Fuzzy Markov Chain Research Articles

Discrete-Time Finite Fuzzy Markov Chains Realized Through Supervised Learning Stochastic Fuzzy Discrete Event Systems

Discrete-Time Finite Fuzzy Markov Chains Realized Through Supervised Learning Stochastic Fuzzy Discrete Event Systems

RETRACTED ARTICLE: Fuzzy Markov chain latent space probabilistic decision-making for feature optimization in content-based image recognition

RETRACTED ARTICLE: Fuzzy Markov chain latent space probabilistic decision-making for feature optimization in content-based image recognition

Weighted Fuzzy Markov Chains for Regions Research on Rainfall Forecasting

The problem of rainfall prediction is of great importance for the study of the hydrological cycle of a watershed or region in China. Since rainfall series are not periodic as well as linear, rainfall series are measured based on Markov’s theorem, and the percentage of precipitation distance is used to classify the historical data. The traditional Markov chain was optimized and a weighted-fuzzy Markov rainfall prediction model was established. The results show that the average absolute error of the two prediction samples is 2.09%, except for 2019, when the rainfall in Guangzhou City is different from the past, and the model has high accuracy, which has good practical significance and extension value.

Predicting the Behavior of Solar Energy in Tulkarm City Using Markov Chains and Fuzzy Markov Chains

Predicting the Behavior of Solar Energy in Tulkarm City Using Markov Chains and Fuzzy Markov Chains

Using fuzzy time series with and without markov chain: to forecast of edible bird nest exported from Indonesia

Edible bird nest (EBN) were traditional medicine consumed by the Tiongkok. This study compared two-algorithm method. Fuzzy time series and Markov chain as forecast method the number of bird nest exported from Indonesia. The secondary data between 2012 and 2018 were from Bureau Central Statistic (BPS). The scope using in this study were bird nest between 2012 until 2018, with a unit of volume kilograms (Kg). Used secondary export data, collected from BPS of Indonesia. Data were analysed using Fuzzy Time Series with and without Markov Chain using R Studio. The result showed that Fuzzy Time Series with and without Markov Chain method performs better in the forecasting ability in short-term period prediction and the values of Mean Absolute Percentage Error (MAPE) and Mean Square Error (MSE) tends to be smaller than the Fuzzy Time Series without Markov Chain. It can be concluded the number of exported can be used Fuzzy time series.

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.

A self-organizing recurrent fuzzy neural network based on multivariate time series analysis

Fuzzy neural networks (FNNs) have attracted considerable interest for modeling nonlinear dynamic systems in recent years. However, the recurrent design and the self-organizing design of FNNs generally lack adaptability, and their analyses on the change rule of networks in continuous time are insufficient. To solve these problems, a self-organizing recurrent fuzzy neural network based on multivariate time series analysis (SORFNN-MTSA) is proposed in this paper. First, a recurrent mechanism, based on wavelet transform fuzzy Markov chain algorithm, is introduced to obtain adaptive recurrent values and accelerate convergence speed of the network. Second, a self-organization mechanism, based on weighted dynamic time warping algorithm and sensitivity analysis algorithm, is presented to optimize the network structure. Third, the convergence of SORFNN-MTSA is theoretically analyzed to show the efficiency in both fixed structure and self-organizing structure cases. Finally, several benchmark nonlinear systems and a real application of wastewater treatment are used to verify the effectiveness of SORFNN-MTSA. Compared with other existing methods, the proposed SORFNN-MTSA performs better in terms of both high accuracy and compact structure.

Data Forecasting and Storage Sizing for PV Battery System Using Fuzzy Markov Chain Model

Although photovoltaic (PV) power is a green energy source, the high output variability of PV power generation leads to lags in network availability. To increase PV power plant reliability, an energy storage system can be incorporated. However, improper selection of storage size increases system cost or decreases network availability due to over- or under-sizing of the storage capacity, respectively. For this reason, we develop a generalized Markov chain-based battery charging–discharging procedure for determining proper storage size. In this work, multi-objective clustering and fuzzy decision-making (FDM) techniques for selecting the most optimal storage size with optimal availability are also proposed to avoid issues associated with conventional selection procedures. The reliability of our approach is analyzed based on forecasted data. As better prediction yields more dispatchable storage sizing, thereby improving system reliability, a first-order fuzzy time-series, Markov chain-based prediction method is used owing to its high prediction efficiency. To explore PV power generation performance in both cool and hot, sunny conditions, the temperature effect is considered in the storage sizing–availability analysis.

