Neutrosophic Hesitant Fuzzy Set Research Articles

An Approach to Multi-Attribute Decision-Making Based on Single-Valued Neutrosophic Hesitant Fuzzy Aczel-Alsina Aggregation Operator

A single-valued Neutrosophic hesitant fuzzy set (SVNHFS) is a combination of a single-valued neutrosophic set (SVNS) and hesitant fuzzy set (HFS) that has been developed to address insufficient, unreliable, and vague environments in which each element has several possible options determined by the truthiness, indeterminacy and falsity value. By considering this, in this paper, we have proposed the Aczel-Alsina aggregation operator (AAAO) for SVNHFS, which is more flexible t-norm and t-conorm than the other and due to the flexible nature of parameters to solve Multi-Attribute decision making (MADM) problems. Further, the score function, accuracy function, and certainty function of SVNHFS have been defined. In this paper, we proposed the single-valued neutrosophic hesitant fuzzy Aczel-Alsina Weighted Averaging Operator (SVNHFAAWA), single-valued neutrosophic hesitant fuzzy Aczel-Alsina Weighted ordered Averaging Operator (SVNHFAAWOA), and single-valued neutrosophic hesitant fuzzy Aczel-Alsina hybrid averaging operator (SVNHFAAHA). To testify to the reliability and stability of the newly created aggregation operator (AO), an application of MADM has been discussed.

A Probabilistic Neutrosophic Hesitant Fuzzy Set for Waste Water Treatment Plants

Decision-makers at wastewater treatment plants must increase process efficiency and circularity while preserving economic performance. They must comply with increasing requirements about lowering emissions, sustainability, and human health safety. To operate and choose technologies to fulfil these expectations leads to complicated multi-objective issues. As a consequence, the water industry has developed several decision support systems. Multi-criteria decision-making (MCDM) is used to deal with various criteria in the evaluation process. The MCDM methodology integrated with the probabilistic neutrosophic hesitant fuzzy set (PNHFS) to deal with vague and incomplete information. The PNHFS used the VIKOR method to rank the alternatives and used the optimal wastewater treatment plants. The criteria weights are computed. The results show that safety is of the highest importance—the sensitivity analysis was conducted to show the different ranks under different cases. The main results show the different ranks are stable, and the suggested MCDM methodology is robust compared with other MCDM methods.

A novel algorithm for autonomous parking vehicles using adjustable probabilistic neutrosophic hesitant fuzzy set features

A novel algorithm for autonomous parking vehicles using adjustable probabilistic neutrosophic hesitant fuzzy set features

Developing deep transfer and machine learning models of chest X-ray for diagnosing COVID-19 cases using probabilistic single-valued neutrosophic hesitant fuzzy

This study presents a novel dynamic localisation-based decision (DLBD) with fuzzy weighting with zero inconsistency (FWZIC) under a probabilistic single-valued neutrosophic hesitant fuzzy set (PSVNHFS) environment to benchmark Hybrid Multi Deep Transfer and Machine Learning (HMDTML) models. The novel DLBD method is proposed to generate a dynamic localisation decision matrix based on the upper and lower boundaries and the length of the scale. The superiority of DLBD derives from its ability to manage dynamic changes with boundary value consequences. In addition, the utilization of PSVNHFS in conjunction with DLBD and FWZIC has proven to effectively address the challenges posed by vagueness, uncertainty and hesitancy in the benchmarking procedure. The proposed methodology consists of three primary three steps: i) the adaptation of 48 HMDTML models, including 4 deep transfer learning models and 12 machine learning models trained on a dataset of 936 chest X-ray images obtained from both COVID-19 patients and individuals without the disease. Then, these models were evaluated based on seven evaluation criteria, and a decision matrix was proposed. ii) The development of a PSVNH–FWZIC to assign weights to the evaluation criteria. iii) The formulation of a PSVNH–DLBD for the purpose of benchmarking HMDTML models. Results of the PSVNH–FWZIC revealed that AUC and time were the most important evaluation criteria, while precision was the least important. Furthermore, the results from PSVNH–DLBD, reveal that Model M24 (Painters-Decision Tree) earned the highest rank when λ=2,3,4,5and6, followed by Model M25 (SqueezeNet-AdaBoost) and Model M34 (DeepLoc-kNN), while Model M39 (DeepLoc-SVM) had the lowest rank (rank = 48) across all λ values. The proposed method underwent sensitivity and comparison analyses to confirm its reliability and robustness.

A novel extension of hesitant fuzzy sets on UP (BCC)-algebras: neutrosophic hesitant fuzzy sets

In this paper, we introduce the concepts of neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals of UP (BCC)-algebras. The characteristic neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals have also been studied. The relationshipbetween neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals and their level subsets is provided. The Cartesian product of neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals is also supplied. Finally, we also find the property of the homomorphic pre-image of neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals.

