Probabilistic Single-Valued (Interval) Neutrosophic Hesitant Fuzzy Set and Its Application in Multi-Attribute Decision Making

Shao, Songtao; Zhang, Xiao­hong; Yu, Li; Bo, Chunxin

doi:10.3390/sym10090419

Cited by 24 publications

(12 citation statements)

References 54 publications

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“…(iii) Utilizing a more sophisticated neutrosophic set to develop new NTS model, e.g. probabilistic singlevalued neutrosophic hesitant fuzzy set [62].…”

Section: Conclusion and Remarksmentioning

confidence: 99%

A Novel Single Valued Neutrosophic Hesitant Fuzzy Time Series Model: Applications in Indonesian and Argentinian Stock Index Forecasting

et al. 2020

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This paper proposed a novel first-order single-valued neutrosophic hesitant fuzzy time series (SVNHFTS) forecasting model. Our aim is to improve the previously proposed neutrosophic time series (NTS) model by incorporating the degree of the hesitancy using single-valued neutrosophic hesitant fuzzy set (SVNHFS) model instead of single-valued neutrosophic set (SVNS). Our paper's novelty is that we incorporate an algorithm that automatically converts the crisp dataset into the neutrosophic set that eliminates the need for experts' input or opinions in determining the membership in each of the partitioned neutrosophic set. We also incorporate Markov Chain algorithm in the de-neutrosophication process to include the weightage of the repeating neutrosophic logical relationships (NLRs). Our paper's significant contribution is to add to the existing body of knowledge related to fuzzy time series (FTS) by developing a new FTS model based on SVNHFS, one of the improved version of fuzzy sets, since this area of research is still relatively underdeveloped. To determine our proposed model's capability, we apply our proposed SVNHFTS model to three real datasets while also comparing the result to the other FTS models based on improved versions of fuzzy sets. Our datasets include benchmark enrollment data of University of Alabama, IDX Composite (Indonesian composite stock index), and MERVAL index (Argentinian composite stock index). The result shows that our proposed SVNHFTS model outperforms most of the other FTS models in terms of AFE and RMSE, especially the previously proposed NTS model. INDEX TERMS Single-valued neutrosophic hesitant fuzzy set (SVNHFS), single-valued neutrosophic hesitant fuzzy time series (SVNHFTS), neutrosophic time series (NTS), fuzzy time series (FTS).

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“…(iii) Utilizing a more sophisticated neutrosophic set to develop new NTS model, e.g. probabilistic singlevalued neutrosophic hesitant fuzzy set [62].…”

Section: Conclusion and Remarksmentioning

confidence: 99%

A Novel Single Valued Neutrosophic Hesitant Fuzzy Time Series Model: Applications in Indonesian and Argentinian Stock Index Forecasting

et al. 2020

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“…For the content of this part, as an extended theory of FS, Shao et al [48] first proposed the probabilistic single-valued neutrosophic hesitant fuzzy set (PSVNHFS). The PSVNHFS can better describe the uncertainty by involving objectively uncertain information and subjective uncertain information.…”

Section: The Distance and Similarity Measures Of Psvnhfsmentioning

confidence: 99%

“…Suppose that X is a finite reference set. A PNHFS on X is denoted by the following mathematical symbol [48]:…”

Section: The Distance and Similarity Measures Of Psvnhfsmentioning

confidence: 99%

“…However, when solving some decision problems, the decision makers will give the indeterminacy-membership hesitant degrees and corresponding probability information. In order to solve this situation, Shao et al [48] and Peng et al [49] established probabilistic single-valued neutrosophic hesitant fuzzy set (PSVNHFS or PNHFS) and probability multi-valued neutrosophic set (PMVN), respectively. Shao et al investigated the basic operation laws of PNHFSs and their characteristics.…”

Section: Introductionmentioning

confidence: 99%

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Measures of Probabilistic Neutrosophic Hesitant Fuzzy Sets and the Application in Reducing Unnecessary Evaluation Processes

Shao

Zhang

2019

Mathematics

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Distance measure and similarity measure have been applied to various multi-criteria decision-making environments, like talent selections, fault diagnoses and so on. Some improved distance and similarity measures have been proposed by some researchers. However, hesitancy is reflected in all aspects of life, thus the hesitant information needs to be considered in measures. Then, it can effectively avoid the loss of fuzzy information. However, regarding fuzzy information, it only reflects the subjective factor. Obviously, this is a shortcoming that will result in an inaccurate decision conclusion. Thus, based on the definition of a probabilistic neutrosophic hesitant fuzzy set (PNHFS), as an extended theory of fuzzy set, the basic definition of distance, similarity and entropy measures of PNHFS are established. Next, the interconnection among the distance, similarity and entropy measures are studied. Simultaneously, a novel measure model is established based on the PNHFSs. In addition, the new measure model is compared by some existed measures. Finally, we display their applicability concerning the investment problems, which can be utilized to avoid redundant evaluation processes.

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“…The probabilistic algorithms are effective solutions to design computational applications under uncertainties offering acceptable results [16][17][18]. The randomized and probabilistic algorithms require input data and a random bit-stream or set of keys to compute on datasets [10].…”

Section: Motivationmentioning

confidence: 99%

Construction and Simulation of Composite Measures and Condensation Model for Designing Probabilistic Computational Applications

Bagchi

2018

Symmetry

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The probabilistic algorithms are widely applied in designing computational applications such as distributed systems and probabilistic databases, to determine distributed consensus in the presence of random failures of nodes or networks. In distributed computing, symmetry breaking is performed by employing probabilistic algorithms. In general, probabilistic symmetry breaking without any bias is preferred. Thus, the designing of randomized and probabilistic algorithms requires modeling of associated probability spaces to generate control-inputs. It is required that discrete measures in such spaces are computable and tractable in nature. This paper proposes the construction of composite discrete measures in real as well as complex metric spaces. The measures are constructed on different varieties of continuous smooth curves having distinctive non-linear profiles. The compositions of discrete measures consider arbitrary functions within metric spaces. The measures are constructed on 1-D interval and 2-D surfaces and, the corresponding probability metric product is defined. The associated sigma algebraic properties are formulated. The condensation measure of the uniform contraction map is constructed as axioms. The computational evaluations of the proposed composite set of measures are presented.

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Probabilistic Single-Valued (Interval) Neutrosophic Hesitant Fuzzy Set and Its Application in Multi-Attribute Decision Making

Cited by 24 publications

References 54 publications

A Novel Single Valued Neutrosophic Hesitant Fuzzy Time Series Model: Applications in Indonesian and Argentinian Stock Index Forecasting

A Novel Single Valued Neutrosophic Hesitant Fuzzy Time Series Model: Applications in Indonesian and Argentinian Stock Index Forecasting

Measures of Probabilistic Neutrosophic Hesitant Fuzzy Sets and the Application in Reducing Unnecessary Evaluation Processes

Construction and Simulation of Composite Measures and Condensation Model for Designing Probabilistic Computational Applications

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