Information Processing and Management of Uncertainty in Knowledge-Based Systems

Based on the representation of OWA operators as Choquet integrals with respect to symmetric capacities, a new kind of OWA generalizations based on decomposition integrals is proposed and discussed. The symmetry of the underlying capacity is not sufficient to guarantee the symmetry of the resulting operator, and thus we deal with symmetric saturated decomposition systems only. All possible generalized OWA operators on $$X = \{1,2\}$$ are introduced. Similarly, when considering the maximal decomposition system on $$X = \{1,2,3\},$$ all generalized OWA operators are shown, based on the ordinal structure of the normed weighting vector $${\mathbf w} = (w_1,w_2,w_3).$$

In this paper we deal with the problem of obtaining the set of k-additive measures dominating a fuzzy measure. This problem extends the problem of deriving the set of probabilities dominating a fuzzy measure, an important problem appearing in Decision Making and Game Theory. The solution proposed in the paper follows the line developed by Chateauneuf and Jaffray for dominating probabilities and continued by Miranda et al. for dominating k-additive belief functions. Here, we address the general case transforming the problem into a similar one such that the involved set functions have non-negative Möbius transform; this simplifies the problem and allows a result similar to the one developed for belief functions. Although the set obtained is very large, we show that the conditions cannot be sharpened. On the other hand, we also show that it is possible to define a more restrictive subset, providing a more natural extension of the result for probabilities, such that it is possible to derive any k-additive dominating measure from it.

We are interested in aggregation function based on two weights vectors: the criteria weights p and the rank weights w. The main drawback of the existing proposals based on p and w (in particular the Weighted OWA (WOWA) and the Semi-Uninorm OWA (SUOWA) operators) is that their expression is rather complex and the contribution of the weights p and w in the aggregation is obscure as there is no clear interpretation of these weights. We propose a new approach to define aggregation functions based on the weights p and w. We consider the class of capacities (which subsumes the WOWA and SUOWA). We start by providing clear interpretations of these weights that are seen as constraints on the capacity. We consider thus the whole class of capacities fulfilling these constraints. A simulation shows that the WOWA and SUOWA almost never satisfy these constraints in a strict sense.

Every coalitional game can be extended from the powerset onto the real unit cube. One of possible approaches is the Lovász extension, which is the same as the discrete Choquet integral with respect to the coalitional game. We will study some solution concepts for coalitional games (core, Weber set) using superdifferentials developed in non-smooth analysis. It has been shown that the core coincides with Fréchet superdifferential and the Weber set with Clarke superdifferential for the Lovász extension, respectively. We introduce the intermediate set as the limiting superdifferential and show that it always lies between the core and the Weber set. From the game-theoretic point of view, the intermediate set is a non-convex solution containing the Pareto optimal payoff vectors, which depend on some ordered partition of the players and the marginal coalitional contributions with respect to the order.

We propose an axiomatization of the Choquet integral model for the general case of a heterogeneous product set $$X = X_1 \times \ldots \times X_n$$. In MCDA elements of X are interpreted as alternatives, characterized by criteria taking values from the sets $$X_i$$. Previous axiomatizations of the Choquet integral have been given for particular cases $$X = Y^n$$ and $$X = \mathbb {R}^n$$. However, within multicriteria context such indenticalness, hence commensurateness, of criteria cannot be assumed a priori. This constitutes the major difference of this paper from the earlier axiomatizations. In particular, the notion of “comonotonicity” cannot be used in a heterogeneous structure, as there does not exist a “built-in” order between elements of sets $$X_i$$ and $$X_j$$. However, such an order is implied by the representation model. Our approach does not assume commensurateness of criteria. We construct the representation and study its uniqueness properties.

Aggregation functions acting on the lattice of all Choquet integrals on a fixed measurable space $$(\mathrm {X},\mathcal {A})$$ are discussed. The only direct aggregation of Choquet integrals resulting into a Choquet integral is linked to the convex sums, i.e., to the weighted arithmetic means. We introduce and discuss several other approaches, for example one based on compatible aggregation systems. For $$\mathrm {X}$$ finite, the related aggregation of OWA operators is obtained as a corollary. The only exception, with richer structure of aggregation functions, is the case $$card \ \mathrm {X} = 2$$, when the lattice of all OWA operators forms a chain.

