Probabilistic Hesitant Fuzzy Set Research Articles

Bipolar valued probabilistic hesitant fuzzy sets based on Generalized Hybrid Operators in multi-criteria decision-making problems based on TOPSIS

This paper aims to present Bipolar valued probabilistic hesitant fuzzy sets (BVPHFSs) by combining bipolar fuzzy sets and probabilistic hesitant fuzzy sets (PHFSs). PHFSs are a strong version of hesitant fuzzy sets (HFSs) in terms of evaluated as probabilistic of each element. Probabilistic hesitant fuzzy sets (PHFSs) are a set structure that argues that each alternative should be evaluated probabilistically. In this framework, the proposed cluster allows probabilistic evaluation of decision- makers’ opinions as negative. Thus, this case proposes flexibility about selection of an element and aids to overcome with noise channels. Furthermore, some new aggregation operators are discussed called bipolar valued probabilistic hesitant fuzzy weighted average operator (BVPHFWA), Generalized bipolar valued probabilistic hesitant fuzzy weighted average operator (GBVPHFWA), bipolar valued probabilistic hesitant fuzzy weighted geometric operator (BVPHFWG), Generalized bipolar valued probabilistic hesitant fuzzy weighted geometric operator (GBVPHFWG), bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric operator (BVPHFHWAG) and Generalized bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric (GBVPHFHWAG) and some basic properties are presented. A score function is defined ranking alternatives. Moreover, two different algorithms are put forward with helping to TOPSIS method and by using aggregation operators over BVPHFSs. The validity of proposed operators are analyzed with an example and results are compared in their own.

Prospect-regret theory based decision-making approach for incomplete probabilistic hesitant fuzzy environment: An application to medical field

In the era of uncertainty and indeterminacy, probabilistic hesitant fuzzy sets (PHFS) an extension of hesitant fuzzy sets (HPS) have received much attention due to their ability to increase the reliability of information by considering the occurrence probabilities of each opinion. Considering the studies of PHFS following points can be identified, (i) preferences are aggregated without considering the inter-relationship among arguments, (ii) occurrence probabilities are not always prior known, (iii) approaches for attribute weights do not consider interactions among attributes (iv) decision-makers are not completely rational. Thus, we present a decision-making approach in which incomplete probabilities are estimated using the Shannon entropy optimization model. A projection entropy-based Shapley value method is used to attain attribute weights. Heronian operator (HM) is extended under the PHFS environment to capture the inter-relationship among arguments. Considering the psychological behavior of decision-makers, final ranking is provided combining the merits of prospect and regret theory. Finally, the proposed framework is applied to a real case study from the medical field. Comparative analysis verifies the effectiveness, and the sensitivity analysis determines the stability of the proposed approach.

Probabilistic hesitant fuzzy multiple criteria decision-making with triangular norm based similarity and entropy measures

Existing probabilistic hesitant fuzzy set (PHFS) measures are constructed using two information measures: hesitancy and unwrapped probabilities. We argue that unifying these semantic terms in PHFS information theory is not logical. We introduce a new class of information measures for PHFSs, which address the logical wrapping of hesitant fuzzy sets (HFS) and probability. We propose several similarity measures for these sets that use the Triangular norm operator. We consider the relationship between measures of entropy and similarity and represent the axiomatic definition of PHFS entropy measures. Finally, we use case studies to demonstrate applications of these information measures. We describe two multiple-criteria decision-making algorithms. The last step is devoted to PHFS ranking procedures: one based on the score function of alternatives and the other based on the relative closeness of alternatives. This contribution describes new information measures and uses case studies to illustrate how they can be applied to decision-making processes.

An ideal plastic waste management system based on an enhanced MCDM technique

The Fermatean probabilistic hesitant fuzzy set (FPHFS) concept is a method that combines Fermatean fuzzy sets and PHFS to provide detailed MCDM problem solutions. The management of solid waste is facing challenges in disposing of environmentally harmful plastic products. The study primarily focuses on plastic waste from the packaging industry, as it is the primary contributor to overall waste generation. The packaging sector has proposed a concept for the recycling of waste at various levels. This study aims to assess the effectiveness of the hybrid analytic hierarchy process and the combinative distance-based assessment (AHP-CODAS) method FPHFS in determining the most suitable plastic waste collection system. The AHP analysis identified the most effective methods for collecting plastic waste for recycling, emphasizing successful segregation for efficient recycling. A deposit and refund system promotes waste collection and a circular economy by facilitating efficient waste management. The research offers valuable insights into selecting packaging waste collection (PWC) technology in uncertain environments and enhances decision-making methods in the field.

