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The data envelopment analysis (DEA) models have been widely recognized and applied in various fields. However, these models have limitations, such as their inability to globally rank DMUs, the efficiency values are definite numerical values, they are unable to reflect potential efficiency changes, and they fail to adequately reflect the degree of the decision maker's preference. In order to address these shortcomings, this paper combines possibility theory with self-interest and non-self-interest principles to improve the DEA model to provide a more detailed reflection of the differences between DMUs. First, the self-interest and non-self-interest principles are employed to establish the DEA evaluation model, and the determined numerical efficiency is transformed into efficiency intervals. Second, an attitude function is added to the common possible-degree formula to reflect the decision maker's preference, and a more reasonable method for solving the attitude function is presented. Finally, the improved possible-degree formula proposed in this paper is used to rank and compare the interval efficiencies. This improved method not only provides more comprehensive ranking information but also better captures the decision maker's preferences. This model takes preference issues into account and has improved stability and accuracy compared with existing models. The application of the improved model in airlines shows that the model proposed in this paper effectively achieved a full ranking. From a developmental perspective, the efficiency levels of Chinese airlines were generally comparable. Joyair and One Two Three performed poorly, exhibiting significant gaps compared with other airlines. [ABSTRACT FROM AUTHOR]

This paper presents a method for estimating reservoir storage capacity using the Gould–Dincer normal formula (G-DN), enhanced by the possibility theory. The G-DN equation is valuable for regional studies of reservoir reliability, particularly under climate change scenarios, using regional statistics. However, because the G-DN formula deals with measured data, it introduces a degree of uncertainty and fuzziness that traditional probability theory struggles to address. Possibility theory, an extension of fuzzy set theory, offers a suitable framework for managing this uncertainty and fuzziness. In this study, the G-DN formula is adapted to incorporate fuzzy logic, and the possibilistic nature of reservoir capacity is translated into a probabilistic framework using α-cuts from the possibility theory. These α-cuts approximate probability confidence intervals with high confidence. Applying the proposed methodology, in the present crisp case with the storage capacity D = 0.75, the value of the capacity C was found to be 1271 × 10 6   m 3 , and that for D = 0.5 was 634.5 × 10 6   m 3 . On the other hand, in the fuzzy case using the possibility theory, the value of the capacity for D = 0.75 is the internal [ 315 , 5679 ] × 10 6   m 3 and for D = 0.5 the value is interval [ 158 , 2839 ] × 10 6   m 3 , with a probability of ≥95% and a risk level of α = 5% for both cases. The proposed approach could be used as a robust tool in the toolkit of engineers working on irrigation, drainage, and water resource projects, supporting informed and effective engineering decisions. [ABSTRACT FROM AUTHOR]

The possibilistic mean–variance (MV) model is the counterpart of Markowitz’s MV model in the possibility theory. This study aims to examine the possibilistic MV model when the possibility distributions of stock returns are uncertain triangular fuzzy numbers. We define an uncertainty vector and use its ellipsoidal uncertainty set in a minimax optimization problem to model this uncertainty. We also show that this minimax optimization problem reduces to a strictly convex minimization problem. Thus, unlike the possibilistic MV model, we get diversified optimal portfolios uniquely with our approach. After laying down the theoretical points of our approach, we illustrate it with a real-world example in the literature by using a software package for convex optimization. To the best of our knowledge, this is the first paper that considers uncertain possibility distributions in the possibilistic MV model.

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. [ABSTRACT FROM AUTHOR]

In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called scenarios, is specified. This possibility distribution induces a necessity measure in a scenario set, which in turn describes an ambiguity set of probability distributions in a scenario set. The distributionally robust approach is then used to convert the imprecise constraints into deterministic equivalents. Namely, the left-hand side of an imprecise constraint is evaluated by using a risk measure with respect to the worst probability distribution that can occur. In this paper, the Conditional Value at Risk is used as the risk measure, which generalizes the strict robust, and expected value approaches commonly used in literature. A general framework for solving such a class of problems is described. Some cases which can be solved in polynomial time are identified. [ABSTRACT FROM AUTHOR]