A data analysis model using the inclusion-exclusion integral and a new construction method of a model utilizing t-norms are proposed. This model is based on the integral with respect to the nonadditive measure and is constructed in three steps of specifications of monotone functions, t-norm and of monotone measures. The model has good description ability and can be applied flexibly to real problems. Applying this model to the data set of a multiple criteria decision making problem, the efficiency of the model is verified by comparing it with the classical linear regression model and with the Choquet integral model.

The fuzzy inference system (FIS) has been tuned and revamped many times over and applied to numerous domains. New and improved techniques have been presented for fuzzification, implication, rule composition and defuzzification, leaving one key component relatively underrepresented, rule aggregation. Current FIS aggregation operators are relatively simple and have remained more-or-less unchanged over the years. For many problems, these simple aggregation operators produce intuitive, useful and meaningful results. However, there exists a wide class of problems for which quality aggregation requires non-additivity and exploitation of interactions between rules. Herein, we show how the fuzzy integral, a parametric non-linear aggregation operator, can be used to fill this gap. Specifically, recent advancements in extensions of the fuzzy integral to “unrestricted” fuzzy sets, i.e., subnormal and non-convex, makes this now possible. We explore the role of two extensions, the gFI and the NDFI, discuss when and where to apply these aggregations, and present efficient algorithms to approximate their solutions.

We propose the Choquet integral with respect set to a function defined as the product-sum calculation between a set function and a fuzzy measure. The fuzzy integral is an extension of the Choquet integral. The Choquet integral assumes that the interactions among input values are interact fully but the extension assumes the values partially interaction. In this paper, we define another integral expression and analyze its properties. For an input vector the optimal set function is calculated through linear programming. Lastly, we analyze coalitions among set functions that are a cooperative game using the proposed integral.

In a context of Multiple Criteria Decision Aid, we present a decision model explaining some French hospitals rankings in weight loss surgery. To take into account interactions between medical indicators, we elaborated a model based on the 2-additive Choquet integral. The reference subset, defined during the elicitation process of this model, is composed by some specific alternatives called binary alternatives. To validate our approach, we showed that the proposed 2-additive Choquet integral model is able to approximate the hospitals ranking, in weight loss surgery, published by the French magazine “Le Point” in August 2013.

We provides an axiomatic characterization of preorders in lattices that are representable as benchmarking procedure. We show that the key axioms are related to compatibility with lattice operations.This paper propose also a characterization and a generalization of Sugeno integral in a ordinal framework.

Survival signature has been presented recently to quantify the system reliability. However, survival signature-based analytical methods are generally intractable for the analysis of realistic systems with multi-state components and imprecisions on the transition time. The availability of numerical simulation methods for the analysis of such systems is required. In this paper, novel simulation methods for computing system reliability are presented. These allow to estimate the reliability of realistic and large-scale systems based on survival signature including parameter uncertainties and imprecisions. The simulation approaches are generally applicable and efficient since only one estimation of the survival signature is needed while Monte Carlo simulation is used to generate component transition times. Numerical examples are presented to show the applicability of the proposed methods.

We investigate the properties of the upper probability associated with a bivariate p-box, that may be used as a model for the imprecise knowledge of a bivariate distribution function. We give necessary and sufficient conditions for this upper probability to be maxitive, characterize its focal elements, and study which maxitive functions can be obtained as upper probabilities of bivariate p-boxes.

In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge. This has the advantage that prior-data conflict sensitivity can be modelled: Ranges of posterior inferences should be larger when prior and data are in conflict. We propose a new method for generating prior sets which, in addition to prior-data conflict sensitivity, allows to reflect strong prior-data agreement by decreased posterior imprecision.

Accelerated life testing provides an interesting challenge for quantification of the uncertainties involved, in particular due to the required linking of items’ failure times, or failure time distributions, at different stress levels. This paper provides an initial exploration of the use of statistical methods based on imprecise probabilities for accelerated life testing, with explicit emphasis on prediction of a future observation at the actual stress level of interest. We apply nonparametric predictive inference at that stress level, in combination with an estimated parametric form for the function linking different levels. For the latter aspect imprecision is introduced, leading to observations at stress levels other than the actual level of interest, to be transformed to intervals at the latter level. We believe that this is the first attempt to apply imprecise probability methods to accelerated life testing scenarios, and argue in favour of doing so. The paper concludes with a discussion of related research topics.