Correlation measures under single-valued neutrosophic hesitant fuzzy sets environment for multi-criteria decision-making problems

We examine correlation coefficients for single-valued neutrosophic hesitant fuzzy sets (SVNHFSs) to point out their questionable results for the ideal alternative. Then, we propose three similarity measure methods to solve multi-criteria decision-making (MCDM) problems. Three applications, namely, ranking of alternatives, dysfunctional comments of turbine engine generators, and disease diagnoses for patients, illustrate the stability and effectivity of our new similarity. Our findings will help researchers deal with similarity measures in the future.

An Optimization Approach with Single-Valued Neutrosophic Hesitant Fuzzy Dombi Aggregation Operators

Using the strength of a single-valued neutrosophic set (SVNS) with the flexibility of a hesitant fuzzy set (HFS) yields a robust model named the single-valued neutrosophic hesitant fuzzy set (SVNHFS). Due to the ability to utilize three independent indexes (truthness, indeterminacy, and falsity), an SVNHFS is an efficient model for optimization and computational intelligence (CI) as well as an intelligent decision support system (IDSS). Taking advantage of the flexibility of operational parameters in Dombi’s t-norm and t-conorm operations, new aggregation operators (AOs) are proposed, which are named the SVN fuzzy Dombi weighted averaging (SVNHFDWA) operator, SVN hesitant fuzzy Dombi ordered weighted averaging (SVNHFDOWA) operator, SVN hesitant fuzzy Dombi hybrid averaging (SVNHFDHWA) operator, SVN hesitant fuzzy Dombi weighted geometric (SVNHFDWG) operator, SVN hesitant fuzzy Dombi ordered weighted geometric (SVNHFDOWG) operator as well as SVN hesitant fuzzy Dombi hybrid weighted geometric (SVNHFDHWG) operator. The efficiency of these AOs is investigated in order to determine the best option using SVN hesitant fuzzy numbers (SVNHFNs) in an IDSS. Additionally, a practical application of SVNHFDWA and SVNHFDWG is also presented to examine symmetrical analysis in the selection of wireless charging station for vehicles.

Topological Structure of Single-Valued Neutrosophic Hesitant Fuzzy Sets and Data Analysis for Uncertain Supply Chains

From production to retail, the food supply chain (FSC) encompasses all stages of food production. Food is now transmitted across continents over long ranges. People depend on supply chains for basic necessities such as food, water, drinks, etc. Any disruption in these shipment pipelines poses a serious threat to human life. Supplier selection (SS) has been identified as a crucial component of FSC, which has been contemplated as a multi-criteria decision-making (MCDM) problem in many studies. The failure of some specific MCDM problems is due to failure in contemplating the relationships between alternatives under uncertain circumstances. To address such challenges, we present a contemporary method for designating green suppliers based on single-valued neutrosophic hesitant fuzzy (SVNHF) information, in which the input assessment is taken into account using single-valued neutrosophic hesitant fuzzy numbers (SVNHFNs). The foremost purpose of this analysis is to construct a topological structure on single-valued neutrosophic hesitant fuzzy sets (SVNHFSs) as well as to validate several key properties with examples. We discuss certain properties of SVNHF topology such as the SVNHF closure, SVNHF interior, SVNHF exterior, and SVNHF frontier. We also examine the conceptualization of the SVNHF dense set and SVNHF base in SVNHF topology using comprehensive examples. Eventually, to demonstrate and validate the superiority and inferiority ranking (SIR) method and choice value (CV) method in terms of their rationality and scientific basis, a real-world example of supplier selection in a food supply chain is provided. A comparative analysis is also performed to discuss the symmetry, validity and advantage of the proposed techniques.

Decision-Making Approach Based on Generalized Aggregation Operators with Complex Single-Valued Neutrosophic Hesitant Fuzzy Set Information

A strategic decision-making technique can help the decision maker to accomplish and analyze the information in an efficient manner. However, in our real life, an uncertainty will play a dominant role during the information collection phase. To handle such uncertainties in the data, we present a decision-making algorithm under the single-valued neutrosophic (SVN) environment. The SVN is a powerful way to deal the information in terms of three degrees, namely, “truth,” “falsity,” and “indeterminacy,” which all are considered independent. The main objective of this study is divided into three folds. In the first fold, we state the novel concept of complex SVN hesitant fuzzy (CSVNHF) set by incorporating the features of the SVN, complex numbers, and the hesitant element. The various fundamental and algebraic laws of the proposed CSVNHF set are described in details. The second fold is to state the various aggregation operators to obtain the aggregated values of the considered CSVNHF information. For this, we stated several generalized averaging operators, namely, CSVNHF generalized weighted averaging, ordered weighted average, and hybrid average. The various properties of these operators are also stated. Finally, we discuss a multiattribute decision-making (MADM) algorithm based on the proposed operators to address the problems under the CSVNHF environment. A numerical example is given to illustrate the work and compare the results with the existing studies’ results. Also, the sensitivity analysis and advantages of the stated algorithm are given in the work to verify and strengthen the study.