WordNet-like Lexical Databases (WLDs) group English words into sets of synonyms called “synsets.” Synsets are utilized for several applications in the field of text mining. However, they were also open to criticism because although, in theory, not all the members (i.e. word senses) of a synset represent the meaning of that synset with the same degree, in practice, in WLDs they are considered as members of the synset identically. Correspondingly, the fuzzy version of synonym sets, called fuzzy-synsets were proposed. But, to the best or our knowledge. In this study, we present an algorithm for constructing fuzzy version of WLDs of any language, given a corpus of documents and a word-sense-disambiguation system of that language. A theoretical proof is also proposed for the validity of results of the proposed algorithm. Then, inputting the open-American-online-corpus (OANC) and UKB word-sense-disambiguation to the algorithm, we construct and publish online the fuzzified version English WordNet (FWN), and apply them in a Sentiment Analysis problem.

One of the main problems to be addressed in a multi-robot system is the selection of the best robot, or group of them, to carry out a specific task. Among the large number of solutions provided to allocate tasks to a group of robots, this work focuses on swarm-like approaches, and more specifically on response-threshold algorithms, where each robot selects the next task to perform by following a Markov process. To the best of our knowledge, the current response-threshold algorithms do not provide any formal method to generate new transition functions between tasks. Thus, this paper provides, for the first time, a mathematical model, as based on the so-called fuzzy preorders, for the allocation of tasks to a collective of robots with communication capabilities. In our previous work, we proved that transitions in the aforementioned process can be modeled as fuzzy preorders, constructed through the aggregation of asymmetric distances, in such a way that each robot makes its decision without taking into account the decisions of its teammates. Now, we extend this model in such a way that each robot will take into account the number of robots previously allocated for each task. To implement this method, a very simple communication mechanism has been considered. Several simulations have been carried out in order to validate our approach. The results confirm that fuzzy preorders are able to model the evolution of the system when this type of communication is considered and show when and how the communication process improves the system's performance. Experimental results show the existence of a set of good values for the maximum communication distance between robots and that these values depend on the distribution of the tasks in the environment. Thus, in some cases, a better communication mechanism does not imply better results.

One of the main problems to be addressed in a multi-robot system is the selection of the best robot, or group of them, to carry out a specific task. Among the large number of solutions provided to allocate tasks to a group of robots, this work focuses on swarm-like approaches, and more specifically on response-threshold algorithms, where each robot selects the next task to perform by following a Markov process. To the best of our knowledge, the current response-threshold algorithms do not provide any formal method to generate new transition functions between tasks. Thus, this paper provides, for the first time, a mathematical model, as based on the so-called fuzzy preorders, for the allocation of tasks to a collective of robots with communication capabilities. In our previous work, we proved that transitions in the aforementioned process can be modeled as fuzzy preorders, constructed through the aggregation of asymmetric distances, in such a way that each robot makes its decision without taking into account the decisions of its teammates. Now, we extend this model in such a way that each robot will take into account the number of robots previously allocated for each task. To implement this method, a very simple communication mechanism has been considered. Several simulations have been carried out in order to validate our approach. The results confirm that fuzzy preorders are able to model the evolution of the system when this type of communication is considered and show when and how the communication process improves the system's performance. Experimental results show the existence of a set of good values for the maximum communication distance between robots and that these values depend on the distribution of the tasks in the environment. Thus, in some cases, a better communication mechanism does not imply better results. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Data Acquisition & Processing / Shu Ju Cai Ji Yu Chu Li is the property of Editorial Department of Journal of Nanjing University of Aeronautics & Astronautics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents a method for estimating reservoir storage capacity using the Gould–Dincer normal formula (G-DN), enhanced by the possibility theory. The G-DN equation is valuable for regional studies of reservoir reliability, particularly under climate change scenarios, using regional statistics. However, because the G-DN formula deals with measured data, it introduces a degree of uncertainty and fuzziness that traditional probability theory struggles to address. Possibility theory, an extension of fuzzy set theory, offers a suitable framework for managing this uncertainty and fuzziness. In this study, the G-DN formula is adapted to incorporate fuzzy logic, and the possibilistic nature of reservoir capacity is translated into a probabilistic framework using α-cuts from the possibility theory. These α-cuts approximate probability confidence intervals with high confidence. Applying the proposed methodology, in the present crisp case with the storage capacity D = 0.75, the value of the capacity C was found to be 1271×106 m3, and that for D = 0.5 was 634.5×106 m3. On the other hand, in the fuzzy case using the possibility theory, the value of the capacity for D = 0.75 is the internal [315,5679]×106 m3 and for D = 0.5 the value is interval [158,2839]×106 m3, with a probability of ≥95% and a risk level of α = 5% for both cases. The proposed approach could be used as a robust tool in the toolkit of engineers working on irrigation, drainage, and water resource projects, supporting informed and effective engineering decisions.

