Fuzzy Transition Research Articles

ImFTP: Deep imbalance learning via fuzzy transition and prototypical learning

Although many methods have been proposed for tackling the class-imbalance problem, they still suffer from the insufficient feature representative capability and the overfitting problem. This paper proposes a new deep imbalance learning approach based on the Fuzzy set Theory and the Prototypical learning mechanism, abbreviated as imFTP for short, which consists of an adaptive smooth sampling module, a self-learnable prototypical learning module, and a fuzzy transition module. The adaptive smooth sampling module adaptively adjusts the sampling frequency of different classes to ensure their adequate opportunity to participate in the training process, which can mitigate the overfitting problem. The self-learnable prototypical learning module devises a clustering distance based Softmax cross-entropy loss and an intra-class clustering loss to improve the feature representation and discrimination capability of the model. The fuzzy transition module utilizes the fuzzy set theory to transform sample features effectively, which further enhances the feature representation capability of the model, meanwhile alleviates the overfitting problem. Experimental results on 15 benchmark datasets demonstrate that our method outperforms the best competitor by more than 3% in terms of the Macro-F1 metric, which is very significant.

Estimating time-varying epidemiological parameters and underreporting of Covid-19 cases in Brazil using a mathematical model with fuzzy transitions between epidemic periods.

Our study conducts a comprehensive analysis of the Covid-19 pandemic in Brazil, spanning five waves over three years. We employed a novel Susceptible-Infected-Recovered-Dead-Susceptible (SIRDS) model with a fuzzy transition between epidemic periods to estimate time-varying parameters and evaluate case underreporting. The initial basic reproduction number (R0) is identified at 2.44 (95% Confidence Interval (CI): 2.42-2.46), decreasing to 1.00 (95% CI: 0.99-1.01) during the first wave. The model estimates an underreporting factor of 12.9 (95% CI: 12.5-13.2) more infections than officially reported by Brazilian health authorities, with an increasing factor of 5.8 (95% CI: 5.2-6.4), 12.9 (95% CI: 12.5-13.3), and 16.8 (95% CI: 15.8-17.5) in 2020, 2021, and 2022 respectively. Additionally, the Infection Fatality Rate (IFR) is initially 0.88% (95% CI: 0.81%-0.94%) during the initial phase but consistently reduces across subsequent outbreaks, reaching its lowest value of 0.018% (95% CI: 0.011-0.033) in the last outbreak. Regarding the immunity period, the observed uncertainty and low sensitivity indicate that inferring this parameter is particularly challenging. Brazil successfully reduced R0 during the first wave, coinciding with decreased human mobility. Ineffective public health measures during the second wave resulted in the highest mortality rates within the studied period. We attribute lower mortality rates in 2022 to increased vaccination coverage and the lower lethality of the Omicron variant. We demonstrate the model generalization by its application to other countries. Comparative analyses with serological research further validate the accuracy of the model. In forecasting analysis, our model provides reasonable outbreak predictions. In conclusion, our study provides a nuanced understanding of the Covid-19 pandemic in Brazil, employing a novel epidemiological model. The findings contribute to the broader discourse on pandemic dynamics, underreporting, and the effectiveness of health interventions.

Distribution-based limited fuzzy bisimulations for nondeterministic fuzzy transition systems

Bisimulation techniques have been adopted and developed in fuzzy transition systems (FTSs) to compare their behavior. Recently, distribution-based bisimulation has been introduced to nondeterministic fuzzy transition systems (NFTSs) to measure the similarity between two distributions which can be regarded as generalized states. However, the new bisimulation does not consider the similarity of states. In terms of limited approximate bisimilarity, in this article, a notion of distribution-based k-limited bisimulation is proposed for NFTSs, which can measure the similarity between two distributions in the neighboring subgraphs (subsystems) and take the similarity of states into account, where k is a natural number. This article discusses some properties of limited bisimulation and the nonexpansiveness of typical parallel composition operators with respect to the limited bisimulation which makes compositional verification possible. Then a fixed point characterization of the limited bisimulation is investigated and an algorithm is given to compute the degree of k-limited similarity between two distributions. Moreover, a fuzzy modal logic interpreted on distributions is adopted to characterize the limited bisimulation.

