Triangular Sets Research Articles

Triangular neutrosophic set and its application to reliability analysis of gas turbine system

Triangular neutrosophic set and its application to reliability analysis of gas turbine system

Enhanced Cross-Entropy Technique for Triangular Fuzzy Neutrosophic Multiple-Attribute Decision-Making and Applications to Quality Evaluation of Urban-Park Environmental Design

The evaluation of urban park environmental design quality is essential for ensuring that parks meet community needs and environmental sustainability. By comprehensively considering indicators such as functionality, aesthetics, sustainability, and user experience, this evaluation helps designers optimize spatial layouts and enhance the efficiency and aesthetic value of parks. Additionally, good environmental design promotes ecological protection, improves the quality of life for residents, and adds more green spaces to the city, making parks an integral part of daily urban life. The evaluation of urban park environmental design quality is framed as a multiple-attribute decision-making (MADM) problem. This study introduces the triangular fuzzy neutrosophic number cross-entropy (TFNN-CE) method, which integrates traditional cross-entropy with triangular fuzzy neutrosophic sets (TFNSs). Subsequently, the TFNN-CE technique for MADM is established. A numerical example illustrating the evaluation of urban park environmental design quality is provided, alongside several comparative analyses to highlight the advantages of the proposed approach. The key contributions of this research are as follows: (1) the TFNN-CE technique is introduced through the integration of cross-entropy and TFNSs; (2) the TFNN-CE technique is formulated to address MADM problems using TFNSs; (3) an empirical application for assessing urban park environmental design quality is presented to validate the proposed methodology; (4) comparative studies are conducted to substantiate the rationality of the TFNN-CE technique.

Lines on $$K3$$–Quartics Via Triangular Sets

AbstractWe prove the sharp upper bound of at most 52 lines on a complex $$K3$$ K 3 –surface of degree 4 with a non-empty singular locus. We also classify the configurations of more than 48 lines on smooth complex quartics.

Transference and countertransference in couples therapy

This article, initially presented as part of the series “Lectures from the Tavistock Relationship Model”, aims to give a brief overview of the development and current understanding and usage of the central psychoanalytic concepts of transference and countertransference in psychoanalytic couple therapy. The article discusses the clinical manifestations of the above concepts and compares and contrasts these phenomena in couple work with how they might manifest in individual analytic treatment. The author argues that the terrain of transference and countertransference in analytically informed couple therapy is multi‐layered, offering challenges and opportunities for the therapist. Some of the clinical challenges of working analytically with couples in the transference and formulating interpretations based on the therapist’s countertransference are highlighted. It is suggested that, while the triangular setting of psychoanalytic couple therapy can invite enactments that draw in the therapist, these enactments taking place in the triadic setting made up of the couple and their therapist also offer rich opportunities for working through the couple‐patients’ deepseated oedipal complexes which permeate the problematic relationship presented in couple therapy. The above is illustrated throughout by reference to historical texts from the Tavistock Relationship tradition, as well as literary examples, such as Jane Austen’s novel, 'Persuasion'.

Future workplace reimagination: A multiscenario analysis on entrepreneurial small and medium internationalisers

AbstractThis paper aims to encounter the scholarly demand for comprehensive identification and investigation of the factors that highlight the sense of the “workplace of the future.” Besides, this study sheds in‐depth qualitative and quantitative insights into analysing such drivers in international entrepreneurial small and medium enterprises of emerging economies like Iran. A mixed method of systematic literature review and hesitant triangular fuzzy Delphi was initially employed to identify and finalise the significant factors. Afterwards, the causal level‐based relationship network and the finalised factors' power map were accomplished for three distinct scenarios (i.e., the pessimistic, probable and optimistic conditions). To this end, a novel integration of hesitant triangular fuzzy sets and interpretive structural modelling‐matrix‐based multiplication applied to a classification was designed and applied. As a result, future workplace concerns were systematically reviewed. From the initial list of 34 factors, eight were selected from the perspective of three panels of experts (15 international entrepreneurs) as the most crucial for international small and medium enterprises due to implementing the hesitant triangular fuzzy sets. Furthermore, the selected factors were categorised and levelled according to the novel interpretive structural modelling‐matrix‐based multiplication applied to a classification method developed in this article. Accordingly, for each scenario studied, from low to high uncertainty and indeterminacy, a separate conceptual model illustrating the relationship among the factors propelling the reimagining of the future of the workplace was presented.