In this paper, we investigated the evolution of prioritized E L ontologies in the presence of new information that can be certain or uncertain. We propose an extension of E L description logic, named E L ⊥ + , within possibility theory to encode such knowledge. This extension provides a natural way to deal with the ordinal scale and represent knowledge in a way that can handle incomplete information and conflicting data. We provided a polynomial algorithm for computing the possibilistic entailment. Then, we defined the evolution process at the semantic and syntactic levels. Interestingly enough, we show that the syntactical algorithm is done in polynomial time. [ABSTRACT FROM AUTHOR]

Possibility theory is the one of the most important and widely used uncertainty theories because it is closely related to the imprecise probability and expert knowledge. The possibilistic mean - variance (MV) model is the counterpart of the Markowitz’s MV model in the possibility theory. There are variants of the possibilistic MV model, which are called as the upper and lower possibilistic MV models. However, to the best of our knowledge, analytical solutions and exact efficient frontiers of these variants are not presented in the literature when the possibil-ity distributions are given with trapezoidal fuzzy numbers. In this study, under this assumption, we make mathemat-ical analyses of the upper and lower possibilistic MV models and derive their analytical solutions and exact efficient frontiers. Based on the max-min optimization framework, we also propose their extensions where there are multiple upper (lower) possibilistic mean scenarios. We show that the proposed extensions have the ease of use as the upper and lower possibilistic MV models. We also illustrate and compare the upper and lower possibilistic mean - variance models and their proposed extensions with an explanatory example. As we expect, we see that these extensions can be effectively used in portfolio selection by conservative investors.

Nowadays renewable energy sources, such as wind and solar, whether independently or integrated with other resources, are considered in power system, specifically self-scheduling, bidding and offering strategy problems. However, the uncertain nature of these sources has turned out the greatest challenge for their owners, which makes the bidding and offering in the restructured electricity market more complicated because wind energy generation may cause penalty fees for its generation mismatches. Hence, the primary objective of this paper is to suggest a novel bidding strategy framework based on fuzzy random variable for a wind-thermal system in the electricity market for the first time. The uncertainties associated with day ahead energy, spinning reserve market prices and imbalance prices, are characterized by random fuzzy variables and the uncertainties associated with wind power outputs are modeled as a LR fuzzy numbers. The proposed self-scheduling model maximizes the expected profits while it controls the risk by providing different possibility and probability levels for decision makers.A mathematical modeling approach is applied in this research by using a mixed-integer non-linear programming model which is implemented in Lingo software in a case study of thermal generation unit to investigate the efficiency of the proposed model. A sensitivity analysis is applied to validate the performance of the proposed model. Numerical results reveal that taking advantage of wind power generation alongside with thermal generation will substantially increase the profitability of the integrated generation company.