Supervised Learning of Multievent Transition Matrices in Fuzzy Discrete-Event Systems.

In this article, supervised learning of fuzzy discrete-event systems (FDES) is investigated. A learning algorithm that performs supervised learning for multievent transition matrices of a sequence of fuzzy discrete events is derived. FDES can be used to describe a large class of practical systems that consist of fuzzy discrete states, fuzzy discrete events, and transitions among fuzzy discrete states via fuzzy discrete events. Because fuzzy discrete states, fuzzy discrete events, and fuzzy transitions are well defined in FDES, the FDES model is highly explainable, which is important in many applications, especially in biomedical applications. Based on this explainable model, the proposed learning algorithm can be used to learn events and event sequences in the model. Hence, it allows system developers to build an explainable model for a complex system based on the data available. Simulations using MATLAB are conducted to verify the effectiveness of the proposed algorithm.

Material handling machine activity recognition by context ensemble with gated recurrent units

Research on machine activity recognition (MAR) is drawing more attention because MAR can provide productivity monitoring for efficiency optimization, better maintenance scheduling, product design improvement, and potential material savings. A particular challenge of MAR for human-operated machines is the overlap when transiting from one activity to another: during transitions, operators often perform two activities simultaneously, e.g., lifting the fork already while approaching a rack, so the exact time when one activity ends and another begins is uncertain. Machine learning models are often uncertain during such activity transitions, and we propose a novel ensemble-based method adapted to fuzzy transitions in a forklift MAR problem. Unlike traditional ensembles, where models in the ensemble are trained on different subsets of data, or with costs that force them to be diverse in their responses, our approach is to train a single model that predicts several activity labels, each under a different context. These individual predictions are not made by independent networks but are made using a structure that allows for sharing important features, i.e., a context ensemble. The results show that the gated recurrent unit network can provide medium or strong confident context ensembles for 95% of the cases in the test set, and the final forklift MAR result achieves accuracies of 97% for driving and 90% for load-handling activities. This study is the first to highlight the overlapping activity issue in MAR problems and to demonstrate that the recognition results can be significantly improved by designing a machine learning framework that addresses this issue.

Three-dimensional measurement of fringe projection based on the camera response function of the quantified exposure time

Fringe projection technology is usually used for three-dimensional (3D) measurement, but there will be large errors when the measurement is overexposed or the surface is too dark. Polarizing filters can be used to eliminate the highlights of the image, but they may also cause the image to be too dark and affect the measurement accuracy. Otherwise, to ensure measurement accuracy, the complexity of the operation of the polarization system will be increased. In order to ensure the measurement accuracy and improve the measurement efficiency, a 3D measurement method of quantified exposure time is proposed in this paper, and the intensity response function of the light intensity captured by the camera and the exposure time is established, and more meaningful variable value intervals can be selected by the method of this paper. It can avoid the complex polarization bidirectional reflectance distribution function model, and the required exposure time can be calculated quantitatively within the already screened intervals. Then it is combined with the image fusion algorithm to generate the optimal fringe pattern. Experimental results demonstrate that this method significantly eliminates the effects of highlights in the image. The fuzzy transition area between the black and white fringes is effectively reduced, and the edge information of the fringes is correctly restored.