Cyber security control selection based decision support algorithm under single valued neutrosophic hesitant fuzzy Einstein aggregation information

<abstract><p>The single-valued neutrosophic hesitant fuzzy set (SV-NHFS) is a hybrid structure of the single-valued neutrosophic set and the hesitant fuzzy set that is designed for some incomplete, uncertain, and inconsistent situations in which each element has a few different values designed by the truth membership hesitant function, indeterminacy membership hesitant function, and falsity membership hesitant function. A strategic decision-making technique can help the decision-maker accomplish and analyze the information in an efficient manner. However, in our real lives, uncertainty will play a dominant role during the information collection phase. To handle such uncertainties in the data, we present a decision-making algorithm in the SV-NHFS environment. In this paper, we first presented the basic operational laws for SV-NHF information under Einstein's t-norm and t-conorm. Furthermore, important properties of Einstein operators, including the Einstein sum, product, and scalar multiplication, are done under SV-NHFSs. Then, we proposed a list of novel aggregation operators' names: Single-valued neutrosophic hesitant fuzzy Einstein weighted averaging, weighted geometric, order weighted averaging, and order weighted geometric aggregation operators. Finally, we discuss a multi-attribute decision-making (MADM) algorithm based on the proposed operators to address the problems in the SV-NHF environment. A numerical example is given to illustrate the work and compare the results with the results of the existing studies. Also, the sensitivity analysis and advantages of the stated algorithm are given in the work to verify and strengthen the study.</p></abstract>

Cosine Similarity Measure of Interval Valued Bipolar Neutrosophic Hesitant Fuzzy Set and Their Applications to Multi-Attribute Decision-Making Process

Cosine similarity measure plays a significant role in various fields. Literature consultation confirms that the theory of cosine similarity measure has received a great interest and attention from the researchers in the world. The concept of Interval Valued Bipolar Neutrosophic Hesitant Fuzzy Sets (IVBNHFS) is recently presented and very interesting. Every element in IVBNHFS is characterized by six independent membership functions (three positive and three negative). There is no investigation on the Cosine Similarity Measure (CSM) of IVBNHFS. In this study, we firstly define a CSM and a weighted CSM between two IVBNHFS and their applications to Multi-Attribute Decision Making (MADM) process in the Interval Valued Bipolar Neutrosophic Hesitant Fuzzy (IVBNHF) setting. And, we establish some properties of CSM and a weighted CSM. We use this strategy to find out the best alternative in MADM case. Then, the new approach to clarify MADM problems in IVBNHF setting is presented in algorithmic form. And, we solve an illustrative case of MADM to demonstrate the effectiveness, workability, and appropriateness of the proposed approach. Finally, the main conclusion and future opportunity of research paper are overviewed and compiled.

Interval Valued Bipolar Neutrosophic Hesitant Fuzzy Sets and its Application on Multi-Attribute Decision-Making by Using Aggregation Operator Method

Interval Valued Bipolar Neutrosophic Hesitant Fuzzy Sets (IVBNHFS) can express complex multi-attribute decision-making (MADM) problems with its interval valued, bipolar, neutrosophic, and hesitant fuzzy elements simultaneously. The two weighted operators, average and geometric, are accustomed aggregation operator method for handling MADM problems. However, we give the Interval Valued Bipolar Neutrosophic Hesitant Fuzzy Weighted Average (IVBNHFWA) and Interval Valued Bipolar Neutrosophic Hesitant Fuzzy Weighted Geometric (IVBNHFWG) operators to aggregate the IVBNHFS and their properties are also discussed in detail. Occasionally, we predestined a MADM method based on the IVBNHFWA and IVBNHFWG operators. Finally, this paper provides an illustrative numerical example of a case study of MADM to authenticate the application and effectiveness of the proposed approaches. Also, we give a comparative study with the existing methods.