Fuzzy Markov chains modeling of aggregation processes

In this paper, the fuzzy Markov chain method is proposed as a new discrete solution of a population balance equation for an aggregation process. In order to validate the proposed method, analytical solution of an aggregation equation is compared with the fuzzy Markov chain method for the constant aggregation kernel. According to the results, if the size range of the system is divided into a sufficient number of states and an appropriate transition time step is chosen, then the fuzzy Markov chain method displays a good approximation for the particle size distribution(PSD) while the main equation is driven by a constant aggregation kernel.

Stock Market Prediction Using Nonparametric Fuzzy and Parametric GARCH Methods

Prediction of stock market value is one the most complicated issue during the past decades. Due to its importance, in this research, we consider the prediction of stock values based on non-parametric and parametric methods. In this first method, we use the fuzzy Markov chain procedure in order to prediction problem. In this regard, all of the rising and falling probabilities during the weekdays are calculated and then they applied to obtain the increasing and decreasing rate. Then, based on this information we model and predict the stock values. In the sequel, we implement different methods of parametric time series such as generalized autoregressive conditionally heteroskedastic (GARCH), ARIMA-GARCH, Exponential GARCH (E-GARCH) and GJR-GARCH by assuming the normal and t-student distribution for the error terms to obtain the best model in terms of minimum mean square errors. Finally, the mythologies developed here are applied for the Tehran Stock Exchange Index (TEDPIX).

A review of applications of fuzzy sets to safety and reliability engineering

Safety and reliability are rigorously assessed during the design of dependable systems. Probabilistic risk assessment (PRA) processes are comprehensive, structured and logical methods widely used for this purpose. PRA approaches include, but not limited to Fault Tree Analysis (FTA), Failure Mode and Effects Analysis (FMEA), and Event Tree Analysis (ETA). In conventional PRA, failure data about components is required for the purposes of quantitative analysis. In practice, it is not always possible to fully obtain this data due to unavailability of primary observations and consequent scarcity of statistical data about the failure of components. To handle such situations, fuzzy set theory has been successfully used in novel PRA approaches for safety and reliability evaluation under conditions of uncertainty. This paper presents a review of fuzzy set theory based methodologies applied to safety and reliability engineering, which include fuzzy FTA, fuzzy FMEA, fuzzy ETA, fuzzy Bayesian networks, fuzzy Markov chains, and fuzzy Petri nets. Firstly, we describe relevant fundamentals of fuzzy set theory and then we review applications of fuzzy set theory to system safety and reliability analysis. The review shows the context in which each technique may be more appropriate and highlights the overall potential usefulness of fuzzy set theory in addressing uncertainty in safety and reliability engineering.

Dynamical systems on weighted lattices: general theory

In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces which we call complete weighted lattices and include as special cases the nonlinear vector spaces of minimax algebra. Their algebraic structure has a polygonal geometry. Some of the special cases unified include max-plus, max-product, and probabilistic dynamical systems. We study problems of representation in state and input-output spaces using lattice monotone operators, state and output responses using nonlinear convolutions, solving nonlinear matrix equations using lattice adjunctions, stability and controllability. We outline applications in state-space modeling of nonlinear filtering; dynamic programming (Viterbi algorithm) and shortest paths (distance maps); fuzzy Markov chains; and tracking audio-visual salient events in multimodal information streams using generalized hidden Markov models with control inputs.

Technological Optimization of Devices for Safe Storage of Platelet-Containing Transfusion Media

A mathematical model of process optimization based on adaptive fuzzy Markov chain algorithms is presented. The model is shown to be effective in optimizing storage devices for platelet-containing transfusion media. The problem of maintaining the technological process state near the extremum of the objective function with the steady state-probability of ~90 % is solved.

Indistinguishability Operators Applied to Task Allocation Problems in Multi-Agent Systems

In this paper we show an application of indistinguishability operators to model response functions. Such functions are used in the mathematical modeling of the task allocation problem in multi-agent systems when the stimulus, perceived by the agent, to perform a task is assessed by means of the response threshold model. In particular, we propose this kind of operators to represent a response function when the stimulus only depends on the distance between the agent and a determined task, since we prove that two celebrated response functions used in the literature can be reproduced by appropriate indistinguishability operators when the stimulus only depends on the distance to each task that must be carried out. Despite the fact there is currently no systematic method to generate response functions, this paper provides, for the first time, a theoretical foundation to generate them and study their properties. To validate the theoretical results, the aforementioned indistinguishability operators have been used to simulate, with MATLAB, the allocation of a set of tasks in a multi-robot system with fuzzy Markov chains.

