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 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 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 MADM Strategy Based on Some Similarity Measures in Interval Bipolar neuTrosophic Set Environment

2018 ◽  
Author(s):  
Surapati Pramanik ◽  
Partha Pratim Dey ◽  
Florentin Smarandache
Keyword(s):  
Decision Making ◽  
Euclidean Distance ◽  
Similarity Measures ◽  
Distance Functions ◽  
Neutrosophic Set ◽  
Comparison Analysis ◽  
Neutrosophic Sets ◽  
Basic Properties ◽  
Multi Attribute Decision Making ◽  
Euclidean Distances

The paper investigates some similarity measures in interval bipolar neutrosophic environment for multi-attribute decision making problems. At first, we define Hamming and Euclidean distances measures between interval bipolar neutrosophic sets and establish their basic properties. We also propose two similarity measures based on the Hamming and Euclidean distance functions. Using maximum and minimum operators, we define new similarity measures and prove their basic properties. Using the proposed similarity measures, we propose a novel multi attribute decision making strategy in interval bipolar neutrosophic set environment. Lastly, we solve an illustrative example of multi attribute decision making and present comparison analysis to show the feasibility, applicability and effectiveness of the proposed strategy.

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 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 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 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

Sign in / Sign up

Export Citation Format

Share Document