Probabilistic Hesitant Fuzzy Set Research Articles

Large group emergency decision-making with bi-directional trust in social networks: A probabilistic hesitant fuzzy integrated cloud approach

With the rapid development of society, the number of major emergencies in human society is gradually increasing. They are often accompanied by strong uncertainty and randomness, which makes traditional emergency decision-making methods unable to satisfy the practical needs. Hence, large group emergency decision-making (LGEDM) has gradually become an effective way to solve such problems. However, the existing decision-making methods usually employ a single model, which can't fully handle the uncertainty and randomness in LGEDM. In this paper, the probabilistic hesitant fuzzy set (PHFS) is used to adequately express the uncertainty of information, and the cloud model (CM) is served as a tool for dealing with the randomness of information. Therefore, a decision-making method based on PHFS and CM is proposed to tackle LGEDM. First, the probabilistic hesitant fuzzy integrated cloud (PHFIC) is raised, which can subjectively settle the uncertainty of LGEDM and objectively handle the randomness of LGEDM. Second, a hybrid correlation coefficient based on PHFS is advanced to reduce the complexity of LGEDM through hierarchical clustering. Third, a bi-directional trust model based on PHFIC is put forward to solve information conflict. Finally, an example is offered to prove the application of the proposed method. In addition, the sensitivity and comparison analyses show that the proposed method is able to deal with the uncertainty and randomness of information excellently.

Research on college physical education teaching effect evaluation based on probabilistic hesitant fuzzy QUALIFLEX method

The evaluation of physical education teaching effectiveness is an important component of physical education teaching, and plays a multifaceted role in the process of physical education teaching. The information provided by it can control and regulate the progress of physical education teaching activities as a whole, ensuring that physical education teaching activities develop towards predetermined goals. With the development of the popularization of physical education, people’s requirements for the quality of physical education continue to improve, and the role and position of evaluation in teaching has become increasingly evident. Evaluation of physical education teaching effectiveness has become an indispensable process in teaching activities. The college physical education teaching effect evaluation can be regarded as a multiple attribute decision making (MADM). Thus, this paper collected information in probabilistic hesitant fuzzy sets (PHFSs) and using CRITIC method to obtain the unknown weight among attributes. Further, a novel probabilistic hesitant fuzzy QUALIFLEX (PHF-QUALIFLEX) method was constructed for MADM. Finally, a numerical case for college physical education teaching effect evaluation was illustrated with this proposed model and other methods were utilized to compare with PHF-QUALIFLEX method to verify the feasibility and applicability.

Evaluating Information Risk Propagation in Complex Public Opinion Environments Based on the Improved Grey Relational Analysis—Decision Making Trial and Evaluation Laboratory Method

The propagation of information risk in complex public opinion environments not only leads to severe direct reputational losses for companies but also results in significant economic damages. Therefore, during the nascent stage of information risk, identifying potential propagation pathways, determining key dissemination channels, and taking timely measures become crucial. To address this issue, this paper proposes a multi-criteria decision-making method for evaluating information risk propagation in complex public opinion environments. In this method, this paper utilizes probabilistic hesitant fuzzy sets to express the evaluation information, and provide several distance and similarity measurement methods for probabilistic hesitant fuzzy elements. To ensure the rationality of the evaluation indicator weights, this study first applies these distance measurement methods to improve the Grey Relational Analysis—Decision Making Trial and Evaluation Laboratory (GRA-DEMATEL) method for determining the objective weights of evaluation indicators. Next, this paper uses the Delphi method to establish the subjective weights of each evaluation indicator. Finally, by employing a weight synthesis operator, this paper combines the subjective and objective weights to obtain the final indicator weights. Additionally, this paper utilizes the similarity measurement methods for probabilistic hesitant fuzzy elements to improve the combined compromise solution (CoCoSo) method in evaluating and ranking potential information risk propagation pathways. Furthermore, this paper incorporates the “Probability Splitting Algorithm” to handle probabilistic hesitant fuzzy elements, enabling their application in these methodologies. Finally, based on a case study of information risk propagation in the catering industry, we conducted a sensitivity analysis and effectiveness verification of the proposed approach. The results demonstrate the effectiveness of the method and its ability to address real-world issues.

