Intuitionistic fuzzy sets
A definition of the concept ‘intuitionistic fuzzy set’ (IFS) is given, the latter being a generalization of the concept ‘fuzzy set’ and an example is described. Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
References (4)
- K. Atanassov
Intuitionistic fuzzy sets
- K. Atanassov et al.
Intuitionistic fuzzy sets
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Dynamic case-based emergency decision-making model under time-varying single-valued neutrosophic set
2024, Expert Systems with ApplicationsCase-based emergency decision-making (CEDM) models are effective tools for generating emergency response alternatives. Existing studies have indicated their merits in emergency response; however, representing and fusing ambiguous and dynamically changing case information remains a challenging issue. To address these problems, this study investigates a dynamic CEDM (DCEDM) model in a time-varying single-valued neutrosophic set (TVSNS) environment. First, TVSNS is defined to depict complex case information, which is not only fuzzy and uncertain but also continuously changing. Concurrently, the integral of the TVSNS is explored to aggregate the case information over multiple periods, which can preserve the integrity of case information in hesitation and ambiguous situations. Subsequently, a new attribute similarity measure under a neutrosophic set is developed. Additionally, an optimization model considering the interactive relationships among attributes is proposed to determine the attribute weights with Shapley values. Subsequently, a novel case similarity calculation method by incorporating the gained and lost dominance score and regret theory is explored, considering the regret avoidance behavior of decision-makers and fairness among attributes. The effectiveness of the proposed DCEDM model is verified with the generation of treatment alternatives for infectious COVID-19. Sensitivity and comparison analyses are provided to demonstrate the superiority of the proposed DCEDM model. The results reveal that the proposed DCEDM model can reflect the actual demand and better assist decision-makers in emergency response.
A novel twin-center intuitionistic fuzzy large margin classifier with unified pinball loss for improving the performance of E-noses system
2024, Expert Systems with ApplicationsGas sensor drift has consistently been a bottleneck in the progression of electronic noses (E-noses) systems. In contrast to target-domain-adaptive anti-drift classification algorithms, target-domain-free methods exhibit independence from target domain information, thereby possessing broader applicability. Support vector machine (SVM), as a popular target-domain-free classifier, is widely employed to solve the E-noses drift problem. However, SVM-based methods have some inherent flaws in drift resistance performance: (1) The objective of maximizing minimum margin, rendering it highly sensitive to disturbances; (2) The utilization of hinge loss, resulting in poor robustness; (3) The absence of sample reliability measurement, contributing to noise susceptibility. To tackle these problems, we present a novel twin-center intuitionistic fuzzy large margin classifier with unified pinball loss (TC-IFUPLMC), which effectively improves the anti-drift performance in E-noses system. Specifically, the model achieves strong disturbance resistance by adopting marginal mean and variance as the optimization objective. Furthermore, the unified pinball loss is utilized to measure the distance between two categories of sample sets, which essentially further enhances the robustness. Additionally, a novel twin-center based IF function is used to obtain the confidence level of each sample, which further weakens the noise susceptibility. Comparative experiments based on different sensor drift datasets demonstrate the effectiveness of the proposed model in improving the anti-drift performance. The high stability of TC-IFUPLMC is also substantiated by the parameter sensitivity analysis experiments.
A novel knowledge-based similarity measure on intuitionistic fuzzy sets and its applications in pattern recognition
2024, Expert Systems with ApplicationsSimilarity measure is a useful tool to determine the similarity of two intuitionistic fuzzy sets (IFSs). Theoretically, there are two free variables of membership and non-membership on IFSs, and the most fuzzy set is not solely. Therefore, it is impossible to establish a similarity measure satisfying the classical axiom on it by using only the distance between any given IFSs and the assumed most fuzzy set. The motivation and innovation of this study lies in the exploration and use of the two most fuzzy sets, and the weighted average distance between IFSs and the two most fuzzy sets is used to define the similarity measure. Based on this analysis, a knowledge-based similarity measure on IFSs is proposed and some applications of this proposed measure in pattern recognition are introduced. The advantage of the introduced similarity measure is that it calculates the dissimilarity between the complementary sets well. Furthermore, it proves that the novel similarity measure satisfies axioms of the similarity measure on IFSs, and overcomes the drawbacks of the existing measures. Finally, a series of examples in pattern recognition fields are introduced to demonstrate the effectiveness of the proposed similarity measure.