A brief survey of mathematical gnostics is presented. Mathematical gnostics is a tool of advanced data analysis, consisting of1.theory of individual uncertain data and small samples,2.algorithms to implement the theory,3.applications of the algorithms.The axioms and definitions of the theory are inspired by the Laws of Nature dealt with by physics and the investigation of data uncertainty follows the methods of analysis of physical processes. The first axiom is a reformulation of the measurement theory which mathematically formalizes the empirical cognitive activity of physics. This axiom enables the curvature of the data space to be revealed and quantified. The natural affinity between uncertain data and relativistic mechanics is also shown. Probability, informational entropy and information of individual uncertain data item are inferred from non-statistical Clausius’ thermodynamical entropy. The quantitative cognitive activity is modeled as a closed cycle of quantification and estimation, which is proved to be irreversible and maximizes the result’s information. A proper estimation of the space’s curvature ensure a reliable robustness of the algorithms successfully proven in many applications. Gnostic formulae of data weights and errors, probability and information, which has been proved as valid for small samples of strongly uncertain data converge to statistical ones when uncertainty becomes weak. From this point of view, the mathematical gnostics can be considered as an extension of statistics useful under heavy-duty conditions.

Referring Expression Generation (reg) algorithms, a core component of systems that generate text from non-linguistic data, seek to identify domain objects using natural language descriptions. While reg has often been applied to visual domains, very few approaches deal with the problem of fuzziness and gradation. This paper discusses these problems and how they can be accommodated to achieve a more realistic view of the task of referring to objects in visual scenes.

In the recent past, a lot of work has been done on Linguistic Protoform Summaries (LPS). Much of this work focuses on improvement of the ways to compute truth values of LPS as well as on development of different protoforms. However, almost all of the systems using LPS use trapezoidal membership functions. This work investigates the effects of using triangular and pi shaped membership functions and compare their performance when using trapezoids. We start with an experiment using synthetic data and then compare the behavior of the three types of membership functions using real data which is obtained from an eldercare setting.

In our previous work we introduced a novel concept of the multiaspect text categorization (MTC) task meant as a special, extended form of the text categorization (TC) problem which is widely studied in information retrieval. The essence of the MTC problem is the classification of documents on two levels: first, on a more or less standard level of thematic categories and then on the level of document sequences which is much less studied in the literature. The latter stage of classification, which is by far more challenging, is the main focus of this paper. A promising way of attacking it requires some kind of modeling of connections between documents forming sequences. To solve this problem we propose a novel approach that combines a well-known techniques to model sequences, i.e., the Hidden Markov Models (HMM) and the Latent Dirichlet Allocation (LDA) technique for the advanced document representation, hence obtaining a hybrid approach. We present details of our proposed approach as well as results of some computational experiments.

Approximate Numerical Expressions (ANEs) are linguistic expressions involving numbers and referring to imprecise ranges of values, such as “about 100”. This paper proposes to interpret ANEs as fuzzy numbers. A model, taking into account the cognitive salience of numbers and based on critical points from Pareto frontiers, is proposed to characterise the support, the kernel and the 0.5-cut of the corresponding membership functions. An experimental study, based on real data, is performed to assess the quality of these estimated parameters.

When evaluating an odor, non-specialists generally provide descriptions as bags of terms. Nevertheless, these evaluations cannot be processed by classical odor analysis methods that have been designed for trained evaluators having an excellent mastery of professional controlled vocabulary. Indeed, currently, mainly oriented approaches based on learning vocabularies are used. These approaches too restrictively limit the possible descriptors available for an uninitiated public and therefore require a costly learning phase of the vocabulary. The objective of this work is to merge the information expressed by these free descriptions (terms) into a set of non-ambiguous descriptors best characterizing the odor; this will make it possible to evaluate the odors based on non-specialist descriptions. This paper discusses a non-oriented approach based on Natural Language Processing and Knowledge Representation techniques - it does not require learning a lexical field and can therefore be used to evaluate odors with non-specialist evaluators.

In statistical pattern recognition, feature transformation attempts to change original feature space to a low-dimensional subspace, in which new created features are discriminative and non-redundant, thus improving the predictive power and generalization ability of subsequent classification models. Traditional transformation methods are not designed specifically for tackling data containing unreliable and noisy input features. To deal with these inputs, a new approach based on Dempster-Shafer Theory is proposed in this paper. A specific loss function is constructed to learn the transformation matrix, in which a sparsity term is included to realize joint feature selection during transformation, so as to limit the influence of unreliable input features on the output low-dimensional subspace. The proposed method has been evaluated by several synthetic and real datasets, showing good performance.