Developing sustainable management strategies in construction and demolition wastes using a q-rung orthopair probabilistic hesitant fuzzy set-based decision modelling approach

Sustainable management of construction and demolition wastes (CDWs) has become a pressing global issue in social, environmental and economic contexts, and it involves complex technological, engineering, management and regulatory challenges. Recently, many CDW management strategies have been developed based on the barrier attributes of reuse distribution. However, no strategy can simultaneously address all barrier attributes of reuse distribution. Furthermore, no research has assessed and modelled the identified CDW management strategies to determine optimality. On this basis, the presence of multiple barrier attributes, varying attribute priority and a wide range of data allow for the modelling of CDW management strategies under complex multiple-attribute decision-making (MADM) problems. This study develops the fuzzy-weighted zero inconsistency (FWZIC) and fuzzy decision by opinion score method (FDOSM)-based multiplicative multiple objective optimisation by ratio analysis (MULTIMOORA) with the q-rung orthopair probabilistic hesitant fuzzy set (q-ROPHFS) to address this problem. The developed q-ROPHFS–FWZIC method prioritised and weighted the main and sub-barrier attributes of reuse distribution in CDW management strategies. The developed q-ROPHFS–FDOSM is used to score the CDW management strategies. Then, the MULTIMOORA method is used to model 51 CDW management strategies to determine the optimum one. Results showed that Strategy 46 modelled first in six q values because it had the most essential attributes (i.e. cost, market, value-for-money, experience, infrastructure, management, risk and trust). Strategy 17 and Strategy 20 are the least sustainable strategies because they had only one attribute (i.e. experience). Sensitivity analysis, systematic modelling and comparison analysis are conducted to validate and evaluate the stability and robustness of the proposed methods. The implications of this study would likely benefit various stakeholders involved in the construction industry, including construction companies, architects, engineers, policy-makers and members of the public.

An innovative probabilistic hesitant fuzzy set MCDM perspective for selecting flexible packaging bags after the prohibition on single-use plastics

The probabilistic hesitant elements (PHFEs) are a beneficial augmentation to the hesitant fuzzy element (HFE), which is intended to give decision-makers more flexibility in expressing their biases while using hesitant fuzzy information. To extrapolate a more accurate interpretation of the decision documentation, it is sufficient to standardize the organization of the elements in PHFEs without introducing fictional elements. Several processes for unifying and arranging components in PHFEs have been proposed so far, but most of them result in various disadvantages that are critically explored in this paper. The primary objective of this research is to recommend a PHFE unification procedure that avoids the deficiencies of operational practices while maintaining the inherent properties of PHFE probabilities. The prevailing study advances the hypothesis of permutation on PHFEs by suggesting a new sort of PHFS division and subtraction compared with the existing unification procedure. Eventually, the proposed PHFE-unification process will be used in this study, an innovative PHFEs based on the Weighted Aggregated Sum Product Assessment Method–Analytic Hierarchy Process (WASPAS–AHP) perspective for selecting flexible packaging bags after the prohibition on single-use plastics. As a result, we have included the PHFEs-WASPAS in our selection of the most effective fuzzy environment for bio-plastic bags. The ranking results for the suggested PHFEs-MCDM techniques surpassed the existing AHP methods in the research study by providing the best solution. Our solutions offer the best bio-plastic bag alternative strategy for mitigating environmental impacts.

Probabilistic Hesitant Fuzzy Decision-Theoretic Rough Set Model and Its Application in Supervision of Shared Parking

A sophisticated three-way decision model utilizing a multi-granularity probabilistic hesitant fuzzy rough set is introduced to mitigate the issue of information loss arising from hesitant fuzzy sets when characterizing decision information. Initially, the properties of probabilistic hesitant fuzzy sets are examined, subsequently proposing a distance measure and loss function tailored to these sets. Following this, a multi-attribute group decision-making model incorporating probabilistic hesitant fuzzy information is established, and pertinent decision rules that satisfy minimal risk criteria are presented. Building on this foundation, a series of critical steps for resolving a category of multi-attribute group decision-making problems that involve probabilistic hesitant fuzzy information is proposed. Lastly, the multi-attribute group decision-making model with probabilistic hesitant fuzzy information is applied to the supervision of urban shared parking platforms. The results indicate that the decision-making process based on probabilistic hesitant fuzzy sets is more reliable, and the decision-making outcome aligns with the actual situation, thus providing valuable decision-making references for managers.

Early infectious diseases identification based on complex probabilistic hesitant fuzzy N-soft information.