Fuzzy Bisimulations for Nondeterministic Fuzzy Transition Systems

Bisimulations are established forms of behavioral equivalences for discrete event systems. Recently, bisimulations have been introduced to fuzzy transition systems (FTSs) and developed quickly. Relational lifting by using weight functions is one of the most used methods in bisimulation research, which lifts a crisp relation on the state spaces to a crisp relation on the distributions of state spaces of FTSs. This paper proposes a method, called fuzzy relational lifting method, via fuzzy similarity measures induced by residua (implications) in complete residuated lattices. In contrast with the existing method, fuzzy relational lifting method relaxes the conditions of lifting relation by using weight functions and is a generalization of the method. Some properties of fuzzy lifting operation are presented. Based on the fuzzy lifting operation, a fuzzy bisimulation for nondeterministic fuzzy transition systems (NFTSs) is introduced, which is much more natural and robust than some behavioral measures, and can measure the degree of similarity between any two states which are deemed to be equivalent intuitively but simply distinguished by other behavioral measures. Then some properties of fuzzy bisimulations are provided. Moreover, a fixedpoint characterization of fuzzy bisimulations is given and the greatest fuzzy bisimulation is computed. Finally, a real-valued logic is introduced to characterize fuzzy bisimulations over Godel algebra.

Approximate bisimulations for fuzzy-transition systems

Bisimulation techniques have been recently introduced to fuzzy transition systems to compare their behavior. When studying bisimulation, one of the most popular methods is relational lifting. In this paper, we first realize the relational lifting through a function S˜. The new relational lifting method relaxes the condition of lifting relation from using weight functions to function S˜ defined by residua (implications) in complete residuated lattices. We first discuss some properties of the lifting operation, and then define an α-bisimulation under S˜, where α∈[0,1], for nondeterministic fuzzy transition systems (NFTSs). The new bisimulation can handle the case that two states are equivalent intuitively but are simply treated as distinguishable by some behavioral measures, and so it is much more natural and robust. Then we provide some properties of α-bisimulation under S˜. The parallel composition operator of NFTSs is addressed and we show that α-bisimilarity under S˜ is nonexpansive with respect to the operator, which makes compositional verification possible. In addition, we give a fixed-point characterization of α-bisimulation under S˜ and compute α-bisimilarity under S˜. Finally, we introduce a real-valued logic to characterize α-bisimilarity under S˜.

Fuzzy multiset finite automata with output

Fuzzy multiset finite automata with output represent fuzzy version of finite automata (with output) working over multisets. This paper introduces Mealy-like, Moore-like, and compact fuzzy multiset finite automata. Their mutual transformations are described to prove their equivalent behaviours. Furthermore, various variants of reduced fuzzy multiset finite automata are studied where the reductions are directed to decrease the number of fuzzy components (like fuzzy initial distribution, fuzzy transition relation, or fuzzy output relation) of the fuzzy automata. The research confirmed that all fuzzy multiset finite automata with output can be reduced without change of their behaviours.

2D Hexagonal Finite Fuzzy Cellular Automata

In this paper 2D hexagonal finite fuzzy cellular automata defined by fuzzy transition of local rules based on hexagonal cell structure are studied. Here the inverse problem of 2D hexagonal finite fuzzy cellular automata is also studied.

Beyond affectedness – partitive objects and degrees of agenthood in Ancient Greek

Abstract In several ancient and modern Indo-European languages, the partitive-genitive may be used in place of the accusative to encode the second argument of two-place verbs. In Ancient Greek the two types of object encoding can alternate with change-of-state verbs, alternation being viewed as connected with degrees of patient affectedness: the partitive-genitive encodes partially affected objects. Alternation also extends to experiential verbs, which are typically characterized by a low degree of transitivity and do not imply any change of state of the object-stimulus. Rather than concentrating on the implications of case alternation on the construal of the object, I consider the effects of variation on the whole construction, and argue that genitive vs. accusative marking of the object (NomGen vs. NomAcc constructions) reflects the construal of the subject-experiencer. While the different construal of the experiencer in terms of degrees of control cross-linguistically often results in non-nominative encoding of the experiencer, in Ancient Greek it is object encoding that affects the construal of the experiencer and reflects a scale based on possible control. The distribution of constructions with experiential verbs shows that NomAcc is typical of verbs of sight, thought, intellectual knowledge and emotions connected to sight and awareness, such as wonder and fear. NomGen is connected with touch, smell, taste, memory, forgetfulness, care and desire. In the in-between area, verbs of hearing, learning and verbs of affection may feature both accusative and genitive encoding, thus constituting a fuzzy transition area. The connection between sight and other experiential verbs that feature accusative encoding reflects an embodied conceptualization of experiential situations.

