H-Max Single-Valued Neutrosophic Distance Measure in Medical Diagnosis

2021 ◽  
Author(s):  
Ngan Thi Roan ◽  
◽  
Florentin Smarandache ◽  
Keyword(s):  
Similarity Measure ◽  
Medical Diagnosis ◽  
Distance Measure ◽  
Neutrosophic Set ◽  
Characteristic Functions ◽  
Entropy Measure ◽  
Basic Properties ◽  
The Cross

As an instance of a neutrosophic set, a single-valued neutrosophic set (SVNS) can be used to handle uncertainty, inaccuracy, indeterminacy, and inconsistency. In this paper, a new not-so-sophisticated distance measure between two SVNSs is defined by considering the cross-assessment between characteristic functions for the forward and backward differences. Furthermore, a single-valued neutrosophic similarity measure, a single-valued neutrosophic entropy measure, and their basic properties are presented and proven. In addition, an application to medical diagnosis is shown to illustrate the effective applicability of the proposals.

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 Multiple Attribute Group Decision Making Based on Simplified Neutrosophic Integrated Weighted Distance Measure and Entropy Method

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Haibo Zhang ◽  
Zhimin Mu ◽  
Shouzhen Zeng
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Distance Measure ◽  
Group Decision ◽  
Neutrosophic Set ◽  
Entropy Measure ◽  
Uncertain Information ◽  
Entropy Weight ◽  
Weighted Distance ◽  
Multiple Attribute

Simplified neutrosophic set (SNS) is a popular tool in modelling potential, imprecise, and uncertain information within complex environments. In this paper, a method based on the integrated weighted distance measure and entropy weight is proposed for handling SNS multiple attribute group decision-making (MAGDM) problems. To this end, the simplified neutrosophic (SN) integrated weighted distance (SVNIWD) measure is first developed for overcoming the limitations of the existing methods. Afterward, the proposed SNIWD’s several properties and particular status are studied. Moreover, a flexible and useful MAGDM approach that combines the strengths of the SNIWD and the SNS is proposed, wherein the SN entropy measure is applied to calculate the unknown weight information regarding attributes. Finally, a numerical case of investment evaluation and subsequent comparative analysis are conducted to prove the superiority of the proposed framework.

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 NS-Cross Entropy Based MAGDM under Single Valued Neutrosophic Set Environment

2018 ◽  
Author(s):  
Surapati Pramanik ◽  
Shyamal Dalapati ◽  
Shariful Alam ◽  
F. Smarandache ◽  
Tapan Kumar Roy
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Cross Entropy ◽  
Neutrosophic Set ◽  
Entropy Measure ◽  
Numerical Example ◽  
Basic Properties ◽  
Solution Strategies ◽  
The Ideal

Single valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single valued neutrosophic cross entropy bears an asymmetrical behavior and produce an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under single valued neutrosophic set (SVNS) environment namely SN- cross entropy and prove its basic properties. Also we define weighted SN-cross entropy measure and investigate its basic properties. We develop a new multi attribute group decision making (MAGDM) strategy for ranking of the alternatives based on the proposed weighted SN-cross entropy measure between each alternative and the ideal alternative. Finally, a numerical example of MAGDM problem of investment potential is solved to show the validity and efficiency of proposed decision making strategy. We also present comparative anslysis of the obtained result with the results obtained form the existing solution strategies in the solution.

Some Hybrid Soft Sets and Their Application in Decision Making

2016 ◽  
pp. 86-117 ◽  
Author(s):  
Pinaki Majumdar
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Soft Set ◽  
Soft Sets ◽  
Basic Properties ◽  
Two Hybrid

In this chapter the notions of two hybrid soft sets, namely fuzzy parameterized soft sets and vague soft sets has been discussed and some operations on them are defined. Some properties of these two hybrid soft sets under these operations are also studied. Application of fuzzy parameterized soft sets and vague soft sets in decision making has also been shown. Then the notion of similarity measure between two hybrid soft sets has been introduced and their basic properties are studied. Applications of these similarity measures in various problems like medical diagnosis and decision making have been shown. The idea of entropy of a fuzzy parameterized soft set has been introduced.