This paper aims to assess and deal with the challenges experienced by medical professionals caring for infectious diseases. In Pakistan, public health is still a serious concern and the main contributor to morbidity and mortality is infectious diseases. The major issue is a resemblance in the clinical symptoms of infectious diseases such as tuberculosis, hepatitis, COVID-19, dengue, and malaria. Early detection of infectious disease is crucial in order to start treatment with counseling and medication. This can only be done if several infections with similar clinical traits can be diagnosed depending on several criteria, including the availability of various kits, the ability to carry out diagnostic procedures, money, and technical staff. But woefully Pakistan's economy is badly battered due to several circumstances. Therefore, we are unable to provide patients with enough diagnostic testing kits and broadly accessible therapy choices, which makes diagnosis more difficult and create hesitancy with fuzziness and randomness. For this purpose, we introduced the new concept of the complex probabilistic hesitant fuzzy N-soft set. We defined its fundamental operations (like restricted and extended union, restricted and extended intersection, weak, top and bottom weak complements, as well as soft max-AND or soft min-OR) with examples. We also discussed their many properties with their proofs and theorems. Furthermore, we developed the algorithms for decision-making where doctors use the complex probabilistic hesitant fuzzy N-soft information to identify a particular disease. Furthermore, we explained numerical illustration of two case studies. Moreover, a sensitive and comparative analysis is discussed. In the last, we conclude the whole study.

A Modified Correlation Coefficient of Probabilistic Hesitant Fuzzy Sets and Its Applications of Decision Making, Medical Diagnosis, Cluster Analysis

A Modified Correlation Coefficient of Probabilistic Hesitant Fuzzy Sets and Its Applications of Decision Making, Medical Diagnosis, Cluster Analysis

A novel MCDM approach to selecting a biodegradable dynamic plastic product: a probabilistic hesitant fuzzy set-based COPRAS method

The development of biodegradable polymers for both industrial and commercial uses is crucial nowadays due to the detrimental environmental effects of synthetic plastics. For a variety of uses, researchers have created numerous starch-based composites. The current study examines bioplastics made from maize and rice starch for packaging purposes. Several types of bioplastic samples are created using various ratios of gelatin, glycerol, citric acid, maize starch, and rice starch. People have discovered the value of plastics all around the world. It can be used for packaging, trash bags, liquid containers, throwaway quick service restaurant products, and other things. Regarding the negative aspect of plastics, their dumping after durability poses a serious risk to both people and wildlife. This prompted researchers to seek alternative natural resources that may be used to create flexible polymers that are recyclable, eco-friendly, and sustainable. It has been discovered that tuber and grain starches can be used to produce flexible biopolymers. The decision to choose the best among these choices is an MCDM problem because the carbohydrates from these suppliers have varying qualities. The Probabilistic Hesitant Fuzzy Set (PHFS)-based COmplex PRoportional ASsessment (COPRAS) method for solving uncertainty problems is utilized in this research study. To get the objective weights of the criteria in this case, we used the Critic method of weight determination. An example case of selecting the optimal hydrolyzes for biodegradable dynamic plastic synthesis was chosen to represent the applicability of the suggested approach. The findings demonstrate the feasibility of thermoplastic starches derived from rice and corn for packaging applications.

Two-sided matching decision making for probabilistic hesitant fuzzy numbers

Probabilistic hesitant fuzzy set (PHFS), as a complex ambiguous information representation tool, has been widely used in decision making problem, but is rarely applied in a two-sided matching (TSM). Therefore, it is important and necessary to investigate the TSM problem with PHFS. This paper proposes a decision method for TSM with probabilistic hesitant fuzzy Numbers (PHFNs) and applies it to the person-job fit problem. Firstly, a novel TSM decision model on the basis of PHFNs is constructed. In order to solve this model, the TSM model is transformed into a two-goal TSM model by using linear weighted method. And then, the two-goal TSM model with PHFN can be changed into a single-goal TSM model with scores through score function. The perfect alternative of TSM could be obtained through model solution. Finally, an example is given to illustrate the feasibility and effectiveness of the proposed method.