Flux Estimator for Salient Pole Synchronous Machines Driven by the Cycloconverter Based on Enhanced Current and Voltage Model of the Machine with Fuzzy Logic Transition

Flux estimation is a key feature of the field-oriented control for the electrically excited synchronous machine which enables the high-performance, high-dynamic drive behavior. In this work, an electrically excited synchronous machine flux estimator based on a current and voltage model is proposed. In this case, the transition between the estimators is done with a fuzzy logic set of rules. The flux estimator based on the current model of the machine in this paper considers the saturation and cross-coupling effect in both axis and it is suitable for applications where a limited amount of the machine data is available. The flux estimator based on the voltage model is specially designed for the drives where high voltage and current ripple is present under normal operating conditions, e.g., like in cycloconverter applications. To exploit all the advantages of both models, a fuzzy logic transition is proposed based on multiple choices which manages the transition between the models based on a speed and torque reference. The proposed flux estimator is experimentally verified on a cycloconverter fed salient-pole electrically excited synchronous machine. The experimental results clearly show that the proposed flux estimator enables the accurate and stable operating conditions for different operating points of the cycloconverter-fed salient-pole electrically excited synchronous machine.

Risk Analysis of Instability Failure of Earth–Rock Dams Based on the Fuzzy Set Theory

Determining the anti-sliding instability risk of earth–rock dams involves the analysis of complex uncertain factors, which are mostly regarded as random variables in traditional analysis methods. In fact, fuzziness and randomness are two inseparable uncertainty factors influencing the stability of earth–rock dams. Most previous research only focused on the randomness or the fuzziness of individual variables. Moreover, dam systems present a fuzzy transition from a stable state into a failure state. Therefore, both fuzziness and randomness of the influencing factors should be considered in the same framework, where the instability of an earth–rock dam is regarded as a mixed process. In this paper, a fuzzy risk model of instability of earth–rock dams is established by considering the randomness and fuzziness of parameters and the failure criteria comprehensively. We obtained the probability threshold of instability risk of earth–rock dams by Monte-Carlo simulation after the fuzzy parameters were transformed into interval numbers by cut set levels. By applying the proposed model to the instability analysis of the Longxingsi Reservoir, the calculation results showed that the lower limits of risk probability under different cut set levels exceeded the instability risk standard of grade C for earth–rock dams. Compared with the traditional risk determination value, the risk interval obtained with the proposed methods reflects different degrees of dam instability risk and can provide reference for dam structure safety assessment and management.

Three-dimensional measurement of fringe projection based on the camera response function of the polarization system

Fringe projection technology is often used for three-dimensional (3D) measurement, but it is difficult to measure highlight surfaces. Polarization systems are usually used to remove highlight surfaces. Polarizing filters can be used to eliminate the highlights of the image, but they may also cause the image to be too dark and affect the measurement accuracy. Otherwise, to ensure measurement accuracy, the complexity of the operation of the polarization system will be increased. A method of polarization-based camera intensity response function for 3D measurement is proposed. The intensity response function of the camera under the polarization system is established. It can avoid the complicated polarized bidirectional reflectance distribution function model and directly and quantitatively calculate the required angle between the transmission axes of the two polarizing filters. Then it is combined with the image fusion algorithm to generate the optimal fringe pattern. Experimental results demonstrate that this method significantly eliminates the effects of highlights in the image. The fuzzy transition area between the black and white fringes is effectively reduced, and the edge information of the fringes is correctly restored. Moreover, the high signal-to-noise ratio and contrast of the image are retained when the polarization filters are added.

