Hesitant Fuzzy Information Research Articles

Smart city design plan selection through single-valued neutrosophic probabilistic hesitant fuzzy rough aggregation information

One of the hottest areas for applying the solutions currently available is the internet of things-based smart housing society architecture and its uncertainty analysis. When intelligent parking, waste management, public transportation, public safety, and other automatic methods for housing society’s growth were implemented, it became even more crucial. An intelligent, smart system is necessary to manage these problems and provide smooth services. Additionally, it will be helpful in reducing issues with time waste and societal safety. However, the issue comes up when describing accurate, approximate, or questionable parking, transit, safety, and waste management areas. This paper discusses several mathematical solutions for the smart housing society that use fuzzy rough sets, probabilistic hesitant fuzzy sets, and their extensions with neutrosophic sets. For further growth, a few studies on the graphic display of the evolution of the smart housing society are also considered. The rough set theory can be useful when dealing with imprecise, incomplete, or indeterminate data sets. The core contribution of this work is the construction of a novel generalized notion of a single-valued neutrosophic probabilistic hesitant fuzzy rough set (SV-NPHFRS), which is a hybrid structure of the single-valued neutrosophic set, the probabilistic hesitant fuzzy set, and the rough set. In contrast to the present literature, the underlying idea of SV-NPHFRS is that it is a powerful mathematical tool for managing uncertainty and imperfect information. This method is particularly beneficial when there are a number of competing criteria to consider. The aggregation technique plays an important role in decision-making concerns, especially when more competing criteria are present. In the study’s comparison phase, the suggested decision support system is compared to relevant existing approaches. The results suggest that, in terms of choice flexibility, the suggested technique has the potential to outperform the drawbacks of the current decision-making tools. The proposed study is expected to be useful for a number of researchers conducting future work on housing societies, waste management, public safety diagnostics, and hybridization.

Identification of mental disorders in South Africa using complex probabilistic hesitant fuzzy N-soft aggregation information

This paper aims to address the challenges faced by medical professionals in identifying mental disorders. These mental health issues are an increasing public health concern, and middle-income nations like South Africa are negatively impacted. Mental health issues pose a substantial public health concern in South Africa, putting forth extensive impacts on both individuals and society broadly. Insufficient funding for mental health remains the greatest barrier in this country. In order to meet the diverse and complex requirements of patients effective decision making in the treatment of mental disorders is crucial. For this purpose, we introduced the novel concept of the complex probabilistic hesitant fuzzy N-soft set (CPHFNSS) for modeling the unpredictability and uncertainty effectively. Our approach improves the precision with which certain traits connected to different types of mental conditions are recognized by using the competence of experts. We developed the fundamental operations (like extended and restricted intersection, extended and restricted union, weak, top, and bottom weak complements) with examples. We also developed the aggregation operators and their many features, along with their proofs and theorems, for CPHFNSS. By implementing these operators in the aggregation process, one could choose a combination of characteristics. Further, we introduced the novel score function, which is used to determine the optimal choice among them. In addition, we created an algorithm with numerical illustrations for decision making in which physicians employ CPHFNS data to diagnose a specific condition. Finally, comparative analyses confirm the practicability and efficacy of the technique that arises from the model developed in this paper.

A novel multiple attribute decision-making method based on Schweizer-Sklar t-norm and t-conormwith q-rung dual hesitant fuzzy information

A novel multiple attribute decision-making method based on Schweizer-Sklar t-norm and t-conormwith q-rung dual hesitant fuzzy information

A note on “Some dual hesitant fuzzy Hamacher aggregation operators and their applications to multiple attribute decision making”

As dual hesitant fuzzy sets can express the uncertainty of data efficiently, the aggregation of dual hesitant fuzzy information plays an important role in both theory and application. However, some existing dual hesitant fuzzy aggregation operators are not rigorous enough actually. In this note, we show that some theorems in an earlier paper by Ju et al. [1] (Journal of Intelligent & Fuzzy Systems 27 (2014) 2481–2495) are not correct, i.e., the dual hesitant fuzzy Hamacher weighted averaging operator (DHFHWA) and some other aggregation operators proposed by Ju et al. don’t satisfy idempotency and boundedness. Therefore, the purpose of this paper is to make researchers aware of that some aggregation operators in literature [1] are flawed and limited for many applications.