Multi-Attribute Decision-Making Based on Consistent Bidirectional Projection Measures of Triangular Dual Hesitant Fuzzy Set

Multi-Attribute Decision-Making Based on Consistent Bidirectional Projection Measures of Triangular Dual Hesitant Fuzzy Set

Research on Outlier Detection Methods for Dam Monitoring Data Based on Post-Data Classification

Safety monitoring of hydraulic structures is a critical task in the field of hydraulic engineering construction. This study developed a method for preprocessing and classifying monitoring data for the identification of gross errors in hydraulic structures. By utilizing linear regression and wavelet analysis techniques, it effectively differentiated various waveform characteristics in data sets, such as Sinusoidal Wave Cyclical, Triangular Wave Cyclical, Seasonal Cyclical, and Weakly Cyclical growth types. In the experiments for gross error identification, the 3σ algorithm, K-medoids algorithm, and Isolation Forest algorithm were applied to test the data. The results showed that the K-medoids algorithm excelled in processing Sinusoidal Wave Cyclical Data Sets; the 3σ algorithm adapted better to Triangular Wave Cyclical Data Sets; the Isolation Forest algorithm performed well in handling data sets with significant anomalies or atypical fluctuations and excelled in scenarios with strong seasonality and large data fluctuations; and for complex Weakly Cyclical Growth Data Sets, all three algorithms were less effective, indicating the potential need for more advanced analysis methods or a combination of multiple techniques. Testing on actual engineering data further confirmed the importance of using specific gross error identification techniques for special data types after data set pre-classification, providing a more effective technical solution for the safety monitoring of hydraulic structures.

Neural net influenced magdm problem with modified choquet integral aggregation operators and correlation coefficient for triangular fuzzy intuitionistic fuzzy sets

Neural net influenced magdm problem with modified choquet integral aggregation operators and correlation coefficient for triangular fuzzy intuitionistic fuzzy sets

A fire risk assessment method for offshore platforms: applications of 24Model with BN

ABSTRACT This paper integrates the 24Model with a BN and proposes a fire risk assessment method for offshore platforms. Triangular fuzzy membership function fuzzy set theory, coefficient of variation method and the combination of node state distance function and fuzzy inference are used to address the subjectivity and uncertainty due to insufficient objective data and conflicting opinions of multiple experts. Based on the proposed method, the human, organisational and technical factors of an offshore platform are comprehensively analysed from the perspective of the system. Based on diagnostic inference and sensitivity analysis, the main affecting factors and causal path of the risk scenario are determined. The results show that the proposed method could help in identifying the root causes of the failures and provide new insights into the probabilities and relationships among different factors.

A One Health framework for exploring zoonotic interactions demonstrated through a case study

The eco-epidemiology of zoonoses is often oversimplified to host-pathogen interactions while findings derived from global datasets are rarely directly transferable to smaller-scale contexts. Through a systematic literature search, we compiled a dataset of naturally occurring zoonotic interactions in Austria, spanning 1975–2022. We introduce the concept of zoonotic web to describe the complex relationships between zoonotic agents, their hosts, vectors, food, and environmental sources. The zoonotic web was explored through network analysis. After controlling for research effort, we demonstrate that, within the projected unipartite source-source network of zoonotic agent sharing, the most influential zoonotic sources are human, cattle, chicken, and some meat products. Analysis of the One Health 3-cliques (triangular sets of nodes representing human, animal, and environment) confirms the increased probability of zoonotic spillover at human-cattle and human-food interfaces. We characterise six communities of zoonotic agent sharing, which assembly patterns are likely driven by highly connected infectious agents in the zoonotic web, proximity to human, and anthropogenic activities. Additionally, we report a frequency of emerging zoonotic diseases in Austria of one every six years. Here, we present a flexible network-based approach that offers insights into zoonotic transmission chains, facilitating the development of locally-relevant One Health strategies against zoonoses.