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. [ABSTRACT FROM AUTHOR]

Building a sophisticated forecasting framework for solar and photovoltaic power production in geographic zones with severe meteorological conditions is very challenging. This difficulty is linked to the high variability of the global solar radiation on which the energy production depends. A suitable forecasting framework might take into account this high variability and could be able to adjust/re-adjust model parameters to reduce sensitivity to estimation errors. The framework should also be able to re-adapt the model parameters whenever the atmospheric conditions change drastically or suddenly—this changes according to microscopic variations. This work presents a new methodology to analyze carefully the meaningful features of global solar radiation variability and extract some relevant information about the probabilistic laws which governs its dynamic evolution. The work establishes a framework able to identify the macroscopic variations from the solar irradiance. The different categories of variability correspond to different levels of meteorological conditions and events and can occur in different time intervals. Thereafter, the tool will be able to extract the abrupt changes, corresponding to microscopic variations, inside each level of variability. The methodology is based on a combination of probability and possibility theory. An unsupervised clustering technique based on a Gaussian mixture model is proposed to identify, first, the categories of variability and, using a hidden Markov model, we study the temporal dependency of the process to identify the dynamic evolution of the solar irradiance as different temporal states. Finally, by means of some transformations of probabilities to possibilities, we identify the abrupt changes in the solar radiation. The study is performed in Guadeloupe, where we have a long record of global solar radiation data recorded at 1 Hertz.

Multi-objective optimization can be used to address possible conflicting relationships between multiple objectives. However, some objectives have a fuzzy temporal relationship between them, making it difficult to give a common method to portray the fuzzy temporal relationship. To fill this gap, we propose the concept of complex objectives, which can be described by fuzzy temporal logic that includes both temporal and logical operators. Furthermore, we investigated the optimal control problems of complex objectives and developed a fuzzy system called possibilistic decision systems (PDSs) to establish a framework for optimal control. In PDSs, states of fuzzy systems are determined by a family of variables, and transitions induced by actions between fuzzy states of systems are also fuzzy uncertain and determined by a possibility degree. Importantly, we proved that memoryless strategies are sufficient for optimal control of complex objectives. Finally, the theory presented in this paper is illustrated by a mobile robot simulation. [ABSTRACT FROM AUTHOR]

The literature approaches, devoted to sensor improve network coverage, are deterministic in terms of deployment environment and node configuration parameters. Nevertheless, this type of approaches has not proven to be very successful in uncertain deployment environments. This paper aims to deal with this issue using theories of uncertainty. We consider deployment environment's imperfections and the characteristics of the sensor nodes. The selection of a minimum number of nodes for a minimum number of clusters to guarantee coverage in wireless sensor networks (WSNs) is uncertain. As a consequence, this paper proposes a hybrid Fuzzy-Possibilistic model to Schedule the Active/Passive State of Sensor nodes Strategy (FP-3SNS). This model helps to plan the scheduling of node states (Active/Passive) based on possibilistic information fusion to make a possibilistic decision for the node activation at each period. We evaluated our model (FP-3SNS) with (a) a running example (that shows the best choice of the active node with a probability of 0.81215); (b) a statistical evaluation (calculation of the confidence interface), where the average coverage reliability at 95% of FP-3SNS use is between (92.94, 96.27); and (c) a comparison with maximum sensing coverage region problem (MSCR), coverage maximization with sleep scheduling (CMSS), Spider Canvas Strategy, Semi-Random Deployment Strategy (SRDP), Probing Environment and Adaptive Sleeping with Location Information Protocol (PEAS-LI), and Variable Length Particle Swarm Optimization Algorithm with a Weighted Sum Fitness Function (WS-VLPSO). The simulation results highlight the benefits of using the fuzzy and possibility theories for treating the area coverage problem and the proposed model maintained a coverage between 99.99 and 90.00% for a significant period of time. [ABSTRACT FROM AUTHOR]