Visual processing is one of the most essential tasks in robotics systems. However, it may be affected by many unfavourable factors in the operating environment which lead to imprecisions and uncertainties. Under those circumstances, we propose a multi-camera fusing method applied in a scenario of object recognition for a NAO robot. The cameras capture the same scenes at the same time, then extract feature points from the scene and give their belief about the classes of the detected objects. Dempster’s rule of combination is then used to fuse information from the cameras and provide a better decision. In order to take advantages of heterogeneous sensors fusion, we combine information from 2D and 3D cameras. The results of experiment prove the efficiency of the proposed approach.

Link prediction is the problem of determining future or missing associations between social entities. Most of the methods have focused on social networks under a certain framework neglecting some of the inherent properties of data from real applications. These latter are usually noisy, missing or partially observed. Therefore, uncertainty is an important feature to be taken into account. In this paper, proposals for handling the problem of missing link prediction while being attentive to uncertainty are presented along with a technique for uncertain social networks generation. Uncertainty is not only handled in the graph model but also in the method itself using the assets of the belief function theory as a general framework for reasoning under uncertainty. The approach combines sampling techniques and information fusion and returns good results in real-life settings.

Robots are destined to live with humans and perform tasks for them. In order to do that, an adapted representation of the world including human detection is required. Evidential grids enable the robot to handle partial information and ignorance, which can be useful in various situations. This paper deals with an audiovisual perception scheme of a robot in indoor environment (apartment, house..). As the robot moves, it must take into account its environment and the humans in presence. This article presents the key-stages of the multimodal fusion: an evidential grid is built from each modality using a modified Dempster combination, and a temporal fusion is made using an evidential filter based on an adapted version of the generalized bayesian theorem. This enables the robot to keep track of the state of its environment. A decision can then be made on the next move of the robot depending on the robot’s mission and the extracted information. The system is tested on a simulated environment under realistic conditions.

Evidential Hidden Markov Models (EvHMM) is a particular Evidential Temporal Graphical Model that aims at statistically representing the kynetics of a system by means of an Evidential Markov Chain and an observation model. Observation models are made of mixture of densities to represent the inherent variability of sensor measurements, whereas uncertainty on the latent structure, that is generally only partially known due to lack of knowledge, is managed by Dempster-Shafer’s theory of belief functions. This paper is dedicated to the presentation of an Expectation-Maximization procedure to learn parameters in EvHMM. Results demonstrate the high potential of this method illustrated on complex datasets originating from turbofan engines where the aim is to provide early warnings of malfunction and failure.

To ensure the quality of a learned Bayesian network out of limited data sets, evaluation and selection process of variables becomes necessary. With this purpose, two new variable selection criteria N₂S _j and N₃S _j are proposed in this research which show superior performance on limited data sets. These newly developed variable selection criteria with the existing ones from prior research are employed to create Bayesian networks from three different limited data sets. On each step of variable elimination, the performance of the resulting BNs are evaluated in terms of different network performance metrics. Furthermore, a new variable evaluation criteria, IH _j , is proposed which measures the impact of a variable to all the other variables in the network. IH _j serves as an indicator of the most important variables in the network which has a special importance for the use of BNs in social science research, where it is crucial to identify the most important factors in a setting.

Performing probabilistic inference in multi-target dynamic systems is a challenging task. When the system, its evidence and/or its targets evolve, most of the inference algorithms either recompute everything from scratch, even though incremental changes do not invalidate all the previous computations, or do not fully exploit incrementality to minimize computations. This incurs strong unnecessary overheads when the system under study is large. To alleviate this problem, we propose in this paper a new junction tree-based message-passing inference algorithm that, given a new query, minimizes computations by identifying precisely the set of messages that differ from the preceding computations. Experimental results highlight the efficiency of our approach.

Dynamic Bayesian Networks (DBNs) provide a principled scheme for modeling and learning conditional dependencies from complex multivariate time-series data and have been used in a wide scope. However, in most cases, the underlying generative Markov model is assumed to be homogeneous, meaning that neither its topology nor its parameters evolve over time. Therefore, learning a DBN to model a non-stationary process under this assumption will amount to poor predictions capabilities. To account for non-stationary processes, we build on a framework to identify, in a streamed manner, transition times between underlying models and a framework to learn them in real time, without assumptions about their evolution. We show the method performances on simulated datasets. The goal of the system is to model and predict incongruities for an Intrusion Dectection System (IDS) in near real-time, so great care is attached to the ability to correctly identify transitions times. Our preliminary results reveal the precision of our algorithm in the choice of transitions and consequently the quality of the discovered networks. We finally suggest future works.