An improved RAFSI method based on single-valued trapezoidal neutrosophic number and its Harmonic and Arithmetic mean operators for healthcare service quality evaluation
2024, Expert Systems with ApplicationsOver the last twenty years, patient opinions of the received healthcare services have emerged as a crucial quality indicator and a valuable instrument for evaluating the service quality of health organizations. However, many surveyors still utilized uncertain information for conducting this evaluation process. Whereas, in the past few years, the issues of inconsistency, indeterminacy, and uncertainty in data have been growing and have become a matter of concern in dealing with decision-making issues. This paper proposes an improved RAFSI method based on a single-valued trapezoidal neutrosophic number (SVTraNN) as a multi-attribute framework for dealing with a healthcare service quality evaluation. The proposed framework consists of two features: a feature for determining numerical criteria weights involving the procedures of the Ordinal Priority Approach (OPA) and a feature for selecting the best polyclinic through contributing our new SVTraNN Harmonic and arithmetic mean to yield criterion functions in the RAFSI method. This paper then compares the results obtained by the proposed method with other SVTraNN decision-making methods. A comparative analysis and rank reversal testing of the improved method demonstrated that the multi-attribute framework proffers the option of capability and stability in overcoming inconsistency, indeterminacy, and uncertainty information efficiently during the healthcare service quality evaluation.
A circular intuitionistic fuzzy assignment model with a parameterized scoring rule for multiple criteria assessment methodology
2024, Advanced Engineering InformaticsThe notion of circular intuitionistic fuzzy (C-IF) sets, which utilizes a malleable circle to depict uncertainties and encompasses membership and non-membership constituents at its core, constitutes a progressive advancement of standard intuitionistic fuzzy sets. This paper concerns the utilization of a C-IF assignment model along with a parameterized scoring rule for a methodology involving multiple criteria assessment. This study introduces a novel parameterized C-IF scoring function, addressing limitations in current scoring methodologies. The newly proposed scoring function incorporates datum and allocating parameters, offering enhanced adaptability and practicality. Unlike some existing C-IF scoring functions, this parameterized function effectively accounts for the radius of uncertainty, ensuring more accurate and reliable C-IF number comparisons. Comparative assessments with other scoring techniques demonstrate the superiority and stability of proposed function across various C-IF datasets. This newly introduced scoring function proves valuable in addressing multiple criteria assessment challenges within C-IF contexts, providing decision analysts with a dependable tool for complex decision-making scenarios. This research delves into real-world instances, including supplier assessment and healthcare waste disposal, illustrating a practical implementation of the model. Additionally, a comparison study and investigation have been done to emphasize the benefits of the parameterized C-IF scoring procedure employed in the postulated C-IF assignment methodology. This study offers substantial contributions, encompassing: (i) devotion to the establishment of a parameterized C-IF scoring methodology, (ii) assurance of consistent and rational C-IF scoring outcomes through the proposed parameterized scoring rule, (iii) the methodology’s flexibility, allowing customization of parameters to align with decision-makers’ preferences, (iv) improvement in the stability of C-IF assignment modeling through the parameterized C-IF scoring framework, and (v) demonstrated its practical viability through real-world applications in tackling challenges associated with multiple criteria assessment in C-IF contexts.
Risk assessment of fire safety in large-scale commercial and high-rise buildings based on intuitionistic fuzzy and social graph
2024, Journal of Building EngineeringFire risk assessment is a useful method to identify potential fire risks and improve safety management, especially for those large-scale commercial and high-rise buildings. However, after the establishment of the fire risk indexing system, the weight assignment in the existing assessment methods is not scientific and objective enough to synthesize the opinions of multiple experts with different knowledge backgrounds and working experience. To solve this problem, a novel fire risk assessment for large-scale commercial and high-rise buildings is proposed with intuitionistic fuzzy and social graph. First, based on the national standards of fire safety management, the monthly maintenance and the annual fire assessment reports, the indexing system is established. Then, a scientific and objective weight assignment method called Social Graph based Intuitionistic Fuzzy Analytic Hierarchy Process (SGIFAHP) is proposed such that (1) by utilizing the intuitionistic fuzzy and social graph, it can synthesize the positive, negative and hesitant opinions from multiple experts by considering the importance of experts; (2) a novel mechanism is designed to automatically check and repair the consistency of the opinions of each expert when the expert compares the importance of risk factors. To validate the performance of the proposed method, eleven buildings are selected and their fire safety data are collected. A comparison analysis is carried out with the existing methods to compare the assigned weights. The comparison and score validation conclude that the proposed method can assign more reasonable, scientific and objective weights than the existing methods while the scores are comprehensive and strongly interpretable. In the end, a guide is offered to help safety owners and inspectors improve fire safety with the proposed method.