Hesitant Fuzzy Sets Research Articles

Integrated decision-making framework for hospital development: A single-valued neutrosophic probabilistic hesitant fuzzy approach with innovative aggregation operators

This research article proposes an innovative algorithm for analyzing parallelism in the evolution of hospital building features, with the goal of advancing decisionmaking processes in both urban and rural hospitals. As an additional generalization of the concepts of fuzzy sets, intuitionistic fuzzy sets, single-valued neutrosophic sets, hesitant fuzzy sets, and probabilistic fuzzy sets this paper proposes a single-valued neutrosophic probabilistic hesitant fuzzy set (SV-NPHFS). It is derived from the combination of single-valued neutrosophic sets, probabilistic fuzzy sets, and hesitant fuzzy sets. The novel algebraic structure and cosine evaluation function of SV-NPHFSs are then introduced. In addition, we introduce novel operators: the single-valued neutrosophic probabilistic hesitant fuzzy weighted geometric (SV-NPHFWG), the single-valued neutrosophic probabilistic hesitant fuzzy ordered weighted geometric (SV-NPHFOWG), the single-valued neutrosophic probabilistic hesitant fuzzy weighted average (SV-NPHFWA), and the single-valued neutrosophic probabilistic hesitant fuzzy ordered weighted average (SV-NPHFOWA). More complex links between features and alternatives can be made with the multi-attribute decision-making procedures outlined in this work. This characteristic highlights their superior practicality and accuracy over existing methods, which often fail to capture the intricate interplay of elements in real-world scenarios. This demonstrates that applying the decision-making strategies covered in this article can lead to the discovery of even additional trait correlations. Finally, we evaluate the performance of our proposed method on a real choice problem and an experimental comparison. The results demonstrate that the new method will be more advantageous in a range of applications where decision-making is uncertain. Figure 1 illustrates all of the manuscript?s results in a graphical abstract.

A novel MCGDM technique based on correlation coefficients under probabilistic hesitant fuzzy environment and its application in clinical comprehensive evaluation of orphan drugs.

Probabilistic hesitant fuzzy sets (PHFSs) are superior to hesitant fuzzy sets (HFSs) in avoiding the problem of preference information loss among decision makers (DMs). Owing to this benefit, PHFSs have been extensively investigated. In probabilistic hesitant fuzzy environments, the correlation coefficients have become a focal point of research. As research progresses, we discovered that there are still a few unresolved issues concerning the correlation coefficients of PHFSs. To overcome the limitations of existing correlation coefficients for PHFSs, we propose new correlation coefficients in this study. In addition, we present a multi-criteria group decision-making (MCGDM) method under unknown weights based on the newly proposed correlation coefficients. In addition, considering the limitations of DMs' propensity to use language variables for expression in the evaluation process, we propose a method for transforming the evaluation information of the DMs' linguistic variables into probabilistic hesitant fuzzy information in the newly proposed MCGDM method. To demonstrate the applicability of the proposed correlation coefficients and MCGDM method, we applied them to a comprehensive clinical evaluation of orphan drugs. Finally, the reliability, feasibility and efficacy of the newly proposed correlation coefficients and MCGDM method were validated.

Some Information Measures for Interval‐Valued Hesitant Fuzzy Sets in Multiple Criteria Decision‐Making

In the fields of information science and artificial intelligence, dealing with uncertainty, fuzziness, and complexity has always been a hot and difficult research topic. Especially in modern society, with the continuous development of science and technology, people are facing more and more complex problems. Interval‐valued hesitant fuzzy set (IVHFS) is an extended form of a fuzzy set. It can more flexibly express and handle uncertainty and fuzziness in decision‐making processes. However, in the practical application of the IVHFS, its information measurement is crucial, which is directly related to the application value of the IVHFS in various fields. Therefore, studying the information measurement of the IVHFS has important theoretical significance and practical value for the fields of information science and artificial intelligence. In spite of significant advances, entropy and similarity as the well‐known information measures for interval‐valued hesitant fuzzy information have not yet been thoroughly researched. In this contribution, we investigate information measures in the IVHFS, including nonprobabilistic entropy, similarity, and cross‐entropy. We first analyze the change law of hesitating uncertainty and fuzzy uncertainty in geometric space, and a nonprobabilistic entropy measurement method and its axiomatic definition for IVHFS are further developed. Then, a novel similarity measurement formula for IVHFS and its axiomatic requirements are proposed on the basis of the two nonfuzzy elements ( and ). Furthermore, the novel similarity measure is used to construct the cross‐entropy measure for IVHFS and its axiomatic requirements based on the association between the similarity and the cross‐entropy. Lastly, a MAGDM method is proposed by using the developed three information measures, and the efficacy of the proposed method is demonstrated by a numerical example of emergency communication support capacity evaluation. Comparative analysis and computational cost analysis are implemented to demonstrate the superiority and validity of the proposed information measures.