Pythagorean probabilistic hesitant triangular fuzzy aggregation operators with applications in multiple attribute decision making

As a generalization of fuzzy set, hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information. As modern socioeconomic decision-making problems are becoming more and more complex, it also becomes more and more difficult to appropriately depict decision makers' cognitive information in decision-making process. In order to describe the decision information more comprehensively, we define a pythagorean probabilistic hesitant triangular fuzzy set (PPHTFS) by combining the pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set. Firstly, the basic operation and scoring function of the pythagorean probabilistic hesitant triangular fuzzy element (PPHTFE) are proposed, and the comparison rule of two PPHTFEs is given. Then, some pythagorean probabilistic hesitant triangular fuzzy aggregation operators are developed, and their properties are also studied. Finally, a multi-attribute decision-making (MADM) model is constructed based on the proposed operators under the pythagorean probabilistic hesitant triangular fuzzy information, and an illustration example is given to demonstrate the practicability and validity of the proposed decision-making method.

Modified CPT-TODIM method for evaluating the development level of digital inclusive finance under probabilistic hesitant fuzzy environment.

Unlike traditional finance, digital inclusive finance is committed to integrating digital technology with the financial industry to bring groups originally excluded from traditional finance back into formal financial services and provide financial services at reasonable prices and matching needs for all social classes. Digital inclusive finance can effectively reduce the financing costs of SMEs, improve the external financing environment of enterprises, and provide more convenient, equal and perfect financial services for enterprises by using technical support such as "big data + artificial intelligence". The development level of digital inclusive finance is a classical multiple attributes group decision making (MAGDM). The Probabilistic hesitant fuzzy sets (PHFSs), which utilize the possible values and its possible membership degrees to depict decision-makers' behavior in different conditions, has been paid great attention. Though numerous methods have been applied in this environment since PHFSs has been introduced, there are still new fields to be explored. In this paper, we introduce the Cumulative Prospect Theory TODIM (CPT-TODIM) for probabilistic hesitant fuzzy MAGDM(PHF-MAGDM). Meanwhile, the information of entropy is utilized to calculate the weight of attributes, which is used to improve the classical TODIM method. At last, we utilize a numerical case for evaluating the development level of digital inclusive finance to compare the extended CPT-TODIM method with the classical TODIM method.

Multi-attribute decision-making method based on q-rung orthopair probabilistic hesitant fuzzy schweizer-sklar power weighted hamy mean operator.

In order to further improve the computing power of the information aggregation operator in the q-rung orthopair probabilistic hesitant fuzzy environment, this paper proposes a multi-attribute decision-making method based on the q-rung orthopair probabilistic hesitant fuzzy Schweizer-Sklar power weighted Hamy mean operator. Firstly, the algorithm of q-rung orthopair probabilistic hesitant fuzzy set is improved based on the Schweizer-Sklar T-norm. In order to better reflect the degree of hesitation of decision-making experts, a new q-rung orthopair probabilistic hesitant fuzzy distance measure is proposed, which provides a basis for subsequent power weighted calculations. Furthermore, considering the correlation between attributes and the influence of data extremes, some information aggregation operators and their power weighted forms are proposed. Finally, a multi-attribute decision-making model based on the q-rung orthopair probabilistic hesitant fuzzy Schweizer-Sklar power weighted Hamy mean operator is established, and the reliability and validity of the research content in this paper are verified through decision-making examples and comparative analysis.

A Green Supply Chain Member Selection Method Considering Green Innovation Capability in a Hesitant Fuzzy Environment

The purpose of this paper is to propose an improved hesitation fuzzy multi-attribute decision-making method to realize green supply chain member selection under green innovation vision. The method uses hesitation fuzzy sets to express decision information of decision makers, takes green innovation capability as the evaluation perspective, and selects green innovation input, synergy of subjects in green supply chain, green innovation output capability, institutional innovation capability of enterprises in green supply chain, and green innovation sustainability as the indexes to evaluate the green innovation capability of enterprises. The multi-attribute decision method proposed in this paper takes into account the shortcomings of the original hesitant fuzzy multi-attribute decision method considering attribute weight optimization in the determination of attribute weights and scheme ranking, then proposes a three-point estimation method for scheme ranking and optimizes the attribute weights by quantifying the balance coefficients of the original decision method. Finally, an example is used to verify the rationality and effectiveness of the proposed method, and a comparison with the original method is made to highlight the advantages of this paper’s method. This paper provides a certain theoretical basis for the selection of members in green supply chains, which helps the selection of members in green supply chains and provides some insight for similar hesitant fuzzy multi-attribute decision-making problems in other fields. In future research, the method proposed in this paper can be considered to combine with probabilistic hesitant fuzzy sets and some other fuzzy sets for method extensions to solve multi-attribute decision-making problems.

