Special Issue "Neutrosophic Multi-Criteria Decision Making"

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (20 May 2018).

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Guest Editor
Prof. Florentin Smarandache Website E-Mail
University of New Mexico, Mathematics Department, 705 Gurley Ave., Gallup, NM 87301, USA
Interests: uncertainty mathematics; fusion rules; target tracking; neutrosophic fusion; DSmT; subjective probability
Guest Editor
Prof. Dr. Jun Ye Website E-Mail
Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, China
Interests: soft computing; fuzzy decision theory and method; robot intelligent control; pattern recognition and fault diagnosis; neutrosophic theory; rock mechanics; engineering modeling; optimization design
Guest Editor
Dr. Yanhui Guo Website E-Mail
Department of Computer Science, University of Illinois at Springfield, Springfield, IL 62703, USA
Interests: artificial intelligence; computer vision; pattern recognition and image processing; medical information processing; fuzzy logic; neural networks; genetic algorithms

Special Issue Information

Dear Colleagues,

Neutrosophic logic and set are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. A number of new netrosophic theories have been proposed and have been applied in Multi-Criteria Decision Making, computational intelligence, mutiple attribute decision making, image processing, medical diagnosis, fault diagnosis, optimization design, and so on.

Neutrosophic logic, set, probability, statistics, etc., are, respectively, generalizations of fuzzy and intuitionistic fuzzy logic and set, classical and imprecise probability, and classical statistics and so on.

As a founder of the field, I invite original research papers in this special issue that report on state-of-the-art and recent advancements Multi-Criteria Decision Making using neutrosophic environment to computing, artificial intelligence, big and small data mining, group decision making problems, pattern recognition, information processing, image processing, and many other practical achievements.

Prof. Dr. Florentin Smarandache
Prof. Dr. Jun Ye
Dr. Yanhui Guo
Guest Editors

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Keywords

  • Neutrosophic decision making theories and methods
  • Neutrosophic operations used in MCDM
  • Neutrosophic optimization
  • Neutrosophic image processing using MCDM
  • Neutrosophic fault diagnosis
  • Neutrosophic medical diagnosis
  • Neutrosophic data mining
  • Neutrosophic clustering analysis
  • Neutrosophic computational modelling
  • NMCD Neutrosophic applications

Published Papers (11 papers)