Implication functions are crucial operators for many fuzzy logic applications. In this work, we consider the definition of implication functions in the interval-valued setting using admissible orders and we use this interval-valued implications for building comparison measures.

Sugeno integrals are aggregation functions defined on a qualitative scale where only minimum, maximum and order-reversing maps are allowed. Recently, variants of Sugeno integrals based on Gödel implication and its contraposition were defined and axiomatized in the setting of bounded chain with an involutive negation. This paper proposes a more general approach. We consider totally ordered scales, multivalued conjunction operations not necessarily commutative, and implication operations induced from them by means of an involutive negation. In such a context, different Sugeno-like integrals are defined and axiomatized.

Fuzzy implication functions are used to model fuzzy conditional and consequently they are essential in fuzzy logic and approximate reasoning. From the theoretical point of view, the study of how to construct new implication functions from old ones is one of the most important topics in this field. In this paper a construction method of implication functions from a t-conorm S (or any disjunctive aggregation function F), a fuzzy negation N and an implication function I is studied. Some general properties are analyzed and many illustrative examples are given. In particular, this method shows how to obtain new implications from old ones with additional properties not satisfied by the initial implication function.

In fuzzy logic, the Modus Ponens property for fuzzy implication functions is usually considered with respect to a continuous t-norm T and for this reason this property is also known under the name of T-conditionality. In this paper, the t-norm T is substituted by a uninorm U leading to the property of U-conditionality. The new property is studied in detail and it is shown that usual implications derived from t-norms and t-conorms do not satisfy it, but many solutions appear among those implications derived from uninorms. In particular, the case of residual implications derived from uninorms or RU-implications is investigated in detail for some classes of uninorms.

Fuzzy implication functions are logical connectives commonly used to model fuzzy conditional and consequently they are essential in fuzzy logic and approximate reasoning. From the theoretical point of view, the study of how to construct new implication functions from old ones is one of the most important topics in this field. In this paper new ordinal sum construction methods of implication functions based on fuzzy negations N are presented. Some general properties are analysed and particular cases when the considered fuzzy negation is the classical one or any strong negation are highlighted.

In this work we investigate two distributivity equations $$\mathcal {I}(x,\mathcal {U}_1(y,z)) = \mathcal {U}_2(\mathcal {I}(x,y),\mathcal {I}(x,z))$$, $$\mathcal {I}(\mathcal {U}_1(x,y),z) = \mathcal {U}_2(\mathcal {I}(x,z),\mathcal {I}(y,z))$$ for implication operations and uninorms in interval-valued fuzzy sets theory. We consider decomposable (t-representable) uninorms generated from two conjunctive or disjunctive representable uninorms. Our method reduces to solve the following functional equation $$f(u_1+v_1,u_2+v_2) = f(u_1,u_2) + f(v_1,v_2)$$, thus we present new solutions for this equation.

Recently, fuzzy implications based on copulas, i.e. probabilistic implications and probabilistic S-implications, were introduced and their properties were explored. However, the reverse problem of copulas derived from fuzzy implications, suggested by Massanet et al. [11, 12], is also of interest. In the paper we consider geometric properties of those fuzzy implications that generate copulas. Moreover, we consider the reverse problem for some generalizations of copulas like quasi-copulas and semi-copulas.

In this paper we show how the diversity of properties for quantales is well suited for describing multivalence in many-valued logic. Tensor products of quantales will play an important role in showing how more simple valuation scales can be tensored together to provide more complex valuation scales. In health care applications, this is typically seen for disorders and functioning. Classification of disorder is typically quite bivalent, whereas scales used in functioning classifications are multivalent. The role ‘not specified’ or ‘missing’ is shown to be of importance.

In medical diagnosis, information about the health state of a patient can often be obtained through different tests, which may perhaps be combined into an overall decision rule. Practically, this leads to several important questions. For example, which test or which subset of tests should be selected, taking into account the effectiveness of individual tests, synergies and redundancies between them, as well as their cost. How to produce an optimal decision rule on the basis of the data given, which typically consists of test results for patients with or without confirmed health condition. To address questions of this kind, we develop an approach that combines (semi-supervised) machine learning methodology with concepts from (cooperative) game theory. Roughly speaking, while the former is responsible for optimally combining single tests into decision rules, the latter is used to judge the influence and importance of individual tests as well as the interaction between them. Our approach is motivated and illustrated by a concrete case study in veterinary medicine, namely the diagnosis of a disease in cats called feline infectious peritonitis.