On gradual sets, hesitant fuzzy sets and representation theorems

On gradual sets, hesitant fuzzy sets and representation theorems

Pythagorean hesitant fuzzy rough multi-attribute decision-making method with application to wearable health technology devices

<p>Identifying the most optimal wearable health technology devices for hospitals is a crucial step in emergency decision-making. The multi-attribute group decision-making method is a widely used and practical approach for selecting wearable health technology devices. However, because of the various factors that must be considered when selecting devices in emergencies, decision-makers often struggle to create a comprehensive assessment method. This study introduced a novel decision-making method that took into account various factors of decision-makers and has the potential to be applied in various other areas of research. First, we introduced a list of aggregation operators based on Pythagorean hesitant fuzzy rough sets, and a detailed description of the desired characteristics of the operators under investigation were provided. The proposed operators were validated by a newly defined score and accuracy function. Second, this paper used the proposed approach to demonstrate the Pythagorean hesitant fuzzy rough technique for order of preference by similarity to ideal solution (TOPSIS) model for multiple attribute decision-making and its stepwise algorithm. We developed a numerical example based on suggested operators for the evaluation framework to tackle the multiple-attribute decision-making problems while evaluating the performance of wearable health technology devices. In the end, the sensitivity analysis has confirmed the performance and reliability of the proposed framework. The findings indicated that the models being examined demonstrated greater reliability and efficacy compared to existing methodologies.</p>

Electricity Retail Plan Recommendation Method Based on Multigranular Hesitant Fuzzy Sets and an Improved Non-Negative Latent Factor Model

Electricity Retail Plan Recommendation Method Based on Multigranular Hesitant Fuzzy Sets and an Improved Non-Negative Latent Factor Model

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.

Sentiment Propensity Analysis of a Multimodal Chinese Corpus Using Fuzzy Logic

Abstract In the face of massive multimodal information, it has become one of the current research hotspots to categorize it according to its sentiment so as to guide users to find valuable information from a large amount of data. Based on the application of fuzzy logic in sentiment analysis, this paper designs a method to analyze sentiment tendencies in a multimodal Chinese corpus. Firstly, text, audio, and video features of the multimodal Chinese corpus are extracted, and a fuzzy sentiment dictionary is constructed. Then, the double hesitant fuzzy set is used to reduce the intensity of the sentiment, and the fuzzy sentiment value is calculated. Then, the fusion of sentiment lexicon, intuitionistic fuzzy inference, and fuzzy comprehensive evaluation model is used to obtain the final sentiment tendency analysis results. The models constructed based on different lexicons all converge after 4 epochs, indicating that the model has strong feature learning ability. After combining the sentiment lexicon, the accuracy of the model’s sentiment classification improves by 2.27%. Compared with other common sentiment classification models, the precision rate, recall rate and F1 value of this paper’s model are improved by 2.41%-6.57%, 2.36%-4.91% and 2.38%-5.58%, respectively. The result of inclination to positive in the sentiment analysis of this paper’s model is 82.3%, with a difference of only 1% from the average value of 83.3% of user evaluation, and it is better than the analysis model of plain text (80.8%), which proves that the multimodal sentiment analysis model in this paper can correctly complete the analysis of sentiment inclination of the review data. This paper provides a new feasible approach for the propensity analysis of multimodal sentiment.