WordNet-like Lexical Databases (WLDs) group English words into sets of synonyms called “synsets.” Synsets are utilized for several applications in the field of text mining. However, they were also open to criticism because although, in theory, not all the members (i.e. word senses) of a synset represent the meaning of that synset with the same degree, in practice, in WLDs they are considered as members of the synset identically. Correspondingly, the fuzzy version of synonym sets, called fuzzy-synsets were proposed. But, to the best or our knowledge. In this study, we present an algorithm for constructing fuzzy version of WLDs of any language, given a corpus of documents and a word-sense-disambiguation system of that language. A theoretical proof is also proposed for the validity of results of the proposed algorithm. Then, inputting the open-American-online-corpus (OANC) and UKB word-sense-disambiguation to the algorithm, we construct and publish online the fuzzified version English WordNet (FWN), and apply them in a Sentiment Analysis problem. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Economy Business & Management is the property of Journal of Economy, Business & Management and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Edgar Codd introduced the principle of entity integrity in the context of his relational model of data. The principle says that every targeted real-world entity should be uniquely represented in the database. In actual database systems, entity integrity is typically enforced by primary keys. We introduce a framework toward generalizing entity integrity to different dimensions of data, including volume, variety, and veracity. We establish axiomatic and algorithmic foundations for the implication problem of the combined class of uniqueness constraints, functional dependencies, and multivalued dependencies in all combinations of the dimensions we consider. These are based on specific approaches to the semantics of these integrity constraints and to the dimensions of data. We also highlight how our concepts lead to new opportunities for diverse and important areas of applications, such as query optimization, database design and security, and data quality. Overall, this sets out an agenda for future research that extends our approaches or applies different approaches in this area, as driven by application requirements. [ABSTRACT FROM AUTHOR]

It is easy to use possibility theory in modeling incomplete information. Robust optimization is an important tool when there is parameter uncertainty. Thus, in this study, we propose robust versions of the lower and upper possibilistic mean - variance (MV) models when there are multiple possibility distribution scenarios. Here, we use entropy as a diversification constraint. In addition, we reduce these robust versions to concave maximization problems. Furthermore, we generalize them for two periods portfolio selection problem by using fuzzy addition and multiplication. On the other hand, these generalizations are not concave maximization problems. Finally, we give an illustrative example by using different solvers in Gams modeling system. [ABSTRACT FROM AUTHOR]

Modern concepts in concrete engineering – about the application of artificial intelligence methods The application of artificial intelligence methods provides manifold and promising capabilities to develop innovative concepts in science and practice. Selected methods and modern concepts from the field of concrete construction are presented to outline achievable possibilities. Adaptive prestressed concrete structures were realized using Fuzzy Logic‐based self‐tuning closed‐loop control algorithms. A monitoring concept for continuous structural health monitoring of bridges was elaborated that comprises a model adaptation through evolutionary algorithms and artificial neural networks for reliability validations. For an efficient support of preliminary building design, a knowledge‐based system has been developed that enables the formalization and provision of engineering knowledge through crisp and fuzzy knowledge bases and possibility theory. These modern concepts in concrete construction underline substantial potentials that are achievable through the application of artificial intelligence methods. [ABSTRACT FROM AUTHOR]

Low quality of data is one of the most critical issues for consumers of data distributed by autonomous sources. The outcomes of non-quality of data, or of poor quality, on decision-making are considerable and have disastrous effects. In this paper, we deal with this problem in the context of biometric applications, specifically those based on the iris modality. In fact, the iris image can be affected by different types of distortion which greatly affect its quality and generate different imperfection forms. Thus, the deterioration of the quality of these images increases the false rejection rate and therefore decreases significantly the performances of iris identification systems. In order to reduce the impact of bad quality of iris image, we add an Image Quality Assessment (IQA) phase to the identification system to reject poor quality images and thus improves system performances. In this paper, a new method based on the possibilistic modeling of imperfect information extracted from the iris images is proposed to assess the iris image quality. The aim of the proposed approach, noted Poss-IIQA, is to handles the different imperfection forms resulting from any type of distortions. As a result, the suggested method key advantage over the baseline system and other earlier approaches, which focuses more on distortions than on imperfections. [ABSTRACT FROM AUTHOR]

