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This paper addresses the preservation of numerous essential properties of a residuated lattice structure in extended algebras for partial fuzzy set theory and partial fuzzy logics. The preservation includes the residuated lattice axioms, the identities narrowing the classes of the residuated lattices, and some well-known additional properties. In this paper, we consider nine algebras for partial fuzzy logics which incorporate handling undefined values in a bit different way. In particular, we consider the Bochvar, the Bochvar external, the Sobociński, the Kleene, the McCarthy, the Nelson, and the Łukasiewicz algebras, and two recently developed ones, namely the Lower estimation and the Dragonfly algebras. We summarize the obtained results in a comprehensible form which allows readers to easily check the information for the preserved and non-preserved properties in a certain partial algebraic structure. The resulting shape of the contribution is a sort of "atlas book" that aims at providing researchers with a comfortable and comprehensible form of an overview of the (non)preservation of fundamental properties of residuated structures. [ABSTRACT FROM AUTHOR]

Recently the useful redefinition of the intuitionistic and interval-valued intuitionistic fuzzy set theories (A − I F S , A − I V I F S) based on the Dempster-Shafer theory of evidence (DST) was developed. It was named the "Belief-Plausibility" (BP) approach as only the basic mathematical tools of the DST were used for its foundation. In this paper, a new approach to compare the real, interval and fuzzy-valued intuitionistic fuzzy and BP numbers is proposed. Among known approaches to compare intuitionistic fuzzy objects, most justified and used in applications are those based on the so-called score and accuracy functions. The observed multiplicity of these functions treatments and modifications indicates that the source of such a divergence is the impossibility to solve this problem exclusively in the framework of the A − I F S. Therefore, to develop the reliable methods for the considered types of comparison, a redefinition of this problem based on the BP approach is proposed. This redefinition allows us to develop new two and three criteria methods for comparison of real, interval and fuzzy-valued intuitionistic fuzzy and BP numbers, based on the local criteria with transparent interpretation in the framework of the BP approach. [ABSTRACT FROM AUTHOR]

This paper presents the application of abstraction methods in creating concepts that allow to describe and solve more complex problems of knowledge representation in semantic networks. In the Semantic Web, knowledge is represented by the attributive language AL. There are many information granules theories formulated in different theories such as set theory, probability theory, possible data sets in the evidence systems, shadowed sets, fuzzy set theory, and rough set theory. In order to equally interpret AL language expressions in different information granules theories within the Semantic Web, it is assumed that AL language expressions are interpreted in the chosen relational system called a granule system. This paper formally describes information granule system and shows the example how to formulate such granule system in the theory of the contextual rough sets [14] which describes inclusions of fuzzy context relations with some error. Defined granule system allows to interpret AL languages. It is shown that there is such subsystem of this granule system that is adequate i.e. it is homomorphic within some ordered set algebra. [ABSTRACT FROM AUTHOR]

Many geosciences data are imprecise due to various limitations and uncertainties in the measuring process. In other situations, collocated measurements of variables from the same, yet unknown, distribution are characterized with separate models that may not respect the relatedness of the measurements. One way to preserve this imprecision or relatedness in a geostatistical mapping framework is to characterize the measurements as intervals rather than single numbers. To effectively analyze the interval-valued data, this paper develops an interval-valued kriging based on the modification of a previous attempt and the recent development of the random sets theory. Numerical implementation of our interval-valued kriging is provided using a penalty-based constrained optimization algorithm. An interval-valued kriging of design ground snow loads in Ohio, USA, demonstrates the applicability and advantages of the proposed methodology. [ABSTRACT FROM AUTHOR]

In this paper, we first review existing fuzzy extensions of the dominance-based rough set approach (DRSA), and advance the theory considering additional properties. Moreover, we examine the application of Ordered Weighted Average (OWA) operators to fuzzy DRSA. OWA operators have shown a lot of potential in handling outliers and noisy data in decision tables, when they are combined with the indiscernibility-based rough set approach (IRSA). We examine theoretical properties of the proposed hybridisation of OWA operators with fuzzy DRSA. At the end, we experimentally compare the robustness of the standard fuzzy DRSA approach with the OWA one. [ABSTRACT FROM AUTHOR]