The large-scale group consensus multi-attribute decision-making method based on probabilistic dual hesitant fuzzy sets.

We proposed a novel decision-making method, the large-scale group consensus multi-attribute decision-making method based on probabilistic dual hesitant fuzzy sets, to address the challenge of large-scale group multi-attribute decision-making in fuzzy environments. This method concurrently accounted for the membership and non-membership degrees of decision-making experts in fuzzy environments and the corresponding probabilistic value to quantify expert decision information. Furthermore, it applied to complex scenarios involving groups of 20 or more decision-making experts. We delineated five major steps of the method, elaborating on the specific models and algorithms used in each phase. We began by constructing a probabilistic dual hesitant fuzzy information evaluation matrix and determining attribute weights. The following steps involved classifying large-scale decision-making expert groups and selecting the optimal classification scheme based on effectiveness assessment criteria. A global consensus degree threshold was established, followed by implementing a consensus-reaching model to synchronize opinions within the same class of expert groups. Decision information was integrated within and between classes using an information integration model, leading to a comprehensive decision matrix. Decision outcomes for the objects were then determined through a ranking method. The method's effectiveness and superiority were validated through a case study on urban emergency capability assessment, and its advantages were further emphasized in comparative analyses with other methods.

Optimizing Earthquake Response with Fermatean Probabilistic Hesitant Fuzzy Sets: A Decision Support Framework

Optimizing Earthquake Response with Fermatean Probabilistic Hesitant Fuzzy Sets: A Decision Support Framework

An unified fuzzy decision strategy for analysing green fuel alternatives: A road to long-term development

The transportation industry is critical to the economic prosperity of the country. The use of conventional fuels for transportation is hampered by a number of factors, including an insufficiency of fossil fuels, switching crude oil prices, urbanization, and strict environmental regulations. This has sparked a global search for cleaner fuel alternatives that can meet energy requirements and tackle sustainability issues. The development of decision-support tools aid in tackling the issue by studying the difficulties encountered in selecting a better fuel alternative that provides environmental advantages and promotes sustainable mobility. This work attempts to analyse multi-criteria decision making concerns using aggregation operators from the perspective of a linear diophantine hesitant fuzzy setting. The linear diophantine hesitant fuzzy weighted average operator and linear diophantine hesitant fuzzy weighted geometric operator is designed to aggregate linear diophantine hesitant fuzzy data. Furthermore, an integrated model was developed in an attempt to evaluate the value of aggregation operators based on linear diophantine fuzzy sets while taking into account the various clean fuel sources for transportation in India. The versatility and efficacy of the framework are further substantiated by a comparative and susceptibility analysis.

Q- rung orthopair probabilistic hesitant fuzzy hybrid aggregating operators in multi-criteria decision making problems

With the increase of complex information in applications of decision making problems, the use of probabilistic hesitant fuzzy set structure has expanded. Therefore, this paper aims to present two new operators namely q-rung orthopair probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric (q-ROPHHWAG) operator and q-rung orthopair probabilistic hesitant fuzzy hybrid ordered weighted arithmetic and geometric (q-ROPHHOWAG) operator for q>0. The presented operators are better than existing operators in many respects as adding a new parameter, having more flexible structure and presenting comparative analysis in its own. Moreover, we mention from some properties of the proposed operators. In addition to, we give an algorithm and example to indicate effective, reality and flexible of presented method and operators. Then, we solve an example over Pythagorean probabilistic hesitant fuzzy sets with our operators and the results are agreement and the offered operators have superior effect than other operators.

