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Autonomous search is an ongoing cycle of sensing, statistical estimation, and motion control with the objective to find and localise targets in a designated search area. Traditionally, the theoretical framework for autonomous search combines sequential Bayesian estimation with information theoretic motion control. This paper formulates autonomous search in the framework of possibility theory. Although the possibilistic formulation is slightly more involved than the traditional method, it provides a means for quantitative modelling and reasoning in the presence of epistemic uncertainty. This feature is demonstrated in the paper in the context of partially known probability of detection, expressed as an interval value. The paper presents an elegant Bayes-like solution to sequential estimation, with the reward function for motion control defined to take into account the epistemic uncertainty. The advantages of the proposed search algorithm are demonstrated by numerical simulations.

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As important geospatial data, point cloud collected from an aerial laser scanner (ALS) provides three-dimensional (3D) information for the study of the distribution of typical urban land cover, which is critical in the construction of a "digital city". However, existing point cloud classification methods usually use a single machine learning classifier that experiences uncertainty in making decisions for fuzzy samples in confusing areas. This limits the improvement of classification accuracy. To take full advantage of different classifiers and reduce uncertainty, we propose a classification method based on possibility theory and multi-classifier fusion. Firstly, the feature importance measure was performed by the XGBoost algorithm to construct a feature space, and two commonly used support vector machines (SVMs) were the chosen base classifiers. Then, classification results from the two base classifiers were quantitatively evaluated to define the confusing areas in classification. Finally, the confidence degree of each classifier for different categories was calculated by the confusion matrix and normalized to obtain the weights. Then, we synthesize different classifiers based on possibility theory to achieve more accurate classification in the confusion areas. DALES datasets were utilized to assess the proposed method. The results reveal that the proposed method can significantly improve classification accuracy in confusing areas.

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This study proposes an evaluation method for the structural safety of expressway tunnels utilizing possibility and prospect theories to address the influence of multiple indicators on the structural safety of expressway tunnels and the imprecision of human-bounded rationality in assessing results. It constructs the probability distribution of safety level by determining the safety level of the highway tunnel structure. The reference distribution function of each monitoring index is then derived using the expected value of experts. Based on the possibility theory, the possibility distribution of the monitoring results of indicators is obtained, and the mapping relationship between the monitoring indicators and the possibility distribution function of safety status grade is developed. Finally, the prospect theory evaluates the highway tunnel structure's safety status. This method is applied to assess the structural safety of a highway tunnel, which verifies its effectiveness and practicability, and provides a new method for evaluating the structural safety of a highway tunnel.

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In intelligent technical multi-sensor systems, information is often at least partly redundant-either by design or inherently due to the dynamic processes of the observed system. If sensors are known to be redundant, (i) information processing can be engineered to be more robust against sensor failures, (ii) failures themselves can be detected more easily, and (iii) computational costs can be reduced. This contribution proposes a metric which quantifies the degree of redundancy between sensors. It is set within the possibility theory. Information coming from sensors in technical and cyber-physical systems are often imprecise, incomplete, biased, or affected by noise. Relations between information of sensors are often only spurious. In short, sensors are not fully reliable. The proposed metric adopts the ability of possibility theory to model incompleteness and imprecision exceptionally well. The focus is on avoiding the detection of spurious redundancy. This article defines redundancy in the context of possibilistic information, specifies requirements towards a redundancy metric, details the information processing, and evaluates the metric qualitatively on information coming from three technical datasets.

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Uncertainty is at the heart of decision-making processes in most real-world applications. Uncertainty can be broadly categorized into two types: aleatory and epistemic. Aleatory uncertainty describes the variability in the physical system where sensors provide information (hard) of a probabilistic type. Epistemic uncertainty appears when the information is incomplete or vague such as judgments or human expert appreciations in linguistic form. Linguistic information (soft) typically introduces a possibilistic type of uncertainty. This paper is concerned with the problem of classification where the available information, concerning the observed features, may be of a probabilistic nature for some features, and of a possibilistic nature for some others. In this configuration, most encountered studies transform one of the two information types into the other form, and then apply either classical Bayesian-based or possibilistic-based decision-making criteria. In this paper, a new hybrid decision-making scheme is proposed for classification when hard and soft information sources are present. A new Possibilistic Maximum Likelihood (PML) criterion is introduced to improve classification rates compared to a classical approach using only information from hard sources. The proposed PML allows to jointly exploit both probabilistic and possibilistic sources within the same probabilistic decision-making framework, without imposing to convert the possibilistic sources into probabilistic ones, and vice versa.