Three-way group decisions with evidential reasoning in incomplete hesitant fuzzy information systems for liver disease diagnosis

Three-way group decisions with evidential reasoning in incomplete hesitant fuzzy information systems for liver disease diagnosis

Optimization models of consensus measurement and improvement processes with hesitant fuzzy linguistic evaluation information

Optimization models of consensus measurement and improvement processes with hesitant fuzzy linguistic evaluation information

A Supplier Selection Decision-Making Approach for Complex Product Development Based on Hesitant Fuzzy Information

During the development process of complex products, selecting the best desirable alternative supplier is a challenge since an improperly selected alternative may cause losing capacity and increasing the cycle time and cost of development for a company. For this multiple-attribute decision-making problem of supplier selection, in this paper, a supplier selection problem in which the decision data are hesitant fuzzy information and the attribute weight is unknown in complex product development is investigated, and a supplier selection decision-making approach based on hesitant fuzzy information is proposed. Firstly, a bidirectional projection based on hesitant fuzzy information is established, and then the measurement equation for the degree of closeness is improved. Further, an attribute weight determination model which minimizes the projection total deviation for the hesitant fuzzy elements is constructed. By solving this model, scientific and reasonable attribute weights are provided. Subsequently, an illustrative example is employed to not only give the ranking result of alternative suppliers but also demonstrate the validity and feasibility of the developed approach. Meanwhile, sensitivity analysis and comparative analysis are put forward to illustrate the stability of the given final ranking result and the advantages and reliability of the constructed method. For alternative or strategy selection, this proposed approach can be used as a decision-making means when uncertainties are inherent.

A statistical approach to large-scale group decision making with incomplete hesitant fuzzy linguistic information by incorporating risk attitude

In response to the lack of information and the arguments among the decision-makers (DMs) in large-scale group decision making (LSGDM), this study proposes a method that integrates decision risk and risk attitude into LSGDM with hesitant fuzzy linguistic preference relations (HFLPRs) based on statistical estimation. Firstly, the DMs are arranged into several subgroups via their risk attitudes. Next, the whole or part of the five-number summary for subgroups from incomplete information provided by DMs are collected. After that, the optimization model and Monte Carlo simulation are utilized to obtain mean and standard deviation estimators of the decision information, and the mean estimator is regarded as the evaluation information of subgroup. Then, the hesitant fuzzy linguistic term sets (HFLTSs) with different number of linguistic variables are normalized according to their risk attitudes and confidence interval. Meanwhile, the number of members in subgroups and the decision risk level of subgroups are combined to determine the weights of subgroups. Moreover, a minimum deviation model is derived to rank alternatives. Finally, a case study, sensitivity analysis and comparison are used to guarantee the rationality and availability of the proposed method.

Retracted: Multiple-Attribute Decision-Making Method Based on Normalized Geometric Aggregation Operators of Single-Valued Neutrosophic Hesitant Fuzzy Information

Retracted: Multiple-Attribute Decision-Making Method Based on Normalized Geometric Aggregation Operators of Single-Valued Neutrosophic Hesitant Fuzzy Information

The Probabilistic Dual Hesitant Fuzzy Multi-Attribute Decision-Making Method Based on Cumulative Prospect Theory and Its Application

Addressing the complex issue of multi-attribute decision-making within a probabilistic dual hesitant fuzzy context, where attribute weights are unknown, a novel decision-making method based on cumulative prospect theory is proposed, named the probabilistic dual hesitant fuzzy multi-attribute decision-making method based on cumulative prospect theory. Firstly, a decision matrix is formulated, representing probabilistic dual hesitant fuzzy information. Secondly, according to the decision maker’s authentic preference and non-membership information sensitivity, a comprehensive score function suitable for probabilistic dual hesitant fuzzy elements is proposed. The attribute weights are then determined using the entropy method. Next, the value function and decision weight function from the cumulative prospect theory are employed to compute the cumulative prospect value attributed to each available scheme. In addition, a cumulative prospect matrix is constructed, enabling the establishment of scheme rankings based on the comprehensive cumulative prospect value. Finally, the analysis of specific cases and a comparative assessment of methods pertaining to the selection of emergency response schemes collectively demonstrate the rationality and efficacy of the decision-making method presented in this study.

The hesitant fuzzy BiRNN based on twice-cycle mechanism and its intelligent applications

Existing intelligent classification methods could be inefficient to deal with the hybrid environments including hesitant fuzzy information and real numbers. With respect to this real issue, in this study, we propose some new intelligent methods to achieve deep learning and intelligent classification under this hybrid environment. To do this, we construct the hesitant fusion bidirectional recurrent neural network (HF-BiRNN) based on the hesitant fusion mechanism. Then, the twice-cycle mechanism is designed, which includes the extension mechanism and the decomposition-reorganization mechanism, to fully utilize the original data and optimize the classification results. Meanwhile, the overlap degree algorithm is constructed to filter the optimal outputs. After that, we further propose the hesitant expansion BiRNN (HE-BiRNN) by combining with the twice-cycle mechanism, overlap degree algorithm, and BiRNN. Lastly, these new methods are used to the problems of driving route classification and red wine quality assessment. The derived optimal results and comparison analysis fully show the effectiveness and feasibility of the new proposed mechanisms and developed models.