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Research

Open AccessArticle
Neutrosophic Quadruple BCK/BCI-Algebras
Axioms 2018, 7(2), 41; https://doi.org/10.3390/axioms7020041 - 18 Jun 2018
Cited by 7
Abstract
The notion of a neutrosophic quadruple BCK/BCI-number is considered, and a neutrosophic quadruple BCK/BCI-algebra, which consists of neutrosophic quadruple BCK/BCI-numbers, is constructed. [...] Read more.
The notion of a neutrosophic quadruple BCK/BCI-number is considered, and a neutrosophic quadruple BCK/BCI-algebra, which consists of neutrosophic quadruple BCK/BCI-numbers, is constructed. Several properties are investigated, and a (positive implicative) ideal in a neutrosophic quadruple BCK-algebra and a closed ideal in a neutrosophic quadruple BCI-algebra are studied. Given subsets A and B of a BCK/BCI-algebra, the set NQ(A,B), which consists of neutrosophic quadruple BCK/BCI-numbers with a condition, is established. Conditions for the set NQ(A,B) to be a (positive implicative) ideal of a neutrosophic quadruple BCK-algebra are provided, and conditions for the set NQ(A,B) to be a (closed) ideal of a neutrosophic quadruple BCI-algebra are given. An example to show that the set {0˜} is not a positive implicative ideal in a neutrosophic quadruple BCK-algebra is provided, and conditions for the set {0˜} to be a positive implicative ideal in a neutrosophic quadruple BCK-algebra are then discussed. Full article
(This article belongs to the Special Issue Neutrosophic Multi-Criteria Decision Making) Printed Edition available
Open AccessArticle
Decision-Making with Bipolar Neutrosophic TOPSIS and Bipolar Neutrosophic ELECTRE-I
Axioms 2018, 7(2), 33; https://doi.org/10.3390/axioms7020033 - 15 May 2018
Cited by 10
Abstract
Technique for the order of preference by similarity to ideal solution (TOPSIS) and elimination and choice translating reality (ELECTRE) are widely used methods to solve multi-criteria decision making problems. In this research article, we present bipolar neutrosophic TOPSIS method and bipolar neutrosophic ELECTRE-I [...] Read more.
Technique for the order of preference by similarity to ideal solution (TOPSIS) and elimination and choice translating reality (ELECTRE) are widely used methods to solve multi-criteria decision making problems. In this research article, we present bipolar neutrosophic TOPSIS method and bipolar neutrosophic ELECTRE-I method to solve such problems. We use the revised closeness degree to rank the alternatives in our bipolar neutrosophic TOPSIS method. We describe bipolar neutrosophic TOPSIS method and bipolar neutrosophic ELECTRE-I method by flow charts. We solve numerical examples by proposed methods. We also give a comparison of these methods. Full article
(This article belongs to the Special Issue Neutrosophic Multi-Criteria Decision Making) Printed Edition available
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Open AccessArticle
Interval Neutrosophic Sets with Applications in BCK/BCI-Algebra
Axioms 2018, 7(2), 23; https://doi.org/10.3390/axioms7020023 - 09 Apr 2018
Cited by 5
Abstract
For i , j , k , l , m , n { 1 , 2 , 3 , 4 } , the notion of ( T ( i , j ) , I ( k , l ) , F ( [...] Read more.
For i , j , k , l , m , n { 1 , 2 , 3 , 4 } , the notion of ( T ( i , j ) , I ( k , l ) , F ( m , n ) ) -interval neutrosophic subalgebra in B C K / B C I -algebra is introduced, and their properties and relations are investigated. The notion of interval neutrosophic length of an interval neutrosophic set is also introduced, and related properties are investigated. Full article
(This article belongs to the Special Issue Neutrosophic Multi-Criteria Decision Making) Printed Edition available
Open AccessArticle
Cross Entropy Measures of Bipolar and Interval Bipolar Neutrosophic Sets and Their Application for Multi-Attribute Decision-Making
Axioms 2018, 7(2), 21; https://doi.org/10.3390/axioms7020021 - 24 Mar 2018
Cited by 11
Abstract
The bipolar neutrosophic set is an important extension of the bipolar fuzzy set. The bipolar neutrosophic set is a hybridization of the bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent positive membership functions and [...] Read more.
The bipolar neutrosophic set is an important extension of the bipolar fuzzy set. The bipolar neutrosophic set is a hybridization of the 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 their basic properties. We also define cross entropy measures of interval bipolar neutrosophic sets and prove their basic properties. Thereafter, we develop two novel multi-attribute decision-making strategies 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 strategies to show the applicability and effectiveness of the developed strategies. At the end, the main conclusion and future scope of research are summarized. Full article
(This article belongs to the Special Issue Neutrosophic Multi-Criteria Decision Making) Printed Edition available
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Open AccessArticle
Multi-Attribute Decision-Making Method Based on Neutrosophic Soft Rough Information
Axioms 2018, 7(1), 19; https://doi.org/10.3390/axioms7010019 - 20 Mar 2018
