Consensus Building for Probabilistic Hesitant Fuzzy Preference Relations with Expected Additive Consistency

A probabilistic hesitant fuzzy Choquet integral-based TODIM method for multi-attribute group decision-making

The probabilistic hesitant fuzzy set (PHFS) and probabilistic hesitant fuzzy element (PHFE) have drawn the attention of scholars in recent years and have been applied in several disciplines. However, existing PHFE distance measures have several shortcomings. Therefore, in this study, we propose a new PHFE multi-attribute decision-making (MADM) method, based on the comprehensive characteristic distance measure. First, we devise a new PHFE comparison method and then define the comprehensive characteristic distance measure, based on four characteristics. Finally, based on the traditional TODIM method and prospect theory, we propose a new PHFE recognition method. The comprehensive characteristic distance measure avoids the introduction of errors, including an unequal number of elements and order adjustment. Meanwhile, the four characteristics make the measurement results more comprehensive and reasonable, and applicable to a variety of situations while avoiding counterintuitive phenomena. Compared with traditional approaches, the method in this article selects appropriate parameters according to actual situations to obtain more objective conclusions, which results in better flexibility and operability. Besides, the simulation results verify the effectiveness of this recognition method.

The probabilistic hesitant fuzzy element is a common tool to deal with multi-criteria decision-making problems when the decision makers are irresolute in providing their evaluations. The existing methods for ranking probabilistic hesitant fuzzy elements are limited and not reasonable in practical applications. The main purpose of this paper is to find a more precise and appropriate comparison method so that we can deal with multi-criteria decision-making problems more efficiently. We first propose a chart technique to analyze the structure of a probabilistic hesitant fuzzy element. After that, we propose a novel possibility degree formula to rank probabilistic hesitant fuzzy elements. Last but not least, we provide a useful process to solve the actual multi-criteria decision-making problems, and make a real case study which demonstrates that our method is feasible and reliable.

As a generalization of complex fuzzy set (CFS), complex hesitation fuzzy set (CHFS) is a powerful tool to express two-dimensional fuzzy information, but it ignores the randomness that exists widely in real life. Considering the randomness and ambiguity often simultaneously occur in real-world problems, we come up with an innovative fuzzy set called complex probabilistic hesitant fuzzy set (CPHFS) in this article, which is a joint extension of CFS and probabilistic hesitant fuzzy set (PHFS). Moreover, we establish four basic operations for complex probabilistic hesitant fuzzy element(CPHFE) and a series of useful operational laws are also developed. Secondly, several aggregation operators including complex probabilistic hesitant fuzzy weighted averaging operator(CPHFWA), complex probabilistic hesitant fuzzy weighted geometric operator(CPHFWG), complex probabilistic hesitant fuzzy Heronian Mean operator(CPHFHM) and complex probabilistic hesitant fuzzy Geometric Heronian Mean operator(CPHFGHM) as well as their weighted forms that can reflect the interrelationship among all decision attributes are proposed, which is of great use in multi-attribute decision making(MADM) or in multi-attribute group decision making(MAGDM) issues when we want to synthesize multiple evaluation values into one. Besides, we also present a number of valuable properties of these provided aggregation operators. Thirdly, a MADM process is built in the CPHF environment step by step based on the aggregation operators we have just established. Furthermore, we provide an example about purchasing a most suitable car to demonstrate the effectiveness and practicability of the proposed decision process. Finally, we point out the superiorities of MADM in working under the CPHF environment through comparing it with the existing method and also offer some possible prospects for further research. The method displayed in this work can effectively solve the MADM problems where the decision-making information is described by CPHFEs and the attributes are interactive.

A novel probabilistic hesitant fuzzy rough set based multi-criteria decision-making method

Probabilistic hesitant fuzzy sets (PHFSs) are currently attracting the attention of numerous scholars due to their efficiency in representing uncertain and fuzzy information. PHFSs are more convenient than hesitant fuzzy sets for decision makers to provide their preference information. However, several important issues in PHFSs utilization remain to be addressed. The shortcomings of the operations in PHFSs are discussed in this paper. Probabilistic hesitant fuzzy prioritized weighted average (PHFPWA) and probabilistic hesitant fuzzy prioritized weighted geometric (PHFPWG) operators are developed on the basis of idea of prioritized aggregation operators, and their properties are described. The relationship between PHFPWA and PHFPWG operators is investigated. A multi-attribute decision-making method based on the proposed operators is presented. Two practical examples are provided to illustrate the practicality and effectiveness of the proposed method. Comparison analysis and discussion with other aggregation operators based on the same examples are provided.

