Multi-valued Neutrosophic Sets Research Articles

Multivalued neutrosophic power partitioned Hamy mean operators and their application in MAGDM.

The novel multivalued neutrosophic aggregation operators are proposed in this paper to handle the complicated decision-making situations with correlation between specific information and partitioned parameters at the same time, which are based on weighted power partitioned Hamy mean (WMNPPHAM) operators for multivalued neutrosophic sets (MNS) proposed by combining the Power Average and Hamy operators. Firstly, the power partitioned Hamy mean (PPHAM) is capable of capture the correlation between aggregation parameters and the relationship among attributes dividing several parts, where the attributes are dependent definitely within the interchangeable fragment, other attributes in divergent sections are irrelevant. Secondly, because MNS can effectively represent imprecise, insufficient, and uncertain information, we proposed the multivalued neutrosophic PMHAM (WMNPHAM) operator for MNS and its partitioned variant (WMNPPHAM) with the characteristics and examples. Finally, this multiple attribute group decision making (MAGDM) technique is proven to be feasible by comparing with the existing methods to confirm this method's usefulness and validity.

Multi-Valued Neutrosophic Sets for Forecasting Cryptocurrency Volatility

The media, legislators, investors, scholars, and regulatory agencies have all shown increased interest in the Cryptocurrency sector recently. Using different criteria in furthermore to return and risk in the cryptocurrency issue utilizing the multi-criteria decision-making (MCDM) methodologies makes it more practical in the real world. A model for predicting the volatility of cryptocurrencies is proposed in this study, and it is based on the TOPSIS approach. The model uses five criteria and six cryptocurrencies. Using a multi-valued neutrosophic set, also known as MVNS, helps to reduce the amount of uncertainty associated with the problem. MVNS was used to express the criteria and alternatives, and the model might possibly represent the Cryptocurrency with varying degrees of truth, indeterminacy, and falsity values.

An Improved Method Based on TODIM and TOPSIS for Multi-Attribute Decision-Making with Multi-Valued Neutrosophic Sets

An Improved Method Based on TODIM and TOPSIS for Multi-Attribute Decision-Making with Multi-Valued Neutrosophic Sets

Novel Stable Approach with Probability Distribution for Multi-Criteria Decision-Making Problems of Multi-Valued Neutrosophic Sets

In this paper, a novel approach and framework based on interval-dependent degree and probability distribution for multi-criteria decision-making problems with multi-valued neutrosophic sets (MVNSs) is proposed. First, a simplified dependent function and distribution function are given and integrated into a concise formula, which is called the interval-dependent function and contains interval computing and probability distribution information in an interval. Then a transformation operator is defined and it is shown how to convert MVNSs into an interval set. Subsequently, the interval-dependent function with the probability distribution of MVNSs is deduced. Finally, an example and comparative analysis are provided to verify the feasibility and effectiveness of the proposed method. In addition, uncertainty analysis, which reflects the dynamic change of the ranking result with decision-makers’ preferences, is performed by setting different distribution functions, which increases the reliability and accuracy of the proposed method.

An Improved MABAC Group Decision-Making Method Using Regret Theory and Likelihood in Probability Multi-Valued Neutrosophic Sets

Probability multi-valued neutrosophic set (PMVNS) is a preferable tool to capture the preference and hesitancy of decision makers (DMs) and to depict inconsistent and ambiguous information. In this paper, we improve the multi-attributive border approximation area comparison (MABAC) method under the PMVNS environment and establish a three-phase multi-attribute group decision-making (MAGDM) method. Firstly, some concepts of PMVNS, traditional MABAC method and regret theory (RT) are reviewed. Then, the similarity measure for PMVNSs is defined and utilized to derive the important degree of DMs, and the likelihood of preference relations expressed by the probability multi-valued neutrosophic numbers (PMVNNs) is first presented and employed to replace the distance deviation in traditional MABAC method. Furthermore, a novel MAGDM method where the performance of alternatives is expressed by the PMVNN is established by combining the likelihood-based MABAC method and RT which considered given DMs’ behavior psychology. Finally, a case study is implemented to demonstrate the feasibility and applicability of our proposed approach.

Probability multi-valued neutrosophic ELECTRE method for multi-criteria group decision-making

Probability multi-valued neutrosophic sets (PMVNSs) can better describe the incomplete and indeterminate evaluation information, and the ELECTRE method can rank the alternatives in the light of the outranking relations among criteria. To combine their advantages, this paper introduces an extended ELECTRE method to address multi-criteria group decision-making (MCGDM) problems with the information of PMVNSs. Firstly, we introduce the definitions of PMVNSs and the classical ELECTRE method, discuss the ELECTRE-based outranking relations for PMVNSs and analyze some properties of them. Furthermore, the probability multi-valued neutrosophic ELECTRE method is developed to address MCGDM problems based on the proposed distance measure and outranking relations for PMVNSs. Finally, a typical example for logistics outsourcing provider selection is devoted to demonstrate the feasibility of the proposed approach. Moreover, the same example-based comparisons with other existing methods are carried out, the results show our proposed approach outperforms the existing methods in solving the MCGDM problems with PMVNSs.