Применение потоковой кластеризации для идентификации гибридных темпоральных автоматов на аналоговых данных IIoT

Модели класса темпоральных автоматов предоставляют удобную абстракцию для решения задач диагностики и управления в системах промышленного Интернет вещей (IIoT). Для их применения необходимо выполнять идентификацию автомата путем пассивного обучения онлайн, используя только положительные образцы. Такой тип обучения возможен только для гибридных автоматов (HTA) с алгоритмом OTALA. Однако для обучения HTA необходима последовательность дискретных событий вместо непрерывных аналоговых временных рядов, обычно встречающихся в IIoT. A. von Birgelen, O. Niggemann и другие предпринимали попытки восполнить эту пробел за счет предварительной обработки наблюдений самоорганизационными картами (SOM) с преобразованием водораздела, однако полученные модели часто неэффективны в реальных условиях. В данной статье задача идентификации темпорального автомата по аналоговым данным IIoT решается с применением инкрементного алгоритма кластеризации на основе моделей (IMCF). IMCF - это потоковый алгоритм, который обрабатывает входные временные ряды в режиме онлайн и превращает их в последовательность дискретных состояний с четкими или нечеткими переходами между ними. Такие переходы далее используются как события, необходимые для идентификации HTA по алгоритму OTALA. Полученные модели экспериментально исследованы на примере системы IIoT, ранее представлявшей сложность для моделирования. Достигнутое повышение эффективности на 24,9–76,8 % демонстрирует, что дискретизация с помощью IMCF более информативна для идентификации HTA. Также обсуждаются более широкие перспективы применения HTA в системах IIoT и определены ограничения, остающиеся актуальными для подобных практических применений: дискретность переходов между состояниями HTA и отсутствие долговременной памяти переходов.

Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance

Markov chains (MCs) are widely used to model a great deal of financial and actuarial problems. Likewise, they are also used in many other fields ranging from economics, management, agricultural sciences, engineering or informatics to medicine. This paper focuses on the use of MCs for the design of non-life bonus-malus systems (BMSs). It proposes quantifying the uncertainty of transition probabilities in BMSs by using fuzzy numbers (FNs). To do so, Fuzzy MCs (FMCs) as defined by Buckley and Eslami in 2002 are used, thus giving rise to the concept of Fuzzy BMSs (FBMSs). More concretely, we describe in detail the common BMS where the number of claims follows a Poisson distribution under the hypothesis that its characteristic parameter is not a real but a triangular FN (TFN). Moreover, we reflect on how to fit that parameter by using several fuzzy data analysis tools and discuss the goodness of triangular approximates to fuzzy transition probabilities, the fuzzy stationary state, and the fuzzy mean asymptotic premium. The use of FMCs in a BMS allows obtaining not only point estimates of all these variables, but also a structured set of their possible values whose reliability is given by means of a possibility measure. Although our analysis is circumscribed to non-life insurance, all of its findings can easily be extended to any of the abovementioned fields with slight modifications.

An Improved Monte Carlo Method Based on Neural Network and Fuzziness Analysis: A Case Study of the Nanpo Dump of the Chengmenshan Copper Mine

The landslide of dump is a man-made geological disaster which will bring great harm to the surrounding people and environment, and probabilistic reliability analysis is commonly used to analyze the probability of slope landslide or whether protective measures should be taken. Monte Carlo simulation is the most commonly used method, but there are some problems, such as low efficiency, statistical ambiguity of small samples, and the fuzzy transition interval of the stability criterion. This paper proposes an improved Monte Carlo method that uses an improved bootstrap method to process small samples of geotechnical data, employs ELM (extreme learning machine) based on PSO (particle swarm optimization) to fit the limit equilibrium method function, and constructs the safety factor membership function of the dump site considering the fuzzy transition interval. This method was applied to an example slope of the dump site in Chengmenshan, Jiangxi. Comparing the analysis result with the result of the traditional MCS (Monte Carlo Search) method, it was found that after adding the safety factor membership function, the result was closer to the actual situation of the dump site, and the probability of failure and reliability index values were closer to those of the dangerous state; after the original function was replaced by the PSO-ELM model, the efficiency of the MCS method was greatly improved while the results maintained high consistency with the original results; the MCS method combined with the bootstrap method not only simulated the fuzzy uncertainty of the original sample statistics and distribution type but also expressed the reliability index and probability of failure as a two-sided confidence interval with a certain confidence level. The above conclusion proves the effectiveness and superiority of this method compared with the original MCS method.