With the increasing application of (probabilistic) hesitant fuzzy sets in decision-making, the existing integrated methods of hesitant fuzzy information have become too complicated to meet the needs of increasingly complex practical decision-making problems. Therefore, this paper combines the related knowledge of probability theory to firstly introduce the concept of continuous hesitant fuzzy element (C-HFE). Subsequently, the concept of uniform hesitant fuzzy element (U-HFE) is proposed, and discrete (probabilistic) hesitant fuzzy information is transferred to continuous one, benefited from the connection between U-HFEs and C-HFEs with uniform distribution. After then, integration methods of C-HFEs based on mathematical derivation are developed, which lays a theoretical foundation for the continuity of hesitant fuzzy information. Further, facing the problem that the method of mathematical derivation is too tedious, based on computer simulation, this paper proposes another integration method of C-HFEs, which is more concise and easier to apply. Finally, an example of the evaluation of water resources emergency management plans is given to apply the above method to practical decision-making problems.

RNA viruses exhibit high mutation rates, leading to multiple haplotypes (also referred to as quasi-species) within infected hosts and have been described in both acute (e.g. Influenza, DENV) and chronic (e.g. HIV, HCV) infections. This study characterises the mutation hotspots in DENV genomes at both consensus and haplotype levels. Near full-length DENV genomes were sequenced using Oxford Nanopore Technology (ONT) from Sri Lankan dengue patients recruited between 2017 and 2020. Consensus sequences were made with Minimap-2, and haplotypes were reconstructed with Nano-Q, a tool designed for estimation of RNA virus haplotypes and their relative abundance. The genomic variability of DENV genomes was assessed using Shannon Entropy (SE). Codons undergoing diversifying selection were identified with three phylogenetics-based algorithms (FEL, MEME, FUBAR) implemented within the Datamonkey suite. Hotspots were defined as the high entropy codons that were also subject to diversifying selection. From 150 samples tested, both consensus and haplotype sequences were characterised in 90 samples (DENV1: 8, DENV2: 51, DENV3: 31). At the consensus level, the NS2A gene had the greatest number of sites with higher Shannon entropy when adjusted for gene length across all serotypes, while at the haplotype level the NS1 gene had the same. Overall, the haplotypes sequences revealed more sites with high mutability and codons under diversifying selection than those visible at consensus level. This provides proof-in-principle that in acute RNA viruses also have high mutability in haplotypes, which may be inapparent with a consensus-level analysis.

Distributed stream processing frameworks (DSPFs) are the vital engine, which can handle real-time data processing and analytics for IoT applications. How to prioritize DSPFs and select the most suitable one for special IoT applications is an open issue. To help developers of IoT applications to solve this complex issue, a novel probabilistic hesitant fuzzy multicriteria decision making (MCDM) model is put forward in this paper. To characterize the requirements for large-scale IoT data stream processing, a novel evaluation criteria system including qualitative and quantitative criteria is established. To accurately model the collective opinions from skilled developers and consider their psychological distance, the definition of probabilistic hesitant fuzzy sets (PHFSs) is used. To derive the importance degrees of criteria, a novel probabilistic hesitant fuzzy best-worst (PHFBW) method is proposed based on the score value. To prioritize the DSPFs and choose the most suitable one, a novel probabilistic hesitant fuzzy MULTIMOORA method is put forward. Finally, a practical case composed of four Apache stream processing frameworks, namely, Storm, Flink, Spark, and Samza, is studied. The obtained results indicate that throughput, latency, and reliability are considered to be the three most important criteria, and Flink is the most suitable stream framework.

In this paper, a stable two-sided matching (TSM) method considering the matching intention of agents under a hesitant fuzzy environment is proposed. The method uses a hesitant fuzzy element (HFE) as its basis. First, the HFE preference matrix is transformed into the normalized HFE preference matrix. On this basis, the distance and the projection of the normalized HFEs on positive and negative ideal solutions are calculated. Then, the normalized HFEs are transformed into agent satisfactions. Considering the stable matching constraints, a multiobjective programming model with the objective of maximizing the satisfactions of two-sided agents is constructed. Based on the agent satisfaction matrix, the matching intention matrix of two-sided agents is built. According to the agent satisfaction matrix and matching intention matrix, the comprehensive satisfaction matrix is set up. Furthermore, the multiobjective programming model based on satisfactions is transformed into a multiobjective programming model based on comprehensive satisfactions. Using the G-S algorithm, the multiobjective programming model based on comprehensive satisfactions is solved, and then the best TSM scheme is obtained. Finally, a terminal distribution example is used to verify the feasibility and effectiveness of the proposed method.