An integrated hesitant 2-tuple linguistic Pythagorean fuzzy decision-making method for single-pilot operations mechanism evaluation

Single-pilot operations (SPO), i.e., one pilot on board the flight in charge of all the operations, has received extensive attention in recent years. SPO involves several participants including the pilot, the autopilot, and the ground operator, and it is of great significance to determine the roles of these participants under the SPO mechanism. However, the evaluation of SPO mechanism has received little attention. Aiming at providing a reliable approach for SPO mechanism evaluation under uncertainty, this paper proposes a novel hesitant 2-tuple linguistic Pythagorean fuzzy decision-making method based on hesitant fuzzy linguistic term sets (HFLTS), 2-tuple linguistic information, Pythagorean fuzzy sets (PFS), and VIKOR method to handle the SPO mechanism evaluation problem. Firstly, based on the analysis of SPO, the evaluation criteria system for SPO mechanism is established. Then, considering the uncertain information in the SPO mechanism evaluation process, the HFLTS is used to represent the linguistic judgments of experts under uncertainty. Next, the HFLTSs of different experts are converted into 2-tuple linguistic information and PFSs to model the overall judgments of different criteria. Finally, the extended VIKOR method is adopted to evaluate and rank different SPO mechanisms. A case study of SPO mechanism evaluation for the ground proximity warning system (GPWS) is used to demonstrate the effectiveness and feasibility of the proposed method, and the SPO mechanism that the autopilot being responsible for GPWS is evaluated by the proposed method to be optimal. Sensitivity and comparison analyses further confirm that the proposed method could provide reliable and reasonable SPO mechanism evaluation results. In conclusion, the proposed method presents a novel and effective way to evaluate and select appropriate SPO mechanisms.

Fuzzy reliability framework under hesitant and dual hesitant fuzzy sets to air conditioning system

Fuzzy reliability framework under hesitant and dual hesitant fuzzy sets to air conditioning system

Three-way group decisions using evidence theory under hesitant fuzzy linguistic environment

In the actual decision-making process, there will be situations where decision-makers with hesitant attitudes have difficulties in evaluating alternatives numerically, and hesitant fuzzy linguistic term sets can provide decision-makers with an effective way to describe hesitancy in linguistic terms. In multi-attribute group decision-making, each decision maker typically holds different preferences. If the variation in decision makers’ assessment weights across evaluations of each attribute for every alternative is not adequately accounted for, it can result in a problem of coarse-grained calculations, leading to information loss. Additionally, the three-way decision model faces significant challenges in information fusion within the context of the hesitant fuzzy linguistic environment. Therefore, we propose a new three-way decision-making model under the hesitant fuzzy linguistic environment. The model obtains the confidence of different decision makers in attribute evaluations through the fusion of D-S evidence theory, and can perform more fine-grained fusion calculations on the evaluation information of different decision makers. In addition, the model considers the cost function of each alternative in different decision-making actions under hesitant fuzzy linguistic environment, calculates the two thresholds of each alternative in the three-way decision model, and derives the decision rules. The effectiveness of the model is verified through a numerical example and two comparative experiments, therefore, the model can be applied in intelligent classification or recommendation systems of hesitant fuzzy linguistic information systems.

Distance and similarity measures of Hesitant bi-fuzzy set and its applications in renewable energy systems

The concept of Hesitant bi-fuzzy set (HBFS) is an extension of dual hesitant fuzzy set, which play an important role in minimizing uncertainty in an efficient way. Distance and Similarity measures are an important tool for illustrating and integrating the differences between elements and its class and have a great importance in decision making, medical diagnosis and pattern recognition. To enhance and expand the applicability of HBFS, in this study, we have defined a series of distance and similarity measures of HBFS in both continuous and discrete environments. Since the information in day-to-day life may be biased, therefore, to show the importance of each factor/criterion weighted measures are also defined. Due to global warming and climate change, the utilization of renewable energy systems not only plays a significant role but also decreases greenhouse gas emissions. Choosing the right energy system affects each nation's economic, social, and environmental development. To show the efficiency of proposed measures, these measures are implemented in renewable energy systems. An algorithm for hesitant bi-fuzzy TOPSIS has also been developed to demonstrate the application of these measures in decision- making. Finally, a comparative study is done in pattern recognition problem, to show the supremacy and efficiency of the proposed measures.

An Enhanced Interactive and Multi-criteria Decision-Making (TODIM) Method with Probabilistic Dual Hesitant Fuzzy Sets for Risk Evaluation of Arctic Geopolitics

An Enhanced Interactive and Multi-criteria Decision-Making (TODIM) Method with Probabilistic Dual Hesitant Fuzzy Sets for Risk Evaluation of Arctic Geopolitics

Waste-to-energy incineration site selection framework based on heterogeneous fuzzy regret-PROMETHEE model considering life-cycle carbon emissions.