An Extension of ARAS Methodology for Multi-criteria Group Decision-Making Problems within Probability Multi-valued Neutrosophic Sets

Probability multi-valued neutrosophic sets (PMVNSs) can depict the preference and hesitancy of decision makers (DMs) simultaneously, and utility-based additive ratio assessment (ARAS) can effectively evaluate and rank feasible alternatives. In order to make optimal decision making under the environment of the PMVNSs, in this paper, an extended ARAS methodology for multi-criteria group decision making (MCGDM) is developed. Firstly, we propose probability multi-valued neutrosophic normalized weighted Bonferroni distance (PMVNNWBD) to measure the closeness of weighted probability multi-valued neutrosophic numbers (PMVNNs). Then, an entropy measure for PMVNSs is proposed to describe the inaccuracy degree of PMVNSs and to derive the weights of DMs. Further, considering the relationship between criteria, we construct a modified maximizing deviation model based on PMVNNWBD to obtain criteria weights. Moreover, an extended ARAS method for MCGDM is established to handle PMVNSs based on the obtained weight information of DMs and criteria. Finally, the feasibility and superiority of the proposed approach are verified by a case study concerning third-party logistics (3PLs) supplier selection, and sensitive analysis of different parameters shows our proposed approach is flexible.

Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems

Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems

Multi-Valued Neutrosophic Distance-Based QUALIFLEX Method for Treatment Selection

Multi-valued neutrosophic sets (MVNSs) consider the truth-membership, indeterminacy-membership, and falsity-membership simultaneously, which can more accurately express the preference information of decision-makers. In this paper, the normalized multi-valued neutrosophic distance measure is developed firstly and the corresponding properties are investigated as well. Secondly, the normalized multi-valued neutrosophic distance difference is defined and the corresponding partial ordering relation is discussed. Thirdly, based on the developed distances and comparison method, an extended multi-valued neutrosophic QUALItative FLEXible multiple criteria (QUALIFLEX) method is proposed to handle MCDM problems where the weights of criteria are completely unknown. Finally, an example for selection of medical diagnostic plan is provided to demonstrate the proposed method, together with sensitivity analysis and comparison analysis.

An Extended Multi-criteria Group Decision-Making PROMETHEE Method Based on Probability Multi-valued Neutrosophic Sets

The PROMETHEE method, one of the most widely used and best known methods, takes advantage of the outranking principle to rank potential alternatives. The probability multi-valued neutrosophic sets (PMVNSs) have the power to describe complex uncertain information more comprehensively. Thus, in order to integrate the merits of PROMETHEE method and PMVNSs, this paper extends the PROMETHEE method to PMVNSs environment. Firstly, some basic preliminaries are reviewed, such as multi-valued neutrosophic sets (MVNSs), PMVNSs and classical PROMETHEE method. Then, we propose the operational laws of PMVNSs based on the operational rules of the MVNSs and probability distribution. Meanwhile, the score function and accuracy function of PMVNSs are given to simplify the comparison of any two probability multi-valued neutrosophic numbers (PMVNNs). Further, we develop a new distance measure for PMVNNs with unequal length, and then based on the distance measure and deviation maximization method, the attribute weights are determined; an extended PROMETHEE method for multi-criteria group decision-making with the information of PMVNSs is established to achieve the process for optimal alternative selection. In the end, a practical example concerning third party logistics providers is used to highlight the feasibility and superiority of the proposed approach.

A Forecasting Model Based on Multi-Valued Neutrosophic Sets and Two-Factor, Third-Order Fuzzy Fluctuation Logical Relationships

Making predictions according to historical values has long been regarded as common practice by many researchers. However, forecasting solely based on historical values could lead to inevitable over-complexity and uncertainty due to the uncertainties inside, and the random influence outside, of the data. Consequently, finding the inherent rules and patterns of a time series by eliminating disturbances without losing important details has long been a research hotspot. In this paper, we propose a novel forecasting model based on multi-valued neutrosophic sets to find fluctuation rules and patterns of a time series. The contributions of the proposed model are: (1) using a multi-valued neutrosophic set (MVNS) to describe the fluctuation patterns of a time series, the model could represent the fluctuation trend of up, equal, and down with degrees of truth, indeterminacy, and falsity which significantly preserve details of the historical values; (2) measuring the similarities of different fluctuation patterns by the Hamming distance could avoid the confusion caused by incomplete information from limited samples; and (3) introducing another related time series as a secondary factor to avoid warp and deviation in inferring inherent rules of historical values, which could lead to more comprehensive rules for further forecasting. To evaluate the performance of the model, we explored the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) as the major factor we forecast, and the Dow Jones Index as the secondary factor to facilitate the predicting of the TAIEX. To show the universality of the model, we applied the proposed model to forecast the Shanghai Stock Exchange Composite Index (SHSECI) as well.