Multi-criteria group decision-making has gained considerable attention due to its ability to aggregate diverse expert opinions and establish a preference order among alternatives. While probabilistic hesitant fuzzy (PHF) sets offer increased flexibility and generality for representing criteria values compared to traditional fuzzy and hesitant fuzzy set theories, existing aggregation techniques often fail to enhance consensus among biased expert judgments. Motivated by the need for more effective consensus-based decision-making, this paper proposes a new framework that integrates PHF set theory with Aczel-Alsina weighted averaging and geometric aggregation operators. These operators, known for their flexibility and the inclusion of an adjustable parameter, are particularly well-suited for addressing real-world decision-making challenges. The framework employs a cross-entropy based model to determine criteria weights and multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) method to establish priority orders of alternatives. The proposed framework is demonstrated through a case study on manufacturing outsourcing vendor selection. The results show that Bertrandt is the most suitable vendor, with a score of 0.2390, and resources consumption is identified as the most critical criterion, with a weight of 0.20. To validate the robustness of the proposed framework, sensitivity and comparison analyses have also been conducted.

Fuzzy reliability appraisal of a system using probabilistic dual hesitant fuzzy element emphasizing score function

Correlation coefficient is one of the broadly use indexes in multi-criteria decision-making (MCDM) processes. However, some important issues related to correlation coefficient utilization within probabilistic hesitant fuzzy environments remain to be addressed. The purpose of this study is introduced a MCDM method based on correlation coefficients utilize probabilistic hesitant fuzzy information. First, the covariance and correlation coefficient between two PHFEs is introduced, the properties of the proposed covariance and correlation coefficient are discussed. In addition, the northwest corner rule to obtain the expected mean related to the multiply of two PHFEs is introduced. Second, the weighted correlation coefficient is proposed to make the proposed MCDM method more applicable. And the properties of the proposed weighted correlation coefficient are also discussed. Finally, an illustrative example is demonstrated the practicality and effectiveness of the proposed method. An illustrative example is presented to demonstrate the correlation coefficient propose in this paper lies in the interval [−1, 1], which not only consider the strength of relationship between the PHFEs but also whether the PHFEs are positively or negatively related. The advantage of this method is it can avoid the inconsistency of the decision-making result due to the loss of information.

Status Deconstruction Theory: Status Conflict's Destabilization of Group Status Hierarchies

BackgroundDespite a lack of evidence relating to effectiveness and safety, the use of apps in the field of mental health is increasing due to their ease of use and accessibility. The aim of the EvalDepApps project is to develop and validate an assessment tool for evaluating depression management apps based on scientific evidence, expert judgement and end-user needs.ObjectiveThe purpose of this study was to determine the most relevant criteria for evaluating apps intended to manage depression through consensus-based assessment.MethodsA total of 43 individuals were invited to participate in an online modified Delphi study of 51 criteria identified from the literature. In Round 1, participants rated criteria according to relevance and three levels of consensus were defined: high level when ≥80% of respondents scored the criterion at 5 or 6; medium when 60%–79% of respondents scored the criterion at 5 or 6 and low when <60% of respondents scored the criterion at 5 or 6. In Round 2, participants were asked to re-rate criteria that had achieved the medium level of consensus in Round 1 under the same parameters. Comments by participants were collected and analysed. The final assessment list consisted of those criteria that had attained the maximum consensus in either round.FindingsThe response rate was 59.0% (26/43) in Round 1 and 53.4% (23/43) in Round 2. In Round 1, 24 criteria (47.1%) attained the maximum level of consensus, 20 (39.2%) the medium level and 7 (13.7%) the lowest level. In Round 2, 4 out of 20 criteria (20.0%) attained the maximum consensus. Participant comments reinforced the relevance of the selected criteria. The final list consisted of 28 criteria, the majority relating to Safety and Privacy and Clinical Effectiveness (25.0% each), followed by Usability and Functionality (17.9%).ConclusionsBy prioritising criteria relating to data safety and clinical effectiveness, participants in this study emphasised that the assessment of apps for depression management must take both these aspects into full consideration. Despite some limitations of the study (eg, lack of participant sociodemographic data and its implications for generalisation, not face-to-face inter-round), the results of this study will enable the EvalDepApps project to develop an assessment tool for depression management apps that incorporates the most relevant criteria.Clinical implicationsEvalDepApps will support healthcare professionals and users in identifying safe, effective and user-friendly depression management apps.