Waste incineration technology has received extensive attention for its advantages of being harmless, reducing, and recycling. However, the waste-to-energy incineration project confronts significant "not-in-my-backyard (NIMBY) concerns," and irrational location choices will have negative effects on the project's economy and sustainability; it is also a great challenge to the credibility of the government. To this end, a multi-criteria decision-making framework is constructed for the site selection of waste-to-energy incineration projects. To begin with, a site selection criteria system is established including 16 sub-criteria from four aspects, where probabilistic linguistic term sets are introduced to depict the qualitative sub-criteria and probabilistic hesitant fuzzy sets are employed to express the uncertainty of quantitative sub-criteria. An optimization model is then built to determine the weights of criteria based on the Pearson correlation coefficient and least square method. Furthermore, a regret-preference ranking organization methods for enrichment evaluations (PROMETHEE) model is presented to rank alternatives in a heterogeneous decision environment. Finally, a case study in China is conducted to validate the applicability of the proposed framework; the result of the site selection demonstrates that alternative A2 located in Miyun, Beijing, is the most optimal option. This work provides investors with scientific decision reference and also extends the methods in the decision-making field.

A Systematic Decision-Making Approach for Quality Function Deployment Based on Hesitant Fuzzy Linguistic Term Sets

As a powerful tool for improving customer satisfaction, quality function deployment (QFD) can convert customer requirements (CRs) into engineering characteristics (ECs) during product development and design. Aiming to address the deficiencies of traditional QFD in expert evaluation, CRs’ weight determination and ECs’ importance ranking, this paper proposes an enhanced QFD model that integrates hesitant fuzzy binary semantic variables, the Best–Worst Method (BWM), and the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS). The objective is to determine the prioritization of product engineering characteristics. Indeed, hesitant fuzzy linguistic term sets (HFLTS) have found extensive application in decision-making problems. Compared to other fuzzy language methods, HFLTS offers greater convenience and flexibility in addressing decision-makers’ hesitations and uncertainties. Initially, the combination of hesitant fuzzy linguistic term sets with interval binary tuple language variables is employed to articulate the uncertainty in the assessment information provided by QFD team members. Subsequently, the improved BWM and TOPSIS methods based on HFLTS are used to improve the accuracy of the importance ranking of engineering characteristics by determining the weights of CRs and prioritizing ECs in two stages. Finally, the feasibility and effectiveness of the proposed method are validated through an illustrative example.

Evaluation of wave energy converters based on integrated ELECTRE approach

The demand for renewable energy sources is growing rapidly as a result of increasing energy consumption, fossil fuel depletion, climate change, and environmental degradation. The tide is one of the main sources of renewable energy in the ocean because of its huge potential to be harnessed. Wave-energy converters (WECs) are a potential alternative to present energy sources, with an emphasis on improving efficiency and increasing energy. With the goal of improving the uncertainty inherent in data representation, the literature gradually uses various fuzzy extensions that handle fuzzy information in subjective evaluations and decision-making processes. single-valued neutrosophic probabilistic hesitant fuzzy sets (SVNPHFS), a recent extension of neutrosophic fuzzy sets, address limitations associated with membership functions and the representation of hesitancy in multi-criteria decision-making (MCDM) approaches. In the decision-making process, uncertainty is successfully handled by SVNPHFS. The objective of this study is to investigate and select a potential converter for a WEC power plant using SVNPHFS. Seven criteria for WECs are selected as potential sites for establishing a wave-energy power plant. The paper proposes a novel hybrid MCDM methodology. Fuzzy SWARA (Stepwise Weighted Assessment Ratio Analysis) is utilized for assigning weights to the criteria for WEC selection, and fuzzy ELECTRE (Elimination and Choice Expressing Reality) is used to determine the most suitable alternative using these criteria weights. The proposed technique identifies the point absorber in the first rank for the best wave-to-energy converter power plant as it generates a high amount of electricity compared to other alternatives. The result shows that the proposed model is more robust compared to other approaches.