A note on “New aggregation operators of single-valued neutrosophic hesitant fuzzy set and their application in multi-attribute decision making”

Single-valued neutrosophic hesitant fuzzy elements (SVNHFEs) can be used to characterize incomplete, uncertain and inconsistent information effectively, which result in great significance of the aggregation of SVNHFEs. However, some existing aggregation operators for SVNHFEs may not be rigorous enough. In this paper, We show that an assertion (Theorem 1) in a previous paper by Liu and Guo [C.F. Liu, Y.S. Luo, New aggregation operators of single-valued neutrosophic hesitant fuzzy set and their application in multi-attribute decision making, Pattern Analysis Application (2019) 22:417–427] is not correct, i.e., the single-valued neutrosophic hesitant fuzzy ordered weighted aggregation (SVNHFOWA) operator does not satisfy idempotency actually. Thus it is not reasonable to adopt the SVNHFOWA operator in many practical applications. The present paper can effectively prevent many researchers from using the SVNHFOWA operator to aggregate SVNHFEs.

Decision making with MABAC method under probabilistic single-valued neutrosophic hesitant fuzzy environment

Recently, there has been great interest on single valued neutrosophic hesitant fuzzy set theory. When compared single valued neutrosophic set, it is more convenient for real life situations. But even in this case, there is still missing data for some decision problems. Probabilistic single valued neutrosophic hesitant fuzzy sets (PSVNHFSs) are defined to solve this problem. Even though it contains more information, it needs some improvements. In this paper, the modified PSVNHFS is defined and some improvements in the theory of PSVNHFS are proposed. Also, we improve some algebraic properties of this set theory and define a distance operator for PSVNHFSs. Then we introduce two aggregation operators called probabilistic single valued neutrosophic hesitant fuzzy weighted arithmetic average (PSVNHFWA) operator and probabilistic single valued neutrosophic hesitant fuzzy weighted geometric average (PSVNHFWG) operator related to algebraic properties presented in this paper. Also, we extend the MABAC method under the probabilistic single valued neutrosophic hesitant fuzzy set theory. Finally, we give an illustrative example to demonstrate the stability and reliability of the proposed theory.

TOPSIS Method for Neutrosophic Hesitant Fuzzy Multi-Attribute Decision Making

Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a very common and useful method for solving multi-criteria decision making problems in certain and uncertain environments. Single valued neutrosophic hesitant fuzzy set (SVNHFS) and interval neutrosophic hesitant fuzzy set (INHFS) are developed on the integration of neutrosophic set and hesitant fuzzy set. In this paper, we extend TOPSIS method for multi-attribute decision making based on single valued neutrosophic hesitant fuzzy set and interval neutrosophic hesitant fuzzy set. Furthermore, we assume that the attribute weights are known, incompletely known or completely unknown. We establish two optimization models for SVNHFS and INHFS with the help of maximum deviation method. Finally, we provide two numerical examples to validate the proposed approach.

Public-Private Partnership Decision Making Based on Correlation Coefficients of Single-Valued Neutrosophic Hesitant Fuzzy Sets

Public-Private Partnership Decision Making Based on Correlation Coefficients of Single-Valued Neutrosophic Hesitant Fuzzy Sets

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

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.

On hesitant neutrosophic rough set over two universes and its application

As a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single valued neutrosophic refined set, hesitant fuzzy set, and dual hesitant fuzzy set, Ye (J Intell Syst 24(1):23–36, 2015) proposed the concept of hesitant neutrosophic sets (also called single valued neutrosophic hesitant fuzzy sets). Following the idea of hesitant neutrosophic sets as introduced by Ye, in this paper, the model of hesitant neutrosophic rough sets is proposed, then the join semi-lattice structure of lower and upper hesitant neutrosophic rough approximation operators over two universes is given. In addition, an algorithm to handle decision making problem in medical diagnosis based on hesitant neutrosophic rough sets over two universes is provided. Finally, a numerical example is employed to demonstrate the validness of the proposed hesitant neutrosophic rough sets.

Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment

With the development of the social economy and enlarged volume of information, the application of multiple-attribute decision-making (MADM) has become increasingly complex, uncertain, and obscure. As a further generalization of hesitant fuzzy set (HFS), simplified neutrosophic hesitant fuzzy set (SNHFS) is an efficient tool to process the vague information and contains the ideas of a single-valued neutrosophic hesitant fuzzy set (SVNHFS) and an interval neutrosophic hesitant fuzzy set (INHFS). In this paper, we propose a decision-making approach based on the maximizing deviation method and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) to solve the MADM problems, in which the attribute weight information is incomplete, and the decision information is expressed in simplified neutrosophic hesitant fuzzy elements. Firstly, we inaugurate an optimization model on the basis of maximizing deviation method, which is useful to determine the attribute weights. Secondly, using the idea of the TOPSIS, we determine the relative closeness coefficient of each alternative and based on which we rank the considered alternatives to select the optimal one(s). Finally, we use a numerical example to show the detailed implementation procedure and effectiveness of our method in solving MADM problems under simplified neutrosophic hesitant fuzzy environment.

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

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.