Generalized Interval Probability Research Articles

Wireless Sensor Data Fusion Techniques in Estimating Temporal Resource Attributes in Scenarios of Intermittent Connectivity

In data fusion process the fusion centre which lies intermediate distance aggregates the data and forwards to the sink. In scenario of data aggregation at fusion centre an imbalance may occur due to the potential forwarding process of other fusion centres or other sensor nodes to sink. Hence, this back log of time results in forwarding large chunks of data resulting in link imbalance where the associated classical time interval of reporting varies. The problem balancing and coordinating among fusion centres has been achieved in this work using Data Fusion using Generalized Interval Probability Protocol (DFGIPP). DFGIPP is developed considered the duality principle with proper and improper intervals of reporting to provide coherence among the links. Thus allocating and de-allocating links with the quality of fusion metrics in cooperation between fusion centre and sensor nodes within the terrain is being achieved. The simulation using discrete event network simulator-2 provides better fusion capability under data transfer rates and simulation scenarios.

Novel supplier grading approach based on interval probability hesitant fuzzy linguistic TOPSIS

The supplier grading, a typical multi-attribute linguistic group decision-making (MALGDM) problem, is one of the important research topic in the uncertain linguistic environment, especially its aggregation of evaluation information and the establishment of grading approaches. In this paper, first we introduce the generalized interval probability hesitant fuzzy linguistic IOWA weighted average (GVIOWAWA) operator to aggregate the uncertain linguistic information with incomplete reliability. The GVIOWAWA operator can allow decision makers to select the appropriate parameters according to their needs. Then the interval probability hesitant fuzzy linguistic TOPSIS (IPHFL-TOPSIS) based on the interval probability hesitant fuzzy linguistic Euclidean distance is established. The IPHFL-TOPSIS model can effectively and objectively help businesses find the strategic cooperation supplier. Eventually, we give the numerical examples concerning the comprehensive assessment of material supplier and energy supplier to illustrate validity and applicability of the proposed approach and compare the proposed method with different parameters and methods to perform its flexibility.

A Hybrid Generalized Hidden Markov Model-Based Condition Monitoring Approach for Rolling Bearings.

The operating condition of rolling bearings affects productivity and quality in the rotating machine process. Developing an effective rolling bearing condition monitoring approach is critical to accurately identify the operating condition. In this paper, a hybrid generalized hidden Markov model-based condition monitoring approach for rolling bearings is proposed, where interval valued features are used to efficiently recognize and classify machine states in the machine process. In the proposed method, vibration signals are decomposed into multiple modes with variational mode decomposition (VMD). Parameters of the VMD, in the form of generalized intervals, provide a concise representation for aleatory and epistemic uncertainty and improve the robustness of identification. The multi-scale permutation entropy method is applied to extract state features from the decomposed signals in different operating conditions. Traditional principal component analysis is adopted to reduce feature size and computational cost. With the extracted features’ information, the generalized hidden Markov model, based on generalized interval probability, is used to recognize and classify the fault types and fault severity levels. Finally, the experiment results show that the proposed method is effective at recognizing and classifying the fault types and fault severity levels of rolling bearings. This monitoring method is also efficient enough to quantify the two uncertainty components.

A generalized hidden Markov model and its applications in recognition of cutting states

In the traditional hidden Markov model (HMM) for statistical learning and classification, aleatory uncertainty because of randomness and epistemic uncertainty that is due to the lack of knowledge are not differentiated. In this paper, a generalized hidden Markov model (GHMM) in the context of generalized interval probability theory is proposed. The parameters of GHMM are in the form of generalized interval probability, which provides a concise representation for the two kinds of uncertainty simultaneously. The generalized versions of the forward-backward, Viterbi, and Baum-Welch algorithms in GHMM are developed. The proposed algorithms take advantage of the algebraic property in the generalized interval probability. These algorithms provide an efficient approach to train the GHMM. The trained GHMM is used for state recognition with the criterion of maximum log-likelihood. A case study on recognizing the cutting states in manufacturing processes is provided to demonstrate the application of GHMM. The interval forms of the cutting signal are considered as the inputting of GHMM. The cutting states are recognized based on the learning algorithm of GHMM. With the two uncertainty components quantified, the reliability of GHMM in state recognition is superior to that of HMM.

An Extended Kalman Filtering Mechanism Based on Generalized Interval Probability

Abstract Kalman filter has been widely applied for state identification in controllable systems. As a special case of the hidden Markov model, it is based on the assumption of linear dependency relationships and Gaussian noise. The classical Kalman filter does not differentiate systematic error from random error associated with observations. In this paper, we propose an extended Kalman filtering mechanism based on generalized interval probability, where state and observable variables are random intervals, and interval-valued Gaussian distributions model the noises. The prediction and update procedures in the new mechanism are derived. Two examples are used to illustrate the developed mechanism. It is shown that the method is an efficient alternative to sensitivity analysis for assessing the effect of systematic error.

Stochastic dynamics simulation with generalized interval probability

Two types of uncertainties are generally recognized in modelling and simulation, including variability caused by inherent randomness and incertitude due to the lack of perfect knowledge. In this paper, a generalized interval-probability theory is used to model both uncertainty components simultaneously, where epistemic uncertainty is quantified by generalized interval in addition to probability measure. Conditioning, independence, and Markovian probabilities are uniquely defined in generalized interval probability such that its probabilistic calculus resembles that in the classical probability theory. A path-integral approach can be taken to solve the interval Fokker–Planck equation for diffusion processes. A Krylov subspace projection method is proposed to solve the interval master equation for jump processes. Thus, the time evolution of both uncertainty components can be simulated simultaneously, which provides the lower and upper bound information of evolving probability distributions as an alternative to the traditional sensitivity analysis.