Blood vitamin B12 levels are not representative for actual vitamin B12 status in tissue. Instead plasma methylmalonic acid (MMA) levels can be measured because MMA concentrations increase relatively early in the course of vitamin B12 deficiency. However, MMA levels in plasma may also be increased due to renal failure. In this paper we estimate the influence of the kidney function on MMA levels in plasma by using fuzzy inference systems. Using this method diagnosing vitamin B12 deficiencies could be improved when kidney failure is present.

This paper presents a data collecting process using smartphone-based accelerometer in association with geographic information systems (GIS) software to better manage pavement condition data and facilitate with decision making for maintenance and rehabilitation. The smartphone is equipped with an accelerometer (a mobile apps) could record 50 vibration data points per second in three direction (X, Y, and Z). The type of Traditional pavement survey is time-consuming and requires experienced technicians to travel along highway to visualize pavement conditions and record any failures. Combining vibration intensity data with a GIS platform can help public agencies with a strategic plan to prioritize maintenance schedules for both bike trails and highway roads. The objective of this paper is to (1) discuss the processes of vibration data analysis using a smartphone based accelerometer and to (2) demonstrate how to relate vibration intensity data to locate priority areas for immediate.

This work introduces AutoFIS-Class, a methodology for automatic synthesis of Fuzzy Inference Systems for classification problems. It is a data-driven approach, which can be described in five steps: (i) mapping of each pattern to a membership degree to fuzzy sets; (ii) generation of a set of fuzzy rule premises, inspired on a search tree, and application of quality criteria to reduce the exponential growth; (iii) association of a given premise to a suitable consequent term; (iv) aggregation of fuzzy rules to a same class and (v) decision on which consequent class is most compatible with a given pattern. The performance of AutoFIS-Class has been compared to those of other four rule-based systems for 21 datasets. Results show that AutoFIS-Class is competitive with respect to those systems, most of them evolutionary ones.

Viewing the modelling of agrifood chains (AFC) from a multi agent systems (MAS) point of view opens up numerous avenues for research while building upon existing advancements in the state of the art. This paper explores different aspects in MAS research areas in consensus and cooperation (argumentation, negotiation, normative systems, multi agent resource allocation and social affects) and provides insights into how viewing classical AFC problems from this perspective can bring new perspectives and research avenues.

In this paper, we introduce an uncertain data mining driven model for knowledge discovery in chemical database. We aim at discovering relationship between molecule characteristics and properties using uncertain data mining tools. In fact, we intend to predict the Critical Micelle Concentration (CMC) property based on a molecule characteristics. To do so, we develop a likelihood-based belief function modelling approach to construct evidential database. Then, a mining process is developed to discover valid association rules. The prediction is performed using association rule fusion technique. Experiments were conducted using a real-world chemical databases. Performance analysis showed a better prediction outcome for our proposed approach in comparison with several literature-based methods.

Recent years have seen increasing volumes of data generated by online systems, such as internet logs, physical access logs, transaction records, email and phone records. These contain multiple overlapping sequences of events related to different individuals and entities. Information that can be mined from these event sequences is an important resource in understanding current behaviour, predicting future behaviour and identifying non-standard patterns and possible security breaches. Statistical machine learning approaches have had some success but do not allow human insight to be included easily. We have recently presented a framework for representing sequences of related events, with scope for assistance from human experts. This paper describes the framework and presents a new algorithm which (i) allows the addition of new event sequences as they are identified from data or postulated by a human analyst, and (ii) allows subtraction/removal of sequences that are no longer relevant. Examination of the sequences can be used to further refine and modify general patterns of events.

In the last years association rules are being applied to support decision making. However, the main concern is in the precision and not in the interpretability of their results, so they produce large sets of rules difficult to understand for the user. A comprehensible system should work according to the human decision making process, which is quite based on the case study and the scenario projection. Here we propose an association rule based system for scenario query (SQAR), where the user can perform “what if...?” queries, and get as response what usually happens under similar scenarios. Even more we enrich our proposal with a hierarchical structure that allows the definition of scenarios with different detail levels, to comply with the needs of the user.