Modified method for college students’ career planning evaluation based on the probabilistic hesitant fuzzy multiple attributes group decision making

The employment of college graduates is related to the overall situation of China’s social development, and the difficulty of employment has become a social problem that cannot be ignored. Through the analysis of the current situation of employment, it is found that the lack of employment guidance in colleges and universities and the lack of employment concept of college students are important factors for the difficulty of college students’ employment, and college counselors play an irreplaceable role in college students’ career planning. Based on the characteristics of college counselors’ work, the paper constructs a career planning evaluation system, hoping to provide new ideas for counselors’ employment guidance. The college students’ career planning evaluation is a multiple attributes group decision making (MAGDM). Recently, the TODIM and GRA technique has been employed to manage MAGDM. The probabilistic hesitant fuzzy sets (PHFSs) are employed as a useful tool for depicting uncertain information during the college students’ career planning evaluation. In this paper, the probabilistic hesitant fuzzy TODIM-GRA (PHF-TODIM-GRA) technique is built to manage the MAGDM under PHFSs. At last, the numerical example for college students’ career planning evaluation is employed to show the PHF-TODIM-GRA technique. The main contribution of this paper is outlined: (1) the TODIM technique based on GRA technique has been extended to PHFSs based on CRITIC technique; (2) the CRITIC technique is employed to derive weight values under PHFSs. (3) the PHF-TODIM-GRA technique is founded to manage the MAGDM under PHFSs; (4) a numerical case study for college students’ career planning evaluation and some comparative analysis is supplied to validate the proposed PHF-TODIM-GRA technique.

Supplier selection for carbon emission reduction collaboration in green supply chain using an improved multi-criteria decision-making method

PurposePlatform-based enterprises, as micro-entities in the platform economy, have the potential to effectively promote the low-carbon development of both supply and demand sides in the supply chain. Therefore, this paper aims to provide a multi-criteria decision-making method in a probabilistic hesitant fuzzy environment to assist platform-type companies in selecting cooperative suppliers for carbon reduction in green supply chains.Design/methodology/approachThis paper combines the advantages of probabilistic hesitant fuzzy sets (PHFS) to address uncertainty issues and proposes an improved multi-criteria decision-making method called PHFS-DNMEREC-MABAC for aiding platform-based enterprises in selecting carbon emission reduction collaboration suppliers in green supply chains. Within this decision-making method, we enhance the standardization process of both the DNMEREC and MABAC methods by directly standardizing probabilistic hesitant fuzzy elements. Additionally, a probability splitting algorithm is introduced to handle probabilistic hesitant fuzzy elements of varying lengths, mitigating information bias that traditional approaches tend to introduce when adding values based on risk preferences.FindingsIn this paper, we apply the proposed method to a case study involving the selection of carbon emission reduction collaboration suppliers for Tmall Mart and compare it with the latest existing decision-making methods. The results demonstrate the applicability of the proposed method and the effectiveness of the introduced probability splitting algorithm in avoiding information bias.Originality/valueFirstly, this paper proposes a new multi-criteria decision making method for aiding platform-based enterprises in selecting carbon emission reduction collaboration suppliers in green supply chains. Secondly, in this method, we provided a new standard method to process probability hesitant fuzzy decision making information. Finally, the probability splitting algorithm was introduced to avoid information bias in the process of dealing with inconsistent lengths of probabilistic hesitant fuzzy elements.

Probabilistic Hesitant Fuzzy Evidence Theory and Its Application in Capability Evaluation of a Satellite Communication System.

Evaluating the capabilities of a satellite communication system (SCS) is challenging due to its complexity and ambiguity. It is difficult to accurately analyze uncertain situations, making it difficult for experts to determine appropriate evaluation values. To address this problem, this paper proposes an innovative approach by extending the Dempster-Shafer evidence theory (DST) to the probabilistic hesitant fuzzy evidence theory (PHFET). The proposed approach introduces the concept of probabilistic hesitant fuzzy basic probability assignment (PHFBPA) to measure the degree of support for propositions, along with a combination rule and decision approach. Two methods are developed to generate PHFBPA based on multi-classifier and distance techniques, respectively. In order to improve the consistency of evidence, discounting factors are proposed using an entropy measure and the Jousselme distance of PHFBPA. In addition, a model for evaluating the degree of satisfaction of SCS capability requirements based on PHFET is presented. Experimental classification and evaluation of SCS capability requirements are performed to demonstrate the effectiveness and stability of the PHFET method. By employing the DST framework and probabilistic hesitant fuzzy sets, PHFET provides a compelling solution for handling ambiguous data in multi-source information fusion, thereby improving the evaluation of SCS capabilities.

An integrated group decision making framework for business performance evaluation of performing arts enterprises with probabilistic hesitant fuzzy IDOCRIW-MOOSRA method

There is a lack of domestic and foreign research on the evaluation and improvement strategies of business performance of performing arts enterprises, especially in the context of the “restructuring” of cultural groups in China. Most of the existing studies are distributed in bulk, not only lacking in theoretical depth, but also lacking in systematization to a certain extent, which shows that the existing studies have not fully formed a mature and valuable theoretical system. The business performance evaluation of performing arts enterprises is a multiple attributes group decision making (MAGDM). This paper constructs a novel probabilistic hesitant fuzzy Multi-Objective Optimization Simple Ratio Analysis (PHF-MOOSRA) model based on the integrated determination of objective criteria weights (IDOCRIW) under the probabilistic hesitant fuzzy sets (PHFSs) for this issue. The PHFSs provides an evaluation circumstance containing more information which make the final decision-making results more accurately. Additionally, the IDOCRIW method separately and the MOOSRA method based on the MOORA method is proposed in PHFSs circumstance in this model. In the end, this model is then applied in a numerical case study for business performance evaluation of performing arts enterprises and compare this model with other existing methods.