Toward a Possibilistic Swarm Multi-robot Task Allocation: Theoretical and Experimental Results

Selecting the best task to execute (task allocation problem) is one of the main problems in multi-robot systems. Typical ways to address this problem are based on swarm intelligence and very especially using the so-called response threshold method. In the aforementioned method a robot has a certain probability of executing a task which depends on a task threshold response and a task stimulus. Nevertheless, response threshold method cannot be extended in a natural way to allocate more than two tasks when the theoretical basis is provided by probability theory. Motivated by this fact, this paper leaves the probabilistic approach to the problem and provides a first theoretical framework towards a possibilistic approach. Thus, task allocation problem is addressed using fuzzy Markov chains instead of probabilistic processes. This paper demonstrates that fuzzy Markov chains associated to a task allocation problem can converge to a stationary stage in a finite number of steps. In contrast, the probabilistic processes only can converge asymptotically, i.e. the number of steps is not bounded in general. Moreover, fuzzy Markov chains predicts in a better way the future behavior of the system in the presence of vagueness when measuring distances. The simulations performed confirm the theoretical results and show how the number of steps needed to get a stable state with fuzzy Markov chains is reduced more than 10 times and the system's behavior prediction can be improved more than a 60% compared to probabilistic approaches.

Intermittent demand forecasting with fuzzy markov chain and multi aggregation prediction algorithm

Intermittent demand forecasting with fuzzy markov chain and multi aggregation prediction algorithm

On The Ergodic Behaviour of Fuzzy Markov Chains

On The Ergodic Behaviour of Fuzzy Markov Chains

Sufficient conditions for the ergodicity of fuzzy Markov chains

Analogous to the traditional Markov chains which have been studied extensively and have many successful applications, fuzzy Markov chains have been proposed for decision-making in an environment of uncertainty and imprecision for decades. It is known that results of fuzzy Markov chains depend on the transition matrix as well as the algebraic composition involved. In their study of max–min fuzzy Markov chains, Avrachenkov and Sanchez raised an open question for finding conditions to ensure the ergodicity of max–min fuzzy Markov chains. In this paper, we provide sufficient conditions for the ergodicity of both max–min and max-product fuzzy Markov chains. It is not surprising that such sufficient conditions are very different because of the max–min and max-product compositions.

FuzzyStatProb: AnRPackage for the Estimation of Fuzzy Stationary Probabilities from a Sequence of Observations of an Unknown Markov Chain

Markov chains are well-established probabilistic models of a wide variety of real systems that evolve along time. Countless examples of applications of Markov chains that successfully capture the probabilistic nature of real problems include areas as diverse as biology, medicine, social science, and engineering. One interesting feature which characterizes certain kinds of Markov chains is their stationary distribution, which stands for the global fraction of time the system spends in each state. The computation of the stationary distribution requires precise knowledge of the transition probabilities. When the only information available is a sequence of observations drawn from the system, such probabilities have to be estimated. Here we review an existing method to estimate fuzzy transition probabilities from observations and, with them, obtain the fuzzy stationary distribution of the resulting fuzzy Markov chain. The method also works when the user directly provides fuzzy transition probabilities. We provide an implementation in the R environment that is the first available to the community and serves as a proof of concept. We demonstrate the usefulness of our proposal with computational experiments on a toy problem, namely a time-homogeneous Markov chain that guides the randomized movement of an autonomous robot that patrols a small area.

Departures from the formal of actual students' university careers: an application of non-homogeneous fuzzy Markov chains

As in most higher education (HE) systems, the Italian university organisation draws paths of credit progression in formal curricula, which aim at framing the acquisition of knowledge and competencies within each specific major. The resulting yearly syllabi therefore develop in a sequence of examinations that are to be successfully passed, and formal administrative registration allows access to the following academic year. In general, there is a divergence between formal and actual career progression because each university student can proceed at her/his own pace, sketching her/his own trajectories, free to depart from the formal progression. Even if applied to various HE settings, Markov chain models do not fit the aforementioned situation. A methodological extension has been introduced, whereby progression levels are considered as fuzzy states. Markov chains with fuzzy states identify the latter with specified academic years and express each student's situation as a relational link to present and past academic attainments. This link is operationalised by means of a membership function, which is here discussed with reference to the Italian HE system.