The frequent subgraph mining has widespread applications in many different domains such as social network analysis and bioinformatics. Generally, the frequent subgraph mining refers to graph matching. Many research works dealt with structural graph matching, but a little attention is paid to semantic matching when graph vertices and/or edges are attributed. Therefore, the discovered frequent subgraphs should become more pruned by applying a new semantic filter instead of using only structural similarity in the graph matching process. In this paper, we present POSGRAMI, a new hybrid approach for frequent subgraph mining based principally on approximate graph matching. To this end, POSGRAMI first uses an approximate structural similarity function based on graph edit distance function. POSGRAMI then uses a semantic vertices similarity function based on possibilistic information affinity function. In fact, our proposed approach is a new possibilistic version of existing approach in literature named GRAMI. This paper had shown the effectiveness of POSGRAMI on some real datasets. In particular, it achieved a better performance than GRAMI in terms of processing time, number and quality of discovered subgraphs.

The electricity market has been significantly changing in the last decade. The deployment of smart meters is enabling the logging of huge amounts of data relating to the operations of utilities with the potential of being translated into knowledge on consumers and enable personalized energy efficiency programs. This paper proposes an approach for mining characteristics of a residential consumers (income, education and having children) from high-resolution smart meter data using transparent fuzzy models. The system consists in: (1) extraction of comprehensive consumption features from smart meter data, (2) use of fuzzy models in order to estimate the characteristics of consumers, and (3) knowledge extraction from the fuzzy models rules. Accurate estimates of consumer income and education level were not achieved (60 % accuracy), for the presence of children accuracies of over 70 % were achieved. Performance is comparable to the state of the art with the addition of model interpretability and transparency.

We propose a fast algorithm of image pattern (instance) matching which is based on an efficient encoding of the pattern and database images. For each image, the encoding produces a matrix of the F-transform components. The matching is then realized by comparing the F-transform components of the pattern and the database images. The optimal setting of the algorithm parameters is discussed, the success rate and the run time are exhibited.

The paper is focused on demonstration of image inpainting technique using the F-transform theory. Side by side with many algorithms for the image reconstruction we developed a new method of patch-based filling of an unknown (damaged) image area. The unknown area is proposed to be recursively filled by those known patches that have non-empty overlaps with the unknown area and are the closest ones among others from a database. We propose to use the closeness measure on the basis of the F$$^1$$-transform.

Template-based methods for image processing hold a list of advantages over other families of methods, e.g. simplicity and ability to mimic human behaviour. However, they also demand a careful design of the pattern representatives as well as that of the operators in charge of measuring/detecting their presence in the data. This work presents a method for fingerprint analysis, specifically for singular point detection, based on template matching. The matching process sparks the need for similarity measures able to cope with radial data. As a result, we introduce the concepts of Restricted Radial Equivalence Function (RREF) and Radial Similarity Measure (RSM), further used to evaluate the perceptual closeness of scalar and vectorial pieces of radial data, respectively. Our method, which goes by the name of Template-based Singular Point Detection method (TSPD), has qualitative advantages over other alternatives, and proves to be competitive with state-of-the art methods in quantitative terms.

This paper presents an algorithm designed to segment veins in the periventricular region of the brain in susceptibility-weighted magnetic resonance images. The proposed algorithm is based on a Mamdani-type fuzzy rule-based system that enables enhancement of veins within periventricular regions of interest as the first step. Segmentation is achieved after determining the cut-off value providing the best trade-off between sensitivity and specificity to establish the suitability of each pixel to belong to a cerebral vein. Performance of the algorithm in susceptibility-weighted images acquired in healthy volunteers showed very good segmentation, with a small number of false positives. The results were not affected by small changes in the size and location of the regions of interest. The algorithm also enabled detection of differences in the visibility of periventricular veins between healthy subjects and multiple sclerosis patients.

In this work we investigate the use of OWA operators in color image reduction. Since the RGB color scheme can be seen as a Cartesian product of lattices, we use the generalization of OWA operators to any complete lattice. However, the behavior of lattice OWA operators in image processing is not easy to predict. Therefore, we propose an orness measure that generalizes the orness measure given by Yager for usual OWA operators. With the aid of this new measure, we are able to classify each OWA operator and to analyze how its properties affect the results of applying OWA operators in an algorithm for reducing color images.