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.

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.

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

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.

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.

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.

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.

A Probabilistic Hesitant Fuzzy MCDM Approach to Selecting Treatment Policy For COVID-19

The global significant rise in the number of sick individuals and fatalities has made the ongoing struggle against the severe and lethal COVID-19 pandemic a global effort. There are several ongoing therapies for COVID-19, and more are being developed. However, selecting the best therapy option for COVID-19 patients is still needed. Patients may easily choose from the available COVID-19 therapies using the multi-criteria decision-making method. As a result, the present study provides an MCDM method that is created to determine COVID-19 therapies. Probabilistic Hesitant Fuzzy Set numbers, values, and ambiguity are introduced. Theorems and characteristics of PHFS numbers are also investigated in depth. The Complex Proportional Assessment technique is used, based on the PHFS, for dealing with ambiguity issues. This study uses ten criteria and three treatment methods: antibacterial medication and plasma treatment, vaccinations, as well as quarantine and in-house isolation. The study results reveal that quarantine and isolation at home mark the most effective treatment, followed by vaccinations with antibiotics and plasma therapy.

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.

Weight Optimization Decision Algorithm in (p,q)-Rung Probabilistic Hesitant Orthopair Fuzzy Environments

Aiming at the fuzzification of a decision environment and the challenge of determining the weights associated with the interaction among decision-makers, this study offers an original method for (p,q)-rung probabilistic hesitant orthopair fuzzy multi-objective group decision-making, which is founded on the weight optimization principle. Firstly, the notion of a probabilistic hesitant fuzzy set is expanded to a (p,q)-rung. Secondly, the determination of subjective and objective weights is accomplished through the utilization of the Analytic Network Process (ANP) and the Entropy Method. According to the degree of deviation and dispersion of each weight, an optimal objective function is constructed, and the neural network is used to iteratively solve for the best scheme of the comprehensive weight. Subsequently, the Elimination Et Choice Translating Reality (ELECTRE) approach was refined and applied to decision-making in the (p,q)-rung probabilistic hesitant orthopair fuzzy environment. Finally, comparative analysis was used to demonstrate the new method’s effectiveness and superiority.

Research on lean management and innovation capability evaluation of technological small and medium sized enterprises under probabilistic hesitant fuzzy sets

The lean management and innovation capability evaluation of technological small and medium sized enterprises is a classical multi-attributes group decision-making (MAGDM). Recently, the probabilistic hesitant fuzzy sets (PHFSs) have been extended to apply in many fields. However, the existing models don’t evaluate the alternative considering the psychological factors. Thus, in this paper, an extended probabilistic hesitant fuzzy grey relational analysis (PHF-GRA) method is proposed to reduce the restrictions of GRA method by combining with cumulative prospect theory (CPT), considering the psychological preference. In addition, the PHFSs assigns probability values to different degrees of hesitancy, which shows its superiority in complex environment. At the same time, the weight vectors of each attribute are calculated by the entropy values of different foreground decision elements. Then, probabilistic hesitant fuzzy GRA (PHF-GRA) model based on CPT model is constructed for MAGDM under PHFSs. Finally, a practical example study for lean management and innovation capability evaluation of technological small and medium sized enterprises is constructed to validate the proposed GRA (PHF-GRA) model based on model CPT and some comparative studies are constructed to verify the applicability.

An improved TODIM-TOPSIS method for quality evaluation of college students employment and entrepreneurship education with probabilistic hesitant fuzzy sets

In recent years, employers have continuously raised their requirements for college students, not only requiring a solid professional foundation, but also emphasizing personal professional literacy. As the first base for cultivating college students, major universities should not only guide them in their correct employment and entrepreneurship, but also help them find employment and entrepreneurship faster and better. However, in the context of the new era, universities still face some problems in the process of carrying out employment and entrepreneurship education, which hinder the progress of employment and entrepreneurship education. The probabilistic hesitant fuzzy sets (PHFSs), as an extension of hesitant fuzzy sets (HFSs), can more effectively and accurately describe uncertain or inconsistent information during the quality evaluation of college student employment and entrepreneurship education. TODIM and TOPSIS methods are two commonly used multi-attribute decision-making (MADM) methods, each of which has its advantages and disadvantages. The quality evaluation of college student employment and entrepreneurship education is regarded as the defined multiple attribute group decision making (MAGDM). This paper proposes a novel method based on TODIM and TOPSIS to cope with multi-attribute group decision making (MAGDM) problems under PHFSs environment. After introducing the related theory of PHFSs and the traditional TODIM and TOPSIS methods, the novel method based on a combination of TODIM and TOPSIS methods is designed. And then, an illustrative example for quality evaluation of college student employment and entrepreneurship education proved the feasibility and validity of the proposed method. Finally, the result has been compared with some existing methods under the same example and the proposed method’s superiority has been proved.