using Spherical Interval Valued Fuzzy Soft With Aggregation Operators

2021 ◽  
Author(s):  
ARULMOZHI K ◽  
Palanikumar M
Keyword(s):  
Score Function ◽  
Soft Set ◽  
Point Of View ◽  
Ideal Solution ◽  
Fuzzy Soft Set ◽  
Decision Matrix ◽  
Soft Sets ◽  
Strong Point ◽  
Fuzzy Soft Sets ◽  
Interval Valued

Abstract Spherical interval valued fuzzy soft set (SIVFS set) has much stronger ability than Pythagorean interval valued fuzzy soft set and interval valued intuitionistic fuzzy soft set. Now, we talk about aggregated operation for aggregating SIVFS decision matrix. TOPSIS and VIKOR methods are strong point of view for multi criteria group decision making (MCGDM), which is a various extensions of interval valued fuzzy soft sets. We talk through a score function based on aggregating TOPSIS and VIKOR method to the SIVFS-positive ideal solution and the SIVFSnegative ideal solution. Also TOPSIS and VIKOR methods are provides the weights of decision makings. To nd out the optimal alternative under closeness is introduced.

scholarly journals A Chi-square Distance-based Similarity Measure of Single-valued Neutrosophic Set and Applications

2019 ◽  
Vol 14 (1) ◽  
pp. 78-89 ◽  
Author(s):  
Haiping Ren ◽  
Shixiao Xiao ◽  
Hui Zhou
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Distance Measure ◽  
Similarity Measures ◽  
Neutrosophic Set ◽  
Chi Square ◽  
Neutrosophic Sets ◽  
Numerical Examples ◽  
Multi Attribute Decision Making

The aim of this paper is to propose a new similarity measure of singlevalued neutrosophic sets (SVNSs). The idea of the construction of the new similarity measure comes from Chi-square distance measure, which is an important measure in the applications of image analysis and statistical inference. Numerical examples are provided to show the superiority of the proposed similarity measure comparing with the existing similarity measures of SVNSs. A weighted similarity is also put forward based on the proposed similarity. Some examples are given to show the effectiveness and practicality of the proposed similarity in pattern recognition, medical diagnosis and multi-attribute decision making problems under single-valued neutrosophic environment.

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 Cross Entropy Measures of Bipolar and Interval Bipolar Neutrosophic Sets and Their Application for Multi-Attribute Decision Making

2018 ◽  
Author(s):  
Surapati Pramanik ◽  
Partha Pratim Dey ◽  
Florentin Smarandache ◽  
Jun Ye
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Cross Entropy ◽  
Neutrosophic Set ◽  
Membership Functions ◽  
Neutrosophic Sets ◽  
Entropy Measures ◽  
Multi Attribute Decision Making ◽  
Important Extension ◽  
The Ideal

Bipolar neutrosophic set is an important extension of bipolar fuzzy set. This set is a hybridization of bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent positive membership functions and three independent negative membership functions. In this paper, we develop cross entropy measures of bipolar neutrosophic sets and prove its properties. We also define cross entropy measures of interval bipolar neutrosophic sets and prove its properties. Thereafter, we develop two novel multi-attribute decision making methods based on the proposed cross entropy measures. In the decision making framework, we calculate the weighted cross entropy measures between each alternative and the ideal alternative to rank the alternatives and choose the best one. We solve two illustrative examples of multi-attribute decision making problems and compare the obtained result with the results of other existing methods to show the applicability and effectiveness of the developed method. In the end, the main conclusion and future scope of research are summarized.

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 Similarity Measures of Quadripartitioned Single Valued Bipolar Neutrosophic Sets and Its Application in Multi-Criteria Decision Making Problems

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1012
Author(s):  
Subhadip Roy ◽  
Jeong-Gon Lee ◽  
Anita Pal ◽  
Syamal Kumar Samanta
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measures ◽  
Distance Measures ◽  
Neutrosophic Set ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Decision Making Problem ◽  
Definition Of ◽  
Bipolar Fuzzy Sets

In this paper, a definition of quadripartitioned single valued bipolar neutrosophic set (QSVBNS) is introduced as a generalization of both quadripartitioned single valued neutrosophic sets (QSVNS) and bipolar neutrosophic sets (BNS). There is an inherent symmetry in the definition of QSVBNS. Some operations on them are defined and a set theoretic study is accomplished. Various similarity measures and distance measures are defined on QSVBNS. An algorithm relating to multi-criteria decision making problem is presented based on quadripartitioned bipolar weighted similarity measure. Finally, an example is shown to verify the flexibility of the given method and the advantage of considering QSVBNS in place of fuzzy sets and bipolar fuzzy sets.

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.

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