Cited by 6
Abstract
Soft sets (SSs), neutrosophic sets (NSs), and rough sets (RSs) are different mathematical models for handling uncertainties, but they are mutually related. In this research paper, we introduce the notions of soft rough neutrosophic sets (SRNSs) and neutrosophic soft rough sets (NSRSs) as [...] Read more.
Soft sets (SSs), neutrosophic sets (NSs), and rough sets (RSs) are different mathematical models for handling uncertainties, but they are mutually related. In this research paper, we introduce the notions of soft rough neutrosophic sets (SRNSs) and neutrosophic soft rough sets (NSRSs) as hybrid models for soft computing. We describe a mathematical approach to handle decision-making problems in view of NSRSs. We also present an efficient algorithm of our proposed hybrid model to solve decision-making problems. Full article
(This article belongs to the Special Issue Neutrosophic Multi-Criteria Decision Making) Printed Edition available
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Open AccessArticle
Neutrosophic Soft Rough Graphs with Application
Axioms 2018, 7(1), 14; https://doi.org/10.3390/axioms7010014 - 26 Feb 2018
Cited by 15
Abstract
Neutrosophic sets (NSs) handle uncertain information while fuzzy sets (FSs) and intuitionistic fuzzy sets (IFs) fail to handle indeterminate information. Soft set theory, neutrosophic set theory, and rough set theory are different mathematical models for handling uncertainties and they are mutually related. The [...] Read more.
Neutrosophic sets (NSs) handle uncertain information while fuzzy sets (FSs) and intuitionistic fuzzy sets (IFs) fail to handle indeterminate information. Soft set theory, neutrosophic set theory, and rough set theory are different mathematical models for handling uncertainties and they are mutually related. The neutrosophic soft rough set (NSRS) model is a hybrid model by combining neutrosophic soft sets with rough sets. We apply neutrosophic soft rough sets to graphs. In this research paper, we introduce the idea of neutrosophic soft rough graphs (NSRGs) and describe different methods of their construction. We consider the application of NSRG in decision-making problems. In particular, we develop efficient algorithms to solve decision-making problems. Full article
(This article belongs to the Special Issue Neutrosophic Multi-Criteria Decision Making) Printed Edition available
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Open AccessArticle
Neutrosophic Number Nonlinear Programming Problems and Their General Solution Methods under Neutrosophic Number Environments
Axioms 2018, 7(1), 13; https://doi.org/10.3390/axioms7010013 - 24 Feb 2018
Cited by 7
Abstract
In practical situations, we often have to handle programming problems involving indeterminate information. Building on the concepts of indeterminacy I and neutrosophic number (NN) (z = p + qI for p, q), this paper introduces some basic operations [...] Read more.
In practical situations, we often have to handle programming problems involving indeterminate information. Building on the concepts of indeterminacy I and neutrosophic number (NN) (z = p + qI for p, q), this paper introduces some basic operations of NNs and concepts of NN nonlinear functions and inequalities. These functions and/or inequalities contain indeterminacy I and naturally lead to a formulation of NN nonlinear programming (NN-NP). These techniques include NN nonlinear optimization models for unconstrained and constrained problems and their general solution methods. Additionally, numerical examples are provided to show the effectiveness of the proposed NN-NP methods. It is obvious that the NN-NP problems usually yield NN optimal solutions, but not always. The possible optimal ranges of the decision variables and NN objective function are indicated when the indeterminacy I is considered for possible interval ranges in real situations. Full article
(This article belongs to the Special Issue Neutrosophic Multi-Criteria Decision Making) Printed Edition available
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Open AccessArticle
NN-Harmonic Mean Aggregation Operators-Based MCGDM Strategy in a Neutrosophic Number Environment
Axioms 2018, 7(1), 12; https://doi.org/10.3390/axioms7010012 - 23 Feb 2018
Cited by 11
Abstract
A neutrosophic number (a + bI) is a significant mathematical tool to deal with indeterminate and incomplete information which exists generally in real-world problems, where a and bI denote the determinate component and indeterminate component, respectively. We define score functions and [...] Read more.
A neutrosophic number (a + bI) is a significant mathematical tool to deal with indeterminate and incomplete information which exists generally in real-world problems, where a and bI denote the determinate component and indeterminate component, respectively. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine the unknown weight of the criteria. We define the neutrosophic number harmonic mean operators and prove their basic properties. Then, we develop two novel multi-criteria group decision-making (MCGDM) strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility, applicability, and effectiveness of the two proposed strategies. Sensitivity analysis with the variation of “I” on neutrosophic numbers is performed to demonstrate how the preference ranking order of alternatives is sensitive to the change of “I”. The efficiency of the developed strategies is ascertained by comparing the results obtained from the proposed strategies with the results obtained from the existing strategies in the literature. Full article