Multi-criteria decision-making problem based on the novel probabilistic hesitant fuzzy entropy and TODIM method

The probabilistic hesitant fuzzy sets (P-HFSs) allow experts to express their preferences regarding different membership degrees with probabilistic information. Fuzzy entropy is an important concept to measure the uncertainty of probabilistic hesitant fuzzy information. In this paper, we propose a novel fuzzy entropy named as the exponential probabilistic hesitant fuzzy entropy for the P-HFEs. This novel fuzzy entropy not only observes the basic property of fuzzy entropy, but also has the same characteristics and change tends with the existing fuzzy entropy proposed and studied by other scholars. Then, based on the cardinal reconciliation method and TODIM(Tomada de decisao interativa multicriterio) method, we propose a multi-criteria decision-making (MCDM) problem, where the attribute weight is determined by the exponential probabilistic hesitant fuzzy entropy of the integration results. Finally, a application case in green building is given for the sake of illustrating the efficiency of the MCDM problem. Numerical and theoretical results show that a MCDM problem based on the proposed novel fuzzy entropy and the TODIM method have a wide range of application.

Integrated MCDM Approaches for Exploring the Ideal Therapeutic Plastic Disposal Technology: Probabilistic Hesitant Fuzzy Domain.

The probabilistic hesitant fuzzy set (PHFS) is a useful extended version of the hesitant fuzzy set (HFS), which allows decision-makers greater freedom in espousing their preferences through the use of hesitant evidence in the real DM method. As the implications for individuals and global concerns have grown, efficient clinical diagnosis of medical waste has been a major challenge, particularly in developing countries. Medical waste can be disposed of in a variety of ways. The essential thing is to decide which strategies work best. The optimal healthcare plastic waste disposal (HCPWD) option is a MCDM method involving a wide range of qualitative characteristics. The MCDM technique (ARAS) is then described, whereby the criterion weights are assessed using the recommended entropy weighted method (EWM) proportion and score function in order to increase the process utilisation. Moreover, the above-described approach is used to address a real-world problem by determining the optimal treatment option for healthcare waste (HCW) disposal. Finally, a feasibility analysis is given to support the stated viewpoint on HCPWD options being prioritised.

Some uncertainty measures for probabilistic hesitant fuzzy information

The probabilistic hesitant fuzzy sets (PHFSs), which have received a lot of attention and have been widely used in many domains, are effective in describing hesitant evaluations. Despite significant progress, entropy and cross-entropy, as the famous uncertainty measures of probabilistic hesitant fuzzy information, have not yet been thoroughly investigated. However, these uncertainty measures are quite important and useful in the context of multi-attribute decision-making (MADM). In this contribution, we revisit the concept of uncertainty measures for probabilistic hesitant fuzzy information by comprehensively considering their fuzziness and hesitancy, and proposed some novel entropy and cross-entropy measures for them. Specifically, the hybrid entropy measures are designed as convex combinations of the fuzzy entropy factor and the hesitant entropy factor, and in the same line of thought, the hybrid cross-entropy measures are also designed as convex combinations of the fuzzy cross-entropy factor and the hesitant cross-entropy factor. It is shown that the hybrid entropy measures are simple in structure, clear in physical meaning, and strong in discriminating capability, while the hybrid cross-entropy measures can avoid the design flaws of existing cross-entropy measures and employ natural symmetry. It is further shown that the hybrid entropy and cross-entropy measures can be designed in pairs and are mutually supportive, which suggests that they are internally unified as the uncertainty measures of probabilistic hesitant fuzzy information. In the end, based on the proposed uncertainty measures, an MADM model is developed within the TOPSIS framework to evaluate a company’s strategic initiatives under probabilistic hesitant fuzzy environment. Numerical results show that these uncertainty measures can support group decision-making effectively and efficiently with probabilistic hesitant fuzzy information.