A Systematic Approach for Evaluating and Selecting Healthcare Waste Treatment Devices using OWCM-CODAS and Triangular Neutrosophic Sets

Healthcare is a fundamental aspect of human life, impacting individuals, communities, and societies. Investing in healthcare infrastructure, services, and education is essential for fostering a healthy, thriving population. Healthcare waste management is a critical aspect of public health, and it requires a concerted effort from healthcare facilities, governments, and communities to ensure that waste is managed in a way that minimizes risks to human health and the environment. This paper proposes a hybrid methodology combining the Opinion Weight Criteria Method (OWCM) and the Combinative Distance-Based Assessment (CODAS) within the framework of Triangular Neutrosophic Sets (TNS) to evaluate and select the optimal healthcare waste treatment devices. The proposed methodology balances various conflicting criteria and incorporates uncertainty in expert assessments to ensure a robust decision-making process. The paper also provides a comprehensive review of healthcare waste management devices and highlights the need for a comprehensive approach to healthcare waste management. The proposed methodology is applied to a case study involving evaluating healthcare waste treatment devices based on different factors such as economic, environmental, technological, and social aspects. The results show that the OWCM-CODAS methodology, integrated with TNS, effectively evaluates and ranks healthcare waste treatment devices based on multiple criteria. The sensitivity analysis demonstrates the robustness of the proposed model, and the results indicate that the model's performance and the relative ranking of the alternatives are not sensitive to changes in the threshold parameter τ within the tested range.

Exploring the Application of Digital Twin Technology in the Energy Sector using MEREC and MAIRCA Methods

Smart city sustainability initiatives prioritize creating environmentally, economically, and socially sustainable urban environments. Digital Twin (DT) technology creates precise digital replicas of physical assets, systems, or processes. These digital twins play a crucial role in advancing the goals of smart city sustainability. This paper explores the development and application of DT technology for integrated regional energy systems in smart cities, emphasizing its potential to optimize energy consumption, reduce costs, and enhance overall system performance. The CloudIEPS platform, an energy internet planning platform based on digital twin technology, is a great example of how digital twin technology can be applied in practice, helping optimize energy efficiency and reduce costs. Integrating digital twin technology with the Multi-Criteria Decision-Making (MCDM) methods offers a novel approach to managing and optimizing energy systems in smart cities. The paper aims to create a consistent and robust approach to determining the best digital twin solution for energy systems in smart cities. The paper identifies critical factors for decision-making and establishes a method for assessing the significance of criteria using Triangular Neutrosophic Sets (TNS) through the MEthod based on Removal Effects of Criteria (MEREC) and the Multi-Attributive Ideal Real Comparative Analysis (MAIRCA) approach. These methods are used to evaluate and prioritize multiple criteria in decision-making processes. Furthermore, the methods are combined with Triangular Neutrosophic Sets (TNS) to support decision-making for smart cities' energy systems, better accounting for the complex and uncertain nature of energy systems. A case study is conducted to apply and validate the developed methodology and perform a sensitivity analysis of the experimental results. The research outcomes indicated that the proposed methodology is robust and effective in handling the uncertainty and complexity inherent in smart cities' energy systems. The sensitivity analysis further confirms the stability and adaptability of the proposed methodology across different scenarios, making it a valuable tool for policymakers and stakeholders in the energy sector.

Model reference adaptive controller with interpretable fuzzy rules for linear MIMO systems

This paper presents a method for fuzzy model reference adaptive control system design for a partially known multi-input multi-output (MIMO) linear dynamic plant. Differential or convolutional equations can describe the plant to be controlled, and the fuzzy controller is assumed to be from the MIMO sector-bounded nonstationary nonlinearities class. The task is to obtain robust adaptive stabilization. Some absolute stability theorems and integral evaluations of the state and control vectors are applied in the MIMO fuzzy adaptive controller design procedure for the first time. A method for automatically obtaining a near-optimal nonlinear dynamic reference model is described. A practical step-by-step procedure of the MIMO adaptive fuzzy controller design is proposed, resulting in highly interpretable MIMO fuzzy control rules based on triangular fuzzy sets and strong triangular fuzzy partition. An example of the fuzzy controller design according to the proposed procedure is given.