(This article belongs to the Special Issue Neutrosophic Multi-Criteria Decision Making) Printed Edition available
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Open AccessArticle
Rough Neutrosophic Digraphs with Application
Axioms 2018, 7(1), 5; https://doi.org/10.3390/axioms7010005 - 18 Jan 2018
Cited by 6
Abstract
A rough neutrosophic set model is a hybrid model which deals with vagueness by using the lower and upper approximation spaces. In this research paper, we apply the concept of rough neutrosophic sets to graphs. We introduce rough neutrosophic digraphs and describe methods [...] Read more.
A rough neutrosophic set model is a hybrid model which deals with vagueness by using the lower and upper approximation spaces. In this research paper, we apply the concept of rough neutrosophic sets to graphs. We introduce rough neutrosophic digraphs and describe methods of their construction. Moreover, we present the concept of self complementary rough neutrosophic digraphs. Finally, we consider an application of rough neutrosophic digraphs in decision-making. Full article
(This article belongs to the Special Issue Neutrosophic Multi-Criteria Decision Making) Printed Edition available
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Open AccessArticle
Neutrosophic Positive Implicative N -Ideals in BCK-Algebras
Axioms 2018, 7(1), 3; https://doi.org/10.3390/axioms7010003 - 15 Jan 2018
Cited by 15
Abstract
The notion of a neutrosophic positive implicative N -ideal in B C K -algebras is introduced, and several properties are investigated. Relations between a neutrosophic N -ideal and a neutrosophic positive implicative N -ideal are discussed. Characterizations of a neutrosophic positive implicative N [...] Read more.
The notion of a neutrosophic positive implicative N -ideal in B C K -algebras is introduced, and several properties are investigated. Relations between a neutrosophic N -ideal and a neutrosophic positive implicative N -ideal are discussed. Characterizations of a neutrosophic positive implicative N -ideal are considered. Conditions for a neutrosophic N -ideal to be a neutrosophic positive implicative N -ideal are provided. An extension property of a neutrosophic positive implicative N -ideal based on the negative indeterminacy membership function is discussed. Full article
(This article belongs to the Special Issue Neutrosophic Multi-Criteria Decision Making) Printed Edition available
Open AccessArticle
Neutrosophic Hough Transform
Axioms 2017, 6(4), 35; https://doi.org/10.3390/axioms6040035 - 18 Dec 2017
Cited by 2
Abstract
Hough transform (HT) is a useful tool for both pattern recognition and image processing communities. In the view of pattern recognition, it can extract unique features for description of various shapes, such as lines, circles, ellipses, and etc. In the view of image [...] Read more.
Hough transform (HT) is a useful tool for both pattern recognition and image processing communities. In the view of pattern recognition, it can extract unique features for description of various shapes, such as lines, circles, ellipses, and etc. In the view of image processing, a dozen of applications can be handled with HT, such as lane detection for autonomous cars, blood cell detection in microscope images, and so on. As HT is a straight forward shape detector in a given image, its shape detection ability is low in noisy images. To alleviate its weakness on noisy images and improve its shape detection performance, in this paper, we proposed neutrosophic Hough transform (NHT). As it was proved earlier, neutrosophy theory based image processing applications were successful in noisy environments. To this end, the Hough space is initially transferred into the NS domain by calculating the NS membership triples (T, I, and F). An indeterminacy filtering is constructed where the neighborhood information is used in order to remove the indeterminacy in the spatial neighborhood of neutrosophic Hough space. The potential peaks are detected based on thresholding on the neutrosophic Hough space, and these peak locations are then used to detect the lines in the image domain. Extensive experiments on noisy and noise-free images are performed in order to show the efficiency of the proposed NHT algorithm. We also compared our proposed NHT with traditional HT and fuzzy HT methods on variety of images. The obtained results showed the efficiency of the proposed NHT on noisy images. Full article
(This article belongs to the Special Issue Neutrosophic Multi-Criteria Decision Making) Printed Edition available
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