An optimization strategy with SV-neutrosophic quaternion information and probabilistic hesitant fuzzy rough Einstein aggregation operator

<abstract><p>The single valued neutrosophic probabilistic hesitant fuzzy rough Einstein aggregation operator (SV-NPHFRE-AO) is an extension of the neutrosophic probabilistic hesitant fuzzy rough set theory. It is a powerful decision-making tool that combines the concepts of neutrosophic logic, probability theory, hesitant fuzzy sets, rough sets, and Einstein aggregation operators. SV-NPHFRE-AO can be applied in many fields, including livestock decision making. Making judgments about a wide range of issues, including feed formulation, breeding program design, disease diagnostics, and market analysis, is part of the process of managing livestock. By combining data from many sources, SV-NPHFRE-AO can assist decision-makers in livestock management in integrating and evaluating diverse criteria, which can result in more informed choices. It also provides a more accurate and comprehensive representation of decision-making problems by considering the multiple criteria involved and the relationships between them. The single valued neutrosophic set (SV-NS) aggregation operators (AOs) based on Einstein properties using hesitant fuzzy sets (HFSs) and probabilistic hesitant fuzzy sets (PHFSs) with rough sets (RSs) are proposed in this study and can handle a large volume of data, making them suitable for complex and large-scale livestock decision-making problems. We first defined SV-neutrosophic probabilistic hesitant fuzzy rough weighted averaging (SV-NPHFRWA), SV-neutrosophic probabilistic hesitant fuzzy rough weighted geometric (SV-NPHFRWG), SV-neutrosophic probabilistic hesitant fuzzy rough ordered weighted averaging (SV-NPHFROWA) and SV-neutrosophic probabilistic hesitant fuzzy rough hybrid weighted averaging (SV-NPHFRHWA) AOs. Then, based on Einstein properties, we extended these operators and developed the single-valued neutrosophic probabilistic hesitant fuzzy rough Einstein weighted averaging (SV-NPHFREWA) operator. Additionally, an illustrative scenario to show the applicability of the suggested decision-making approach is provided, along with a sensitivity analysis and comparison analysis, which demonstrate that its outcomes are realistic and reliable. We also provide another relation between criteria and alternatives of decision-making using neutrosophic information with quaternion context. By using such type of operators, livestock managers can make more informed decisions, leading to better animal health, higher productivity, and increased profitability.</p></abstract>

Decision-making algorithm based on Pythagorean fuzzy environment with probabilistic hesitant fuzzy set and Choquet integral

<abstract><p>The Pythagorean Probabilistic Hesitant Fuzzy (PyPHF) Environment is an amalgamation of the Pythagorean fuzzy set and the probabilistic hesitant fuzzy set that is intended for some unsatisfactory, ambiguous, and conflicting situations where each element has a few different values created by the reality of the situation membership hesitant function and the falsity membership hesitant function with probability. The decision-maker can efficiently gather and analyze the information with the use of a strategic decision-making technique. In contrast, ambiguity will be a major factor in our daily lives while gathering information. We describe a decision-making technique in the PyPHF environment to deal with such data uncertainty. The fundamental operating principles for PyPHF information under Choquet Integral were initially established in this study. Then, we put up a set of new aggregation operator names, including Pythagorean probabilistic hesitant fuzzy Choquet integral average and Pythagorean probabilistic hesitant fuzzy Choquet integral geometric aggregation operators. Finally, we explore a multi-attribute decision-making (MADM) algorithm based on the suggested operators to address the issues in the PyPHF environment. To demonstrate the work and contrast the findings with those of previous studies, a numerical example is provided. Additionally, the paper provides sensitivity analysis and the benefits of the stated method to support and reinforce the research.</p></abstract>

Simulator selection based on complex probabilistic hesitant fuzzy soft structure using multi-parameters group decision-making

<abstract><p>Simulation software replicates the behavior of real electrical equipment using mathematical models. This is efficient not only in regard to time savings but also in terms of investment. It, at large scale for instance airplane pilots, chemical or nuclear plant operators, etc., provides valuable experiential learning without the risk of a catastrophic outcome. But the selection of a circuit simulator with effective simulation accuracy poses significant challenges for today's decision-makers because of uncertainty and ambiguity. Thus, better judgments with increased productivity and accuracy are crucial. For this, we developed a complex probabilistic hesitant fuzzy soft set (CPHFSS) to capture ambiguity and uncertain information with higher accuracy in application scenarios. In this manuscript, the novel concept of CPHFSS is explored and its fundamental laws are discussed. Additionally, we investigated several algebraic aspects of CPHFSS, including union, intersections, soft max-AND, and soft min-OR operators, and we provided numerical examples to illustrate these key qualities. The three decision-making strategies are also constructed using the investigated idea of CPHFSS. Furthermore, numerical examples related to bridges and circuit simulation are provided in order to assess the validity and efficacy of the proposed methodologies. The graphical expressions of the acquired results are also explored. Finally, we conclude the whole work.</p></abstract>