CoCoSo framework for multi-attribute decision-making with triangular fuzzy neutrosophic sets: “Innovation and entrepreneurship” evaluation case

The “innovation and Entrepreneurship” education focuses on cultivating students’ “innovation and Entrepreneurship” abilities, reflecting the fundamental requirements of economic progress and social development for the knowledge, ability, and quality structure of talents. Local universities should actively promote the reform of talent cultivation models, establish a scientific “innovation and Entrepreneurship” education target system based on the actual situation of the school, strengthen the construction of “innovation and Entrepreneurship” education courses, build various “innovation and Entrepreneurship” practice platforms, pay attention to the interaction between the first and second classrooms, as well as practical and training platforms, serve the growth and talent development of students, and achieve a comprehensive improvement in the quality of school education, teaching, and talent cultivation. The “innovation and Entrepreneurship” education quality evaluation of local colleges could be considered as multiple attribute decision-making (MADM). Recently, the Combined Compromise Solution (CoCoSo) method and information entropy method was employed to deal with MADM. The triangular fuzzy neutrosophic sets (TFNSs) are employed as a better tool for expressing uncertain information during the “innovation and Entrepreneurship” education quality evaluation of local colleges. In this paper, the triangular fuzzy neutrosophic number CoCoSo (TFNN-CoCoSo) based on the TFNN grey rational coefficients (TFNNGRC) from TFNN positive ideal solution (TFNNPIS) is constructed to cope with the MADM under TFNSs. The information entropy method is employed to compute the weight values based on the TFNNGRC from TFNNPIS under TFNSs. Finally, a numerical example of “innovation and Entrepreneurship” education quality evaluation of local colleges is constructed and some decision comparisons are constructed to verify the TFNN-CoCoSo method.

Blending Uncertainty Theory Innovative into Decision Support Framework for Selecting Agricultural Machinery Suppliers

The rivalry among suppliers and stakeholders created pressure, making the selection of the best provider a crucial subject based on a set of criteria for the responsiveness of clients. Consequently, several criteria need to be considered to select the most suitable supplier. As a result, certain criteria may overlap and contradict one another. Multi-criteria decision-making (MCDM) techniques are widely used in many fields to address selection problems when there are numerous competing criteria and multiple alternatives. Hence, we are leveraging MCDM techniques in constructing a decision support framework (DSF) as MEthod based on the Removal Effects of Criteria (MEREC) and Multi-Attributive Border Approximation Area Comparison (MABAC). In our DSF, we harnessed the uncertainty theory of triangular neutrosophic sets (TrNSs) which is considered one of the advantages that DSF provides.TrNSs support experts in their judgments when facing problems such as imprecise judgments and insufficient data. As well, we applied the constructed DSF in a real case study for five suppliers for machinery agriculture and evaluated the suppliers based on ten criteria. The DSF’s findings indicated that supplier 5 is the optimal one for machinery agriculture otherwise supplier 2 is the worst one. Also, we applied another ranker technique of MCDM technique entailed in the weighted sum model (WSM) and compared WSM results with MABAC under the authority of TrNSs.

An [formula omitted]-cut intervals based Fuzzy Best–Worst Method for Multi-Criteria Decision-Making

To address ambiguity arising from linguistic decision judgments, Guo and Zhao introduced a model of the well-known Multi-Criteria Decision-Making (MCDM) method, Best-Worst Method (BWM), using fuzzy sets, known as Fuzzy Best–Worst Method (FBWM). Despite its versatility, FBWM has limitations, such as criteria-weights being independent of fuzzy comparison values’ shape and reliance on approximate fuzzy arithmetic operations. In response to these limitations, we introduce a novel model of Fuzzy Best–Worst Method based on α-cut intervals. In this model, the calculation of optimal weights involves formulating an optimization problem that utilizes exact fuzzy arithmetic operations defined in terms of α-cut intervals. This approach aims to optimize the entire shape of fuzzy comparison values simultaneously. However, it turns out that, although we have proven the existence of optimal solution for this problem, solving it proves to be challenging. To resolve this issue, we approximate optimal weight set(s) using triangular fuzzy weight sets and assess the Error of Approximation (EA). The approximate weight set with the desired EA is then defuzzified to obtain a crisp weight set. In situations where there are multiple approximate weight sets with the same EA, interval-weights are calculated. Following that, we establish the necessary conditions for a Fuzzy Pairwise Comparison System (FPCS) to be consistent. Using these conditions, we calculate a lower bound of the Consistency Index (CI), providing a measure of the accuracy of weights. Finally, we discuss numerical examples and a real-world scenario, ranking of risk factors in supply chain 4.0, to validate the effectiveness of the proposed model.