Limited approximate bisimulations and the corresponding rough approximations

To measure the similarity of nodes in the neighboring subgraphs, Milner introduced the notion of k-limited bisimilarity. Recently, as a weaker version of k-limited bisimilarity, the notion of k-limited similarity was proposed and applied to graph pattern matching. (Bi)simulations have been widely used in comparing the behavior of fuzzy transition systems. In order to study the (bi)simulation semantics of labeled fuzzy transition systems in the residuated lattice-valued logic setting, we introduce an extension of labeled approximation spaces, called the quantitative fuzzy approximation spaces (QFASs), whose labels are equipped with a residuated lattice-valued equality relation. In a QFAS, we define a new notion of limited approximate similarity, to quantify to what extent one state is simulated by another in the neighboring subgraphs, and provide its properties. Based on the new notion, we give a definition of limited approximate simulation and discuss its properties. Then we introduce an ordered pair of relations, one on the state (vertex) set (limited approximate simulation) and one on the edge (transition) set induced by the relation on state set, called VE limited approximate simulation in this paper. We also present a new notion of limited approximate bisimilarity in a QFAS, to quantify to what extent two states are similar in the neighboring subgraphs, and give its properties. One main contribution of the paper is to give a condition for two states to be limited approximate bisimilar and investigate the degree of similarity between two states in a QFAS. Finally, we discuss the relationships between the rough approximations based on the underlying crisp relation induced by underlying labeled fuzzy relation and the rough approximations based on limited approximate bisimilarity.

A Fuzzy Modal Logic for Fuzzy Transition Systems

This paper intends to contribute with a new fuzzy modal logic to model and reason about transition systems involving uncertainty in behaviours. Our formalism supports fuzziness at transitions and on the proposition symbols assignment levels.Against of other approaches in the literature, our bisimulation and bisimilarity notions generalise the analogous standard notions of classic modal logic and of process algebras. Moreover, the outcome of our logic is also fuzzy, with the semantic interpretation of connectives supported by the Gödel algebra.

Synchronization of Stochastic Modeling with Square Fuzzy Transition Probability Relational Matrix

There are number of fields like agriculture, industry, insurance, tourism and others get affected directly or indirectly by a most common phenomenon known as the Rainfall. Till now we are not able to predict rainfall and it is one of the unsolved problems. This paper aims to synchronize stochastic modeling and square fuzzy transition probability relational matrix and it is obtained from the lexical terms along with the help of fuzzy value which in turn calculated form the lexical value. Fuzzy matrices are necessary in modeling uncertain situations in various fields. Here the lexical values are specially assigned heptagonal fuzzy numbers which in turn converted into fuzzy value to measure relation mappings. Along with this, synchronization is done for stochastic models with transition probability matrix and also with square fuzzy transition probability relation matrix to get a clear picture of the result. In this work, the changes in annual rainfall of Tamil Nadu depending on markov chain models are monitored. Statistical technique like Markov chain is applied at metrological stations in order to predict short term precipitation. The annual rainfall from 1901 to 2000 is derived and the frequency distribution table is formed. The class intervals are denoted as states and the transition probability matrix is formed due to the variations in annual rainfall. The uniform random states are formed by generating random number. The available stochastic climate models presently be adapted to form new climatic conditions if the forthcoming conditions is identified with necessary accuracy. Finally, prediction of rainfall based on two categories such as climatic factors and through states is analyzed in this study.