Hesitant fuzzy time series forecasting model of higher order based on one and two-factor aggregate logical relationship

Fuzzy time series forecasting is a methodology that incorporates fuzzy logic to handle uncertainty in time series data. It allows for more flexible and accurate predictions by considering the linguistic terms and membership functions associated with each data point, enabling a better representation of complex patterns and trends within the time series. A time series forecasting model examines the relationships between present and past observations for future measurement. This article proposes a hesitant fuzzy time series forecasting (FTSF) technique for higher order based on one and two-factor aggregate fuzzy relationships. The proposed method presents a new approach to partitioning intervals into an unequal and equal length. The hesitant fuzzy sets are defined for each observation, and fuzzification is based on their maximum score function. Further, aggregated triangular fuzzy numbers are defined using an aggregation operator corresponding to the fuzzified datum. In order to enhance forecasting performance, this work also introduces a novel defuzzification rule based on aggregated fuzzy logical relationship groups (AFLRGs) for higher order one and two-factor fuzzy time series. The implementation of the proposed approach is verified on two data sets to the forecasting of enrollment data and TAIFEX and TAIEX stock index data sets, and the forecasting error is tested in term of different statistical parameters. Thus, the model validates the effectiveness of the proposed method with higher forecasting accuracy rate in the environment hesitant fuzzy information.

An improved TOPSIS-based rank preservation approach for hesitant fuzzy information processing

In this study, a novel approach based on the reduction of the attribution and the rank preservation is analyzed, which intends to solve the issue of multi-attribute decision making (MADM) with the hesitant fuzzy information. Firstly, several new concepts are shown to simplify the representation of hesitant fuzzy information, such as single point fuzzification estimated value, and single point fuzzification weighted Euclidean distance. Secondly, a new improved HF-TOPSIS method based on the overall situation and these new concepts are put forward, in which the positive and negative ideal solutions are fixed to calculate the complex hesitant fuzzy decision process. The proposed method in this paper achieves the purpose of compression of the complex hesitant fuzzy information, and the calculation is relatively simple and easy to operate. Finally, two examples are presented to test and verify the credibility and effectiveness of the TOPSIS-Based rank preservation approach, which can achieve the consistency of results before and after evaluation, as well as ensuring rank preservation, while other HF-TOPSIS methods may cause rank reversal problems.

A probability-based fuzzy algorithm for multi-attribute decision-analysis with application to aviation disaster decision-making

This research addresses the challenges of multi-attribute group decision-making in a hesitant fuzzy environment, where randomness and uncertainty introduce biases into practical making choices. A probability-based double uncertain fuzzy (PDHF) algorithm is proposed to overcome these challenges. The algorithm constructs probability-based double hesitant fuzzy information matrices for each decision expert. The maximum deviation and entropy methods determine objective weights for decision experts and attribute indicators. Combining an improved scoring function and deviation function generates a comprehensive decision evaluation information matrix for decision experts. Subsequently, a decision algorithm that integrates probability-based double hesitant fuzzy sets with the preference ranking organization method (PROM) is employed to obtain the final decision result. As part of a case study, the algorithm is used to evaluate emergency action plans for aviation disaster accidents. Comparing the results with those from the TOPSIS, VIKOR, and PDHFS decision-making algorithms shows that the suggested PDHF algorithm works well and can be trusted for the multi-attribute group decision-making problems in hesitant fuzzy environments.

Evaluating power system reform proposals based on the evidential reasoning algorithm with hesitant fuzzy information

Evaluating power system reform proposals based on the evidential reasoning algorithm with hesitant fuzzy information

Novel rough set models based on hesitant fuzzy information

Novel rough set models based on hesitant fuzzy information

Scores of hesitant fuzzy elements revisited: “Was sind und was sollen”

This paper revolves around the notion of score for hesitant fuzzy elements, the constituent parts of hesitant fuzzy sets. Scores allow us to reduce the level of uncertainty of hesitant fuzzy sets to classical fuzzy sets, or to rank alternatives characterized by hesitant fuzzy information. We propose a rigorous and normative definition capable of encapsulating the characteristics of the most important scores introduced in the literature. We systematically analyse different types of scores, with a focus on coherence properties based on cardinality and monotonicity. The hesitant fuzzy elements considered in this analysis are unrestricted. The inspection of the infinite case is especially novel. In particular, special attention will be paid to the analysis of hesitant fuzzy elements that are intervals.