Modeling Livestock Procedures Toward Precision and Sustainable Livestock Farm in Era of Virtual Technologies: Lessons, Opportunities, Avenues of Digitization

Presently, contemporary and virtual technologies that are being embraced by many businesses have a favorable influence. For instance, biometric sensors of the Internet of Things (IoT), artificial intelligence (AI), big data (BD), blockchain technology (BCT), and so on in livestock permit the real-time observation of the health and behavior of animals. Also, monitoring helps prevent deterioration, diagnose injuries, and stress, and sustain productivity. The collected data from biometric sensors is analyzed by using BD securing the processed information and making it transparent for partners using BCT. Achieving safety and security through collaborating human robots (cobots) Accordingly, these technologies turn traditional livestock into precision livestock farms (PrLFs). Currently, the concept of precision serves as the cornerstone for the advancement of sustainable and user-friendly livestock farm management in many nations as well as globally. Hence, the objective of this study is to embrace the concept of precision and illustrate its influence on livestock farms toward sustainability of livestock farm. These objectives consider catalysts for analyzing and evaluating the sustainability of livestock farms that embrace contemporary technologies in their operations and practices. Moreover, we are constructing an evaluation model for obtaining the most sustainable livestock farm through harassing Multi-Criteria Decision Making (MCDM) techniques where each technique is responsible for a certain function. For instance, CRiteria Importance Through Inter-criteria Correlation (CRITIC) is utilized for obtaining the criteria’s weights and the combined compromise solution (CoCoSo) leverages the obtained weights from CRITIC for ranking the alternatives of livestock farms and recommends the most sustainable and worst alternative. The evaluation for alternatives is performed based on rating four main criteria related to sustainability’s pillars and thirteen sub-criteria. Finally, the utilized MCDM techniques are working under the authority of Triangular Neutrosophic Sets (TrNSs) to bolster these techniques when handling incomplete information and perplexed situations.

Fuzzy Optimization Model for Decision-Making in Single Machine Construction Project Planning

Scheduling for a construction project with a limited number of machines is a critical and well-studied problem. Most studies assume that task processing times are exact; in practice, delays frequently occur, rendering the initial work plan invalid. Therefore, adaptability is crucial to the success of a project. This work introduces a fuzzy optimization model for the planning of construction projects executed simultaneously and having only one backhoe. The model assumes imprecise task processing times, represented by triangular fuzzy sets, that accept delays up to a permitted degree of tolerance. The model solution obtains a fuzzy work plan. This is a robust plan that supports incidents (delays). A method to apply the model was created. The fuzzy model can help construction companies reduce delays in the delivery of their projects and avoid excessive penalties. The model was implemented in the CPLEX solver, which can quickly obtain an optimal solution for small and medium instances. For large instances, the model must be solved with metaheuristics. This scientific contribution is important for future work since it consists of the application of fuzzy optimization in a specific area of civil engineering.

Fuzzy Framework for Evaluation Strategies of Climate Change Adaptation on Constructing

This study proposes a decision-making model for ranking strategies to eliminate climate change in construction. The triangular fuzzy set deals with uncertain information in the ranking process. Various criteria are used in this study, so the multi-criteria decision-making (MCDM) methodology is used to deal with these criteria. The TOPSIS method is an MCDM methodology used to rank the alternatives. The TOPSIS method is integrated with triangular fuzzy numbers. The criteria weights are computed by using the average method. The application is applied with 12 criteria and 8 options. The results show that alternative 7 is the best and alternative 3 is the worst. The results are tested with sensitivity analysis to show their stability. The sensitivity analysis was conducted with 13 cases of changing the criteria weights. Then, the TOPSIS method is applied under 13 cases in criteria weights. The results show that the ranking is stable in different cases.

A new energy vehicle battery supplier selection using SWARA-MEREC-MARCOS approach under probabilistic triangular intuitionistic hesitant fuzzy environment

In this manuscript, we construct a Multi-Criteria Decision-Making (MCDM) model to study the new energy vehicle (NEV) battery supplier selection problem. Firstly, we select criteria to build an evaluation index system. Secondly, SAWARA and MEREC methods are used to calculate subjective and objective weights in the ranking process, respectively, and PTIHFS (Probabilistic Triangular Intuitionistic Hesitant Fuzzy Set) is employed to describe the decision maker’s accurate preferences in performing the calculation of subjective weights. Then, the game theory is used to find the satisfactory weights. We use TFNs to describe the original information in the MARCOS method to obtain the optimal alternative. Finally, a correlation calculation using Spearman coefficients is carried out to compare with existing methods and prove the model’s validity.