Since the theory of rough sets was introduced by Zdzislaw Pawlak, several approaches have been proposed to combine rough set theory with fuzzy set theory. In this paper, we examine one of these approaches, namely fuzzy rough sets with crisp reference sets, from a lattice-theoretic point of view. We connect the lower and upper approximations of a fuzzy relation R to the approximations of the core and support of R. We also show that the lattice of fuzzy rough sets corresponding to a fuzzy equivalence relation R and the crisp subsets of its universe is isomorphic to the lattice of rough sets for the (crisp) equivalence relation E , where E is the core of R. We establish a connection between the exact (fuzzy) sets of R and the exact (crisp) sets of the support of R. [ABSTRACT FROM AUTHOR]

In order to explore a unified theory of three-way decisions proposed by Yao, Hu introduced three-way decision spaces through an axiomatic method, established the corresponding three-way decisions, and proposed two open problems on the changes of decision parameters in definition of three-way decisions. For answering these two questions, this paper firstly discusses the parameter changes in the assumptions from 0 ≤ β < α ≤ 1 to 0 ≤ β ≤ α ≤ 1 and inequality E ( A ) ( x ) ≤ β in the rejection region is replaced by E ( A ) ( x ) < β . Under the circumstance, this paper introduces new type of three-way decisions in three-way decision spaces and discusses properties of the three-way decisions, lower and upper approximations induced by three-way decisions, aggregation three-way decisions over multiple three-way decision spaces and dynamic three-way decisions on three-way decision spaces. Then this paper discusses another question on refusal decision region when the uncertain region is defined by using inequality β < E ( A ) ( x ) < α and gives one example to illustrate the similarity and difference among these three-way decisions based on three-way decision spaces. [ABSTRACT FROM AUTHOR]

Abstract The aim of this paper is to establish two new types of rough set structures associated with the Marcus–Wyse (MW -, for brevity) topology, such as an M -rough set and an MW -topological rough set. The former focuses on studying the rough set theoretic tools for 2-dimensional Euclidean spaces and the latter contributes to the study of the rough set structures for digital spaces in Z 2 , where Z is the set of integers. These two rough set structures are related to each other via an M -digitization. Thus, these can successfully be used in the field of applied science, such as digital geometry, image processing, deep learning for recognizing digital images, and so on. For a locally finite covering approximation (LFC -, for short) space (U , C) and a subset X of U , we firstly introduce a new neighborhood system on U related to X. Next, we formulate the lower and upper approximations with respect to X , where all of the sets U and X (⊆ U) need not be finite and the covering C is locally finite. Actually, the notion of M -digitization of a 2-dimensional Euclidean space plays an important role in developing an M -rough and MW -topological rough set structures. Further, we prove that M -rough set operators have a duality between them. However, each of MW -topological rough set operators need not have the property as an interior or a closure from the viewpoint of MW -topology. [ABSTRACT FROM AUTHOR]

Abstract Attribute reduction plays an important role in rough set theory. Many attribute reduction methods have been proposed based on different definitions of attribute reduct, while an attribute reduct can be regarded as a minimal attribute subset that satisfies specific criteria. Most reducts are defined on the basis of a single criterion, which can only affect one specific characteristic of the data or one preference of users. However, the single criterion-based attribute reduct may not meet the requirement of complex problems. To address this problem, based on three-way decision-theoretic rough set model, this paper defines a multi-objective attribute reduct. Three types of criteria for defining attribute reduct including the positive region, decision cost and mutual information are considered and combined to a multi-objective optimization problem. Based on the proposed multi-objective attribute reduct, we also introduce a multi-objective optimization-based attribute reduction method and an ensemble learning-based attribute reduction method. Experimental results on several datasets show that the proposed attribute reduction methods can obtain a robust and better classification performance. [ABSTRACT FROM AUTHOR]

Abstract In the AGM paradigm for belief revision, epistemic states are represented by logically closed sets of sentences, the so-called belief sets. An alternative approach uses belief bases, arbitrary sets of sentences. Both approaches have their problems when it comes to contraction operations. Belief bases are more expressive, but, at the same time, they present a serious syntax dependence. Between those two extremes lie a whole gamut of operations called pseudo-contractions, some of which may be interesting alternatives to the classical ones, providing a good balance between syntax dependence and expressivity. In this paper we explore some very natural and general constructions for pseudo-contractions, showing some of their properties and giving their axiomatic characterizations. We also illustrate possible practical scenarios where they can be employed. [ABSTRACT FROM AUTHOR]