By considering the stock market's fuzzy uncertainty and investors' psychological factors, this paper studies the portfolio performance evaluation problems with different risk attitudes (optimistic, pessimistic, and neutral) by the Data Envelopment Analysis (DEA) approach. In this work, the return rates of assets are characterized as trapezoidal fuzzy numbers, whose membership functions with risk attitude parameters are described by exponential expression. Firstly, these characteristics with risk attitude are strictly derived including the possibilistic mean, variance, semi-variance, and semi-absolute deviation based on possibility theory. Secondly, three portfolio models (mean-variance, mean-semi-variance, and mean-semi-absolute-deviation) with different risk attitudes are proposed. Thirdly, we prove the real frontiers determined by our models are concave functions through mathematical theoretical derivation. In addition, two novel indicators are defined by difference and ratio formulas to characterize the correlation between DEA efficiency and portfolio efficiency. Finally, numerical examples are given to verify the feasibility and effectiveness of our model. No matter what risk attitude an investor holds, the DEA can generate approximate real frontiers. Correlation analysis indicates that our proposed approach outperforms in evaluating portfolios with risk attitudes. At the same time, our model is an improvement of Tsaur's work (2013) which did not study the different risk measures, and an extension of Chen et al.'s work (2018) which only considered risk-neutral attitude. [ABSTRACT FROM AUTHOR]

A new multi-attribute group decision-making ("MAGDM") method is presented to evaluate, on the basis of conflicting attributes (environmental, economic, and technical), the alternatives in a renewable energy technology (RET) selection problem in an uncertain environment. Trapezoidal intuitionistic fuzzy linguistic numbers (TrIFLNs) are used to treat the uncertainty, and the attribute weights are not known. To evaluate the weights, possibility theory and the Shannon entropy are used. Possibility theory covers the maximum ambiguity of the data, while the Shannon entropy preserves the weighting properties. An improved aggregation operator using Einstein's operation laws, called the trapezoidal intuitionistic fuzzy linguistic Einstein's interactive weighted average (TrIFLEIWA) operator, is developed to aggregate the decision experts' assessments. The TrIFLEIWA operator overcomes some of the drawbacks previously identified in the existing aggregation operators, and reduces information loss. Furthermore, the VIKOR ("VlseKriterijumska Optimizacija I Kompromisno Resenje") method is advanced for the MAGDM problem in the intuitionistic fuzzy linguistic environment based on TrIFLNs. The VIKOR method emphasizes prioritizing and selecting alternatives from the available options, maintaining maximum utility from the majority and lowest personal regret from the opponent. TrIFLNs provide accessibility to represent the data in a proper and informative manner. Thus, integrating the VIKOR approach and TrIFLNs provides good results with the flexibility to use in other uncertain environments. A real-world problem of RET selection is included to present numerical insights. The effectiveness of the proposed methodology is demonstrated by comparing it with different MAGDM methods. [ABSTRACT FROM AUTHOR]

Building a sophisticated forecasting framework for solar and photovoltaic power production in geographic zones with severe meteorological conditions is very challenging. This difficulty is linked to the high variability of the global solar radiation on which the energy production depends. A suitable forecasting framework might take into account this high variability and could be able to adjust/re-adjust model parameters to reduce sensitivity to estimation errors. The framework should also be able to re-adapt the model parameters whenever the atmospheric conditions change drastically or suddenly—this changes according to microscopic variations. This work presents a new methodology to analyze carefully the meaningful features of global solar radiation variability and extract some relevant information about the probabilistic laws which governs its dynamic evolution. The work establishes a framework able to identify the macroscopic variations from the solar irradiance. The different categories of variability correspond to different levels of meteorological conditions and events and can occur in different time intervals. Thereafter, the tool will be able to extract the abrupt changes, corresponding to microscopic variations, inside each level of variability. The methodology is based on a combination of probability and possibility theory. An unsupervised clustering technique based on a Gaussian mixture model is proposed to identify, first, the categories of variability and, using a hidden Markov model, we study the temporal dependency of the process to identify the dynamic evolution of the solar irradiance as different temporal states. Finally, by means of some transformations of probabilities to possibilities, we identify the abrupt changes in the solar radiation. The study is performed in Guadeloupe, where we have a long record of global solar radiation data recorded at 1 Hertz. [ABSTRACT FROM AUTHOR]