A Forecasting Model Based on Multi-Valued Neutrosophic Sets and Two-Factor, Third-Order Fuzzy Fluctuation Logical Relationships

A Forecasting Model Based on Multi-Valued Neutrosophic Sets and Two-Factor, Third-Order Fuzzy Fluctuation Logical Relationships

Probability multi-valued neutrosophic sets and its application in multi-criteria group decision-making problems

This paper introduces probability multi-valued neutrosophic sets (PMVNSs) based on multi-valued neutrosophic sets and probability distribution. PMVNS can serve as a reliable tool to depict uncertain, incomplete, inconsistent and hesitant decision-making information and reflect the distribution characteristics of all provided evaluation values.

A projection-based TODIM method under multi-valued neutrosophic environments and its application in personnel selection

The personnel selection is a vital activity for companies, and multi-valued neutrosophic sets (MVNSs) can denote the fuzziness and hesitancy in the processes of the personnel selection.

Probability multi-valued neutrosophic sets and its application in multi-criteria group decision-making problems

This paper introduces probability multi-valued neutrosophic sets (PMVNSs) based on multi-valued neutrosophic sets and probability distribution. PMVNS can serve as a reliable tool to depict uncertain, incomplete, inconsistent and hesitant decision-making information and reflect the distribution characteristics of all provided evaluation values. This paper focuses on developing an innovative method to address multi-criteria group decision-making (MCGDM) problems in which the weight information is completely unknown and the evaluation values taking the form of probability multi-valued neutrosophic numbers (PMVNNs). First, the definition of PMVNSs is described. Second, an extended convex combination operation of PMVNNs is defined, and the probability multi-valued neutrosophic number weighted average operator is proposed. Moreover, two cross-entropy measures for PMVNNs are presented, and a novel qualitative flexible multiple criteria method (QUALIFLEX) is developed. Subsequently, an innovative MCGDM approach is established by incorporating the proposed aggregation operator and the developed QUALIFLEX method. Finally, an illustrative example concerning logistics outsourcing is provided to demonstrate the proposed method, and its feasibility and validity are further verified by comparison with other existing methods.

A multi-valued neutrosophic qualitative flexible approach based on likelihood for multi-criteria decision-making problems

ABSTRACTIn this paper, multi-criteria decision-making (MCDM) problems based on the qualitative flexible multiple criteria method (QUALIFLEX), in which the criteria values are expressed by multi-valued neutrosophic information, are investigated. First, multi-valued neutrosophic sets (MVNSs), which allow the truth-membership function, indeterminacy-membership function and falsity-membership function to have a set of crisp values between zero and one, are introduced. Then the likelihood of multi-valued neutrosophic number (MVNN) preference relations is defined and the corresponding properties are also discussed. Finally, an extended QUALIFLEX approach based on likelihood is explored to solve MCDM problems where the assessments of alternatives are in the form of MVNNs; furthermore an example is provided to illustrate the application of the proposed method, together with a comparison analysis.

A projection-based TODIM method under multi-valued neutrosophic environments and its application in personnel selection

The personnel selection is a vital activity for companies, and multi-valued neutrosophic sets (MVNSs) can denote the fuzziness and hesitancy in the processes of the personnel selection. The extant fuzzy TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) methods take advantage of distance to denote the difference between two fuzzy sets (FSs). Nevertheless, the distance measurement, which ignores the included angle between two FSs, cannot comprehensively reflect the difference between two FSs. To cover this defect, a projection-based TODIM method with MVNSs for personnel selection is established to consider the risk preference of decision-makers and overcome the defect of the extant fuzzy TODIM methods. The proposed TODIM method makes use of an improved comparison method which overcomes the deficiency of extant comparison method. Furthermore, a projection-based difference measurement is defined and utilized in the projection-based TODIM method. We conduct a numerical example of the personnel selection to explain the application of the projection-based TODIM method and discuss the influence of the parameter. Finally, the proposed method is compared with several extant methods to verify its feasibility.

Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems

Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems

Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems

In recent years, hesitant fuzzy sets (HFSs) and neutrosophic sets (NSs) have become a subject of great interest for researchers and have been widely applied to multi-criteria group decision-making (MCGDM) problems. In this paper, multi-valued neutrosophic sets (MVNSs) are introduced, which allow the truth-membership, indeterminacy membership and falsity-membership degree have a set of crisp values between zero and one, espectively.

Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems

AbstractIn recent years, hesitant fuzzy sets (HFSs) and neutrosophic sets (NSs) have become a subject of great interest for researchers and have been widely applied to multi-criteria group decision-making (MCGDM) problems. In this paper, multi-valued neutrosophic sets (MVNSs) are introduced, which allow the truth-membership, indeterminacy- membership and falsity-membership degree have a set of crisp values between zero and one, respectively. Then the operations of multi-valued neutrosophic numbers (MVNNs) based on Einstein operations are defined, and a comparison method for MVNNs is developed depending on the related research of HFSs and Atanassov's intuitionistic fuzzy sets (IFSs). Furthermore, the multi-valued neutrosophic power weighted average (MVNPWA) operator and the multi-valued neutrosophic power weighted geometric (MVNPWG) operator are proposed and the desirable properties of two operators are also discussed. Finally, an approach for solving MCGDM problems is explored by applying the power aggreg...