This paper proposes a method to evaluate hierarchical image segmentation procedures, in order to enable comparisons between different hierarchical algorithms and of these with other (non-hierarchical) segmentation techniques (as well as with edge detectors) to be made. The proposed method builds up on the edge-based segmentation evaluation approach by considering a set of reference human segmentations as a sample drawn from the population of different levels of detail that may be used in segmenting an image. Our main point is that, since a hierarchical sequence of segmentations approximates such population, those segmentations in the sequence that best capture each human segmentation level of detail should provide the basis for the evaluation of the hierarchical sequence as a whole. A small computational experiment is carried out to show the feasibility of our approach.

The paper deals with the higher degree fuzzy transforms (F-transforms with polynomial components) for functions of two variables in the case when two-dimensional generalized fuzzy partition is given by B-splines of two variables. We investigate properties of the direct and inverse F-transform in this case and prove that using B-splines as basic functions of fuzzy partition allows us to improve the quality of approximation.

Many image processing and computer vision applications require a preprocessing of the image to remove or reduce noise. Gaussian noise is a challenging type of noise whose removal has led to the proposal of several noise filters. In this paper we present a novel version of the morphological filters based on amoebas with the aim to incorporate fuzzy logic into them to achieve a better treatment of the uncertainty. The experimental results show that the proposed algorithm outperforms the classical amoeba-based filters both from the visual point of view and the quantitative performance values for images corrupted with Gaussian noise with standard deviation from 10 to 30.

This paper proposes a fuzzy partitioning subspace clustering algorithm that minimizes a variant of the FCM cost function with a weighted Euclidean distance and a penalty term. To this aim it considers the framework of proximal optimization. It establishes the expression of the proximal operator for the considered cost function and derives PFSCM, an algorithm combining proximal descent and alternate optimization. Experiments show the relevance of the proposed approach.

This paper suggests an interval participatory learning fuzzy clustering (iPL) method for partitioning interval-valued data. Participatory learning provides a paradigm for learning that emphasizes the pervasive role of what is already known or believed in the learning process. iPL clustering method uses interval arithmetic, and the Hausdorff distance to compute the (dis)similarity between intervals. Computational experiments are reported using synthetic interval data sets with linearly non-separable clusters of different shapes and sizes. Comparisons include traditional hard and fuzzy clustering techniques for interval-valued data as benchmarks in terms of corrected Rand (CR) index for comparing two partitions. The results suggest that the interval participatory learning fuzzy clustering algorithm is highly effective to cluster interval-valued data and has comparable performance than alternative hard and fuzzy interval-based approaches.

Clustering is an important technique for identifying groups of similar data objects within a data set. Since problems during the data collection and data preprocessing steps often lead to missing values in the data sets, there is a need for clustering methods that can deal with such imperfect data. Approaches proposed in the literature for adapting the fuzzy c-means algorithm to incomplete data work well on data sets with equally sized and shaped clusters. In this paper we present an approach for adapting the fuzzy c-means algorithm to incomplete data that uses the dimension-wise fuzzy variances of clusters for imputation of missing values. In experiments on incomplete real and synthetic data sets with differently sized and shaped clusters, we demonstrate the benefit over the basic approach in terms of the assignment of data objects to clusters and the cluster prototype computation.

Possibilistic clustering methods have gained attention in both applied and theoretical research. In this paper, we formulate a general objective function for possibilistic clustering. The objective function can be used as the basis of a mixed clustering approach incorporating both fuzzy memberships and possibilistic typicality values to overcome various problems of previous clustering approaches. We use numerical experiments for a classification task to illustrate the usefulness of the proposal. Beyond a performance comparison with the three most widely used (mixed) possibilistic clustering methods, this also outlines the use of possibilistic clustering for descriptive classification via memberships to a variety of different class clusters. We find that possibilistic clustering using the general objective function outperforms traditional approaches in terms of various performance measures.

This paper proposes a methodology to define the seasonal load profiles of residential gas consumers using smart metering data. A detailed clustering analysis is performed using fuzzy c-means, k-means and hierarchical clustering algorithms with multiple clustering validity indices. The analysis is based on a sample of more than one thousand households over one year. The results provide evidence that crisp algorithms present the best clustering results overall. However, the fuzzy algorithm proves to be suited when the others generate clusters which are not representative of population groups. Compact and well defined seasonal clusters of gas consumers are obtained, where the representative profiles reflect the consumption patterns that vary according to the season of the year. The knowledge obtained with this methodology can assist decision makers in the energy utilities in developing demand side management programs, consumer engagement strategies, marketing, as well as in designing innovative tariff systems.