In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is used to model imprecise probabilities. In one of interpretation, a possibility distribution (a membership function of a fuzzy set) in the set of coefficient realizations induces a necessity measure, which in turn defines a family of probability distributions in this set. The distributionally robust approach is then used to transform the imprecise constraints into deterministic counterparts. Namely, the uncertain left-hand side of each constraint is replaced with the expected value with respect to the worst probability distribution that can occur. It is shown how to represent the resulting problem by using linear or second-order cone constraints. This leads to problems which are computationally tractable for a wide class of optimization models, in particular for linear programming. [ABSTRACT FROM AUTHOR]

We introduce a general theory of epistemic random fuzzy sets for reasoning with fuzzy or crisp evidence. This framework generalizes both the Dempster-Shafer theory of belief functions, and possibility theory. Independent epistemic random fuzzy sets are combined by the generalized product-intersection rule, which extends both Dempster's rule for combining belief functions, and the product conjunctive combination of possibility distributions. We introduce Gaussian random fuzzy numbers and their multi-dimensional extensions, Gaussian random fuzzy vectors, as practical models for quantifying uncertainty about scalar or vector quantities. Closed-form expressions for the combination, projection and vacuous extension of Gaussian random fuzzy numbers and vectors are derived. [ABSTRACT FROM AUTHOR]

Typical statistical methods of data analysis only handle determinate uncertainty, the type of uncertainty that can be modeled under the Bayesian or confidence theories of inference. An example of indeterminate uncertainty is uncertainty about whether the Bayesian theory or the frequentist theory is better suited to the problem at hand. Another example is uncertainty about how to modify a Bayesian model upon learning that its prior is inadequate. Both problems of indeterminate uncertainty have solutions under the proposed framework. The framework is based on an information-theoretic definition of an incoherence function to be minimized. It generalizes the principle of choosing an estimate that minimizes the reverse relative entropy between it and a previous posterior distribution such as a confidence distribution. The simplest form of the incoherence function, called the incoherence distribution, is a min-plus probability distribution, which is equivalent to a possibility distribution rather than a measure-theoretic probability distribution. A simple case of minimizing the incoherence leads to a generalization of minimizing relative entropy and thus of maximizing entropy. The framework of minimum incoherence is applied to problems of Bayesian-confidence uncertainty and to parallel problems of indeterminate uncertainty about model revision. [ABSTRACT FROM AUTHOR]

Classical data cleaning performs a minimal set of operations on the data to satisfy the given integrity constraints. Often, this minimization is equivalent to vertex cover, for example when tuples can be removed due to the violation of functional dependencies. Classically, the uncertainty of tuples and constraints is ignored. We propose not to view data as dirty but the uncertainty information about data. Since probabilities are often unavailable and their treatment is limited due to correlations in the data, we investigate a qualitative approach to uncertainty. Tuples are assigned degrees of possibility with which they occur, and constraints are assigned degrees of certainty that say to which tuples they apply. Our approach is non-invasive to the data as we lower the possibility degree of tuples as little as possible. The new resulting qualitative version of vertex cover remains NP-hard. We establish an algorithm that is fixed-parameter tractable in the size of the qualitative vertex cover. Experiments with synthetic and real-world data show that our algorithm outperforms the classical algorithm proportionally to the available number of uncertainty degrees. By mining the certainty degrees with which constraints hold, our framework becomes applicable even when uncertainty information is unavailable. [ABSTRACT FROM AUTHOR]

In this paper, we show that the likelihood-ratio measure (a) is invariant with respect to dominating sigma-finite measures, (b) satisfies logical consequences which are not satisfied by standard p values, (c) respects frequentist properties, i.e., the type I error can be properly controlled, and, under mild regularity conditions, (d) can be used as an upper bound for posterior probabilities. We also discuss a generic application to test whether the genotype frequencies of a given population are under the Hardy–Weinberg equilibrium, under inbreeding restrictions or under outbreeding restrictions. [ABSTRACT FROM AUTHOR]