A generalized Markov chain model based on generalized interval probability

In the traditional Markov chain model (MCM), aleatory uncertainty because of inherent randomness and epistemic uncertainty due to the lack of knowledge are not differentiated. Generalized interval probability provides a concise representation for the two kinds of uncertainties simultaneously. In this paper, a generalized Markov chain model (GMCM), based on the generalized interval probability theory, is proposed to improve the reliability of prediction. In the GMCM, aleatory uncertainty is represented as probability; interval is used to capture epistemic uncertainty. A case study for predicting the average dynamic compliance in machining processes is provided to demonstrate the effectiveness of proposed GMCM. The results show that the proposed GMCM has a better prediction performance than that of MCM.

Reliable kinetic Monte Carlo simulation based on random set sampling

Kinetic Monte Carlo (KMC) method has been widely used in simulating rare events such as chemical reactions or phase transitions. Yet lack of complete knowledge of transitions and the associated rates is one major challenge for accurate KMC predictions. In this paper, a reliable KMC (R-KMC) mechanism is proposed in which sampling is based on random sets instead of random numbers to improve the robustness of KMC results. In R-KMC, rates or propensities are interval estimates instead of precise numbers. A multi-event algorithm based on generalized interval probability is developed. The weak convergence of the multi-event algorithm towards the traditional KMC is demonstrated with a generalized Chapman---Kolmogorov equation.

Generalized Fokker–Planck equation with generalized interval probability

The Fokker–Planck equation is widely used to describe the time evolution of stochastic systems in drift-diffusion processes. Yet, it does not differentiate two types of uncertainties: aleatory uncertainty that is inherent randomness and epistemic uncertainty due to lack of perfect knowledge. In this paper, a generalized differential Chapman–Kolmogorov equation based on a new generalized interval probability theory is derived, where epistemic uncertainty is modeled by the generalized interval while the aleatory one is by the probability measure. A generalized Fokker–Planck equation is proposed to describe drift-diffusion processes under both uncertainties. A path integral approach is developed to numerically solve the generalized Fokker–Planck equation. The resulted interval-valued probability density functions rigorously bound the real-valued ones computed from the classical path integral method. The method is demonstrated by numerical examples.

Discrete time Markov chains with interval probabilities

The parameters of Markov chain models are often not known precisely. Instead of ignoring this problem, a better way to cope with it is to incorporate the imprecision into the models. This has become possible with the development of models of imprecise probabilities, such as the interval probability model. In this paper we discuss some modelling approaches which range from simple probability intervals to the general interval probability models and further to the models allowing completely general convex sets of probabilities. The basic idea is that precisely known initial distributions and transition matrices are replaced by imprecise ones, which effectively means that sets of possible candidates are considered. Consequently, sets of possible results are obtained and represented using similar imprecise probability models. We first set up the model and then show how to perform calculations of the distributions corresponding to the consecutive steps of a Markov chain. We present several approaches to such calculations and compare them with respect to the accuracy of the results. Next we consider a generalisation of the concept of regularity and study the convergence of regular imprecise Markov chains. We also give some numerical examples to compare different approaches to calculations of the sets of probabilities.

Generalized basic probability assignments

Dempster–Shafer theory allows to construct belief functions from (precise) basic probability assignments. The present paper extends this idea substantially. By considering sets of basic probability assignments, an appealing constructive approach to general interval probability is achieved, which allows for a very flexible modelling of uncertain knowledge.

Neyman–Pearson testing under interval probability by globally least favorable pairs: Reviewing Huber–Strassen theory and extending it to general interval probability

The paper studies the extension of one of the basic problems of classical statistics to a generalized concept of probability. It is concerned with the generalized Neyman–Pearson problem, i.e. hypothesis testing when both hypotheses are described by interval probability (also called interval-valued probability or lower and upper probability). First the Huber–Strassen theorem and the literature based on it are reviewed. The assumption of two-monotonicity underlying all that work, however, excludes many models of practical interest. Therefore, the second part of the paper goes beyond Huber–Strassen theory. Results not relying on this severe restriction are derived, showing that a neat theory of hypothesis testing can be achieved in the framework of general interval probability.

Expected utility within a generalized concept of probability — a comprehensive framework for decision making under ambiguity

It had often been complained that the standard framework of decision theory is insufficient. In most applications, neither the maximin paradigm (relying on complete ignorance on the states of nature) nor the classical Bayesian paradigm (assuming perfect probabilistic information on the states of nature) reflect the situation under consideration adequately. Typically one possesses some, but incomplete, knowledge on the stochastic behaviour of the states of nature. In this paper first steps towards a comprehensive framework for decision making under such complex uncertainty will be provided. Common expected utility theory will be extended to interval probability, a generalized probabilistic setting which has the power to express incomplete stochastic knowledge and to take the extent of ambiguity (non-stochastic uncertainty) into account. Since two-monotone and totally monotone capacities are special cases of general interval probability, where Choquet integral and interval-valued expectation correspond to one another, the results also show, as a welcome by-product, how to deal efficiently with Choquet Expected Utility and how to perform a neat decision analysis in the case of belief functions.