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In previous studies, there were few portfolio models involving investors' psychological states, market ambiguity and entropy. Some entropy can make the model have the effect of diversifying investment, which is very important. This paper mainly studies four kinds of entropy. First, we obtained four definitions of entropy from the literature, and gave the function of fuzzy entropy in different psychological states through strict mathematical proof. Then, we construct a fuzzy portfolio entropy decision model based on the investor's psychological states, and compared it with the possibilistic mean-variance model. Then we presented a numerical example and compared the five different models established. By comparing the results, we find that: (a) The possibilistic mean-Shannon entropy model solves the problem of the possibility of excessive concentration in the possibilistic mean-variance model, but the dispersion is not enough. Conversely, the possibilistic mean-Yager entropy is over-emphasized due to the definition of its own function, such that it gave an investment pattern of equal weight distribution or approximate average distribution. (b) The results of possibilistic mean-proportional entropy can be said to be the middle status of the portfolios of possibilistic mean-Shannon entropy and possibilistic mean-Yager entropy. This portfolio not only achieves a certain rate of return, but also disperses the risk to some extent. (c) The lines of satisfaction for portfolios derived from different models are approximately U-shaped with the increase in return preference. (d) The possibilistic mean-Shannon entropy model tends to have the highest portfolio satisfaction with the same psychological state of the investor.

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We report a method for counting uncertain data, i.e. observations that cannot be precisely associated to referents. We model data uncertainty through Possibility Theory and we develop the counting method so as to take into account the possibility distributions attached to data. The result is a fuzzy interval on the domain of natural numbers, which can be obtained by two variants of the method: exact counting provides the true fuzzy interval in quadratic time complexity, while approximate counting carries out an estimate of the fuzzy interval in linear time. We give a step-by-step description of the method so that it can be replicated in any programming environment. We also provide a Python implementation and a use case in Bioinformatics. The method usage is the following: •The uncertain data are represented in form of matrix, one row for each observation. Each row is a possibility distribution;•The method variant must be selected. In the case of the approximate variant, the number of α-values of the resulting fuzzy interval must be provided;•For each referent, a fuzzy interval is determined and carried out by the method.

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Sensors, and also actuators or external sources such as databases, serve as data sources in order to realise condition monitoring of industrial applications or the acquisition of characteristic parameters like production speed or reject rate. Modern facilities create such a large amount of complex data that a machine operator is unable to comprehend and process the information contained in the data. Thus, information fusion mechanisms gain increasing importance. Besides the management of large amounts of data, further challenges towards the fusion algorithms arise from epistemic uncertainties (incomplete knowledge) in the input signals as well as conflicts between them. These aspects must be considered during information processing to obtain reliable results, which are in accordance with the real world. The analysis of the scientific state of the art shows that current solutions fulfil said requirements at most only partly. This article proposes the multilayered information fusion system MACRO (multilayer attribute-based conflict-reducing observation) employing the µBalTLCS (fuzzified balanced two-layer conflict solving) fusion algorithm to reduce the impact of conflicts on the fusion result. The performance of the contribution is shown by its evaluation in the scope of a machine condition monitoring application under laboratory conditions. Here, the MACRO system yields the best results compared to state-of-the-art fusion mechanisms. The utilised data is published and freely accessible.

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An important issue faced by risk analysts is how to deal with uncertainties associated with accident scenarios. In industry, one often uses single values derived from historical data or literature to estimate events probability or their frequency. However, both dynamic environments of systems and the need to consider rare component failures may make unrealistic this kind of data. In this paper, uncertainty encountered in Layers Of Protection Analysis (LOPA) is considered in the framework of possibility theory. Data provided by reliability databases and/or experts judgments are represented by fuzzy quantities (possibilities). The fuzzy outcome frequency is calculated by extended multiplication using α-cuts method. The fuzzy outcome is compared to a scenario risk tolerance criteria and the required reduction is obtained by resolving a possibilistic decision-making problem under necessity constraint. In order to validate the proposed model, a case study concerning the protection layers of an operational heater is carried out.

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This study proposes a new condition diagnosis method for rotating machinery developed using least squares mapping (LSM) and a fuzzy neural network. The non-dimensional symptom parameters (NSPs) in the time domain are defined to reflect the features of the vibration signals measured in each state. A sensitive evaluation method for selecting good symptom parameters using detection index (DI) is also proposed for detecting and distinguishing faults in rotating machinery. In order to raise the diagnosis sensitivity of the symptom parameters the synthetic symptom parameters (SSPs) are obtained by LSM. Moreover, possibility theory and the Dempster & Shafer theory (DST) are used to process the ambiguous relationship between symptoms and fault types. Finally, a sequential diagnosis method, using sequential inference and a fuzzy neural network realized by the partially-linearized neural network (PLNN), is also proposed, by which the conditions of rotating machinery can be identified sequentially. Practical examples of fault diagnosis for a roller bearing are shown to verify that the method is effective.

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