scholarly journals Some Similarity Measures of Neutrosophic Sets Based on the Euclidean Distance and Their Application in Medical Diagnosis

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Donghai Liu ◽  
Guangyan Liu ◽  
Zaiming Liu
Keyword(s):  
Similarity Measure ◽  
Medical Diagnosis ◽  
Euclidean Distance ◽  
Distance Measure ◽  
Multiple Criteria Decision Making ◽  
Similarity Measures ◽  
Neutrosophic Sets ◽  
Euclidean Distance Measure ◽  
The Difference ◽  
Interval Valued

Similarity measure is an important tool in multiple criteria decision-making problems, which can be used to measure the difference between the alternatives. In this paper, some new similarity measures of single-valued neutrosophic sets (SVNSs) and interval-valued neutrosophic sets (IVNSs) are defined based on the Euclidean distance measure, respectively, and the proposed similarity measures satisfy the axiom of the similarity measure. Furthermore, we apply the proposed similarity measures to medical diagnosis decision problem; the numerical example is used to illustrate the feasibility and effectiveness of the proposed similarity measures of SVNSs and IVNSs, which are then compared to other existing similarity measures.

scholarly journals NC-Cross Entropy Based MADM under Neutrosophic Cubic Set Environment

2018 ◽  
Author(s):  
Surapati Pramanik ◽  
Shyamal Dalapati ◽  
Shariful Alam ◽  
Florentin Smarandache ◽  
Tapan Kumar Roy
Keyword(s):  
Decision Making ◽  
Incomplete Information ◽  
Family Members ◽  
Cross Entropy ◽  
Neutrosophic Set ◽  
Entropy Measure ◽  
Basic Properties ◽  
Important Family ◽  
Multi Attribute Decision Making ◽  
Interval Valued

Neutrosophic cubic set (NCS) is one of the important family members of neutrosophic hybrid sets. Neutrosophic cubic set has more strength than other family members of neutrosophic hybrid sets to express incomplete information due to the presence of interval valued neutrosophic set (IVNS) and single valued neutrosophic set (SVNS) in its structure. Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. In this paper we first define a new cross entropy measure under NCSs environment which we call NC- cross entropy measure. We investigate the basic properties of NC-cross entropy. We also propose weighted NC-cross entropy and investigate its basic properties. We develop a novel multi attribute decision making (MADM) strategy based on weighted NC-cross entropy. To show the feasibility and applicability, we solve a MADM problem using the proposed strategy.

Extended TOPSIS method based on the entropy measure and probabilistic hesitant fuzzy information and their application in decision support system

2021 ◽  
pp. 1-12
Author(s):  
Muhammad Naeem ◽  
Muhammad Ali Khan ◽  
Saleem Abdullah ◽  
Muhammad Qiyas ◽  
Saifullah Khan
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Group Decision ◽  
Hesitant Fuzzy Set ◽  
Entropy Measure ◽  
Fuzzy Information ◽  
Score Functions ◽  
Fuzzy Environment ◽  
Basic Operating

Probabilistic hesitant fuzzy Set (PHFs) is the most powerful and comprehensive idea to support more complexity than developed fuzzy set (FS) frameworks. In this paper, it can explain a novel, improved TOPSIS-based method for multi-criteria group decision-making (MCGDM) problem through the Probabilistic hesitant fuzzy environment, in which the weights of both experts and criteria are completely unknown. Firstly, we discuss the concept of PHFs, score functions and the basic operating laws of PHFs. In fact, to compute the unknown weight information, the generalized distance measure for PHFs was defined based on the Probabilistic hesitant fuzzy entropy measure. Second, MCGDM will be presented with the PHF information-based decision-making process.

scholarly journals Generalised Interval-Valued Fuzzy Soft Set

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Abdul Razak Salleh
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Interval Valued

We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in a medical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised fuzzy soft set; generalised interval-valued fuzzy soft set; interval-valued fuzzy set; interval-valued fuzzy soft set.

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