Fuzzy Intelligence Learning Based on Bounded Rationality in IoMT Systems: A Case Study in Parkinson’s Disease

As a cause of interfering with routine activities, freezing of gait (FOG) is a severe syndrome of Parkinson’s disease (PD) and usually performs as an abrupt and momentary inability to effective stepping forward. Advanced wearable acceleration sensors based on socially implemented Internet of medical things (IoMT) devices can remotely provide a platform for recognizing FOG. However, due to the diverse data acquisition modes that appear in classic IoMT devices, the obtained data may contain imprecise, hesitant, and incomplete ones. Meanwhile, the bounded rationality owned by neurologists usually has a big impact on using wearable acceleration sensors to predict illnesses. Therefore, the objective of this article lies in exploring a fuzzy intelligence learning approach based on bounded rationality in IoMT systems and providing a valid scheme for biomedical data analysis. Specifically, a brand-new three-way group decision-making approach by means of TODIM (an acronym in Portuguese for interactive multicriteria decision-making) with incomplete dual hesitant fuzzy (DHF) information and its applications in detecting FOG in PD using IoMT devices are systematically explored. First, taking advantage of DHF sets (DHFSs) when depicting realistic group decision information, the concept of multigranulation (MG) incomplete DHF information systems is built. Second, adjustable MG DHF probabilistic rough sets (PRSs) are further put forward via DHF similarity relations. Third, a three-way group decision-making approach is constructed by virtue of adjustable MG DHF PRSs and TODIM. Finally, the validity, effectiveness, and practicality of the constructed three-way group decision-making approach are investigated by a University of California, Irvine (UCI) dataset with several experimental analyses in the background of FOG detection in PD using IoMT devices. The experimental result indicates that the developed fuzzy intelligence learning approach achieves reasonable diagnostic conclusions for FOG detection in PD from the perspective of uncertain information processing abilities, decision risks, and bounded rationality.

A hesitant fuzzy multiple-attribute decision-making method considering rank relation

A decision matrix is typically used to express hesitant information when solving multi-attribute decision problems in an uncertain environment. To further investigate the decision problem, this paper takes the property of matrix rank as the starting point, introduces it into the hesitant fuzzy theory, presents the concept of the rank of the hesitant fuzzy decision matrix and discusses the related properties, and then studies the hesitant fuzzy linear relation, obtaining the attribute reduction method based on the hesitant fuzzy linear relation and applying it to the multi-attribute decision making. It adds to the theoretical understanding of the hesitant fuzzy decision matrix. The aggregation operator first transforms the hesitant fuzzy information into a comprehensive decision matrix, and the row echelon transformation determines the rank of the matrix. Second, the hesitant fuzzy linear relationship is obtained using the rank property. A new hesitant fuzzy matrix is obtained after attribute reduction based on the hesitant fuzzy linear relationship, and the alternatives are sorted using the TOPSIS method. Finally, the effectiveness and superiority of the proposed method are demonstrated through a comparison of actual case analysis and existing methods, and the expected research purpose is met.

Complex dual hesitant fuzzy TODIM method and their application in Russia–Ukraine war’s impact on global economy

The primary objective of this research is to examine how the Russia–Ukraine war impacted the global economy. To achieve this goal, we propose operational laws, a score and accuracy function, and a divergence measure for complex dual hesitant fuzzy sets. Furthermore, we investigate the challenges associated with multi-criteria decision-making (MCR) using aggregation operators and the TODIM method with complex dual hesitant fuzzy (CDHF) information. Drawing inspiration from arithmetic aggregation operations, we introduce several aggregation operators for complex dual hesitant fuzzy information, including the complex dual hesitant fuzzy weighted average (CDHFWA) operator, complex dual hesitant fuzzy ordered weighted average (CDHFOWA) operator, and complex dual hesitant fuzzy hybrid average (CDHFHA) operator. We thoroughly analyze the unique characteristics of these proposed operators and use them in conjunction with the TODIM method to develop practical approaches for solving complex dual hesitant fuzzy multi-criteria decision-making problems. To validate our approach and demonstrate its applicability, we provide a practical example of how the Russia–Ukraine war affected the global economy. Our study confirms the effectiveness of our approach and highlights how it can be used to solve real-world problems.