The term “feature selection” refers to the problem of selecting the most predictive features for a given outcome. Reducing the number of features is important to lower the computation cost of algorithms and also to achieve better generalization capabilities. The rough set theory has rapidly established itself as an effective tool for finding the smallest sets of features without any loss of information. This paper introduces a new approach based on the idea of exploiting rough set theory to compose partitions of the data induced by feature granulation. The partitions are iteratively aggregated in a single representative partition and, at each iteration, the obtained partition is used to evaluate the quality of the subset of features selected, thus reducing the cost of each evaluation. The consequence of using rough set theory is an algorithm that presents good reduction capability with less computational complexity w.r.t. Quickreduct algorithm. The proposed approach, called Roughinement, has been compared with approaches recently appeared in literature yielding comparable to better results. [ABSTRACT FROM AUTHOR]

In covering rough set theory, the basic problem is the calculation of lower and upper approximations for subsets of a covering approximation space. For a covering approximation space with a large cardinal, using definitions to calculate approximations would be tedious and complicated. So it is important to investigate matrix methods by which calculations will become algorithmic and can be easily implemented by computers. Since the covering in a covering approximation space can be represented by a Boolean matrix, every covering rough approximation operator must be closely related to this matrix. In this paper, we investigated 32 pairs of neighborhood-based dual lower and upper approximation operators and successfully obtained all the matrix representations of them. Some examples were presented in the manuscript to illustrate how to use matrix methods to compute lower and upper approximations and examples were also given to solve the inverse problem, i.e., finding all the subsets whose lower or upper approximation is a given subset. [ABSTRACT FROM AUTHOR]

The paper by Eyke Hüllermeier introduces a new set of techniques for learning models from imprecise data. The removal of the uncertainty in the training instances through the input-output relationship described by the model is also considered. This discussion addresses three points of the paper: extension principle-based models, precedence operators between fuzzy losses and possible connections between data disambiguation and data imputation. [ABSTRACT FROM AUTHOR]

Feature selection is the process of selecting a subset of features from the entire dataset such that the selected subset can be used on behalf of the entire dataset to reduce further processing. There are many approaches proposed for feature selection, and recently, rough set-based feature selection approaches have become dominant. The majority of such approaches use attribute dependency as criteria to determine the feature subsets. However, this measure uses the positive region to calculate dependency, which is a computationally expensive job, consequently effecting the performance of feature selection algorithms using this measure. In this paper, we have proposed a new heuristic-based dependency calculation method. The proposed method comprises a set of two rules called Direct Dependency Calculation (DDC) to calculate attribute dependency. Direct dependency calculates the number of unique/non-unique classes directly by using attribute values. Unique classes define accurate predictors of class, while non-unique classes are not accurate predictors. Calculating unique/non-unique classes in this manner lets us avoid the time-consuming calculation of the positive region, which helps increase the performance of subsequent algorithms. A two-dimensional grid was used as an intermediate data structure to calculate dependency. We have used the proposed method with a number of feature selection algorithms using various publically available datasets to justify the proposed method. A comparison framework was used for analysis purposes. Experimental results have shown the efficiency and effectiveness of the proposed method. It was determined that execution time was reduced by 63% for calculation of the dependency using DDCs, and a 65% decrease was observed in the case of feature selection algorithms based on DDCs. The required runtime memory was decreased by 95%. [ABSTRACT FROM AUTHOR]

Idempotence is a desirable property when cautiousness is wanted in an information fusion process, since in this case combining identical information should not lead to the reinforcement of some hypothesis. Idempotent operators also guarantee that identical information items are not counted twice in the fusion process, a very important property in decentralized applications where the information origin cannot always be tracked (ad-hoc wireless networks are typical examples). In the theory of belief functions, a sound way to combine conjunctively multiple information items is to design a combination rule that selects the least informative element among a subset of belief functions more informative than each of the combined ones. In contrast, disjunctive rules can be retrieved by selecting the most informative element among a subset of belief functions less informative than each of the combined ones. One interest of such approaches is that they provide idempotent rules by construction. The notions of less and more informative are often formalized through partial orderings extending usual set-inclusion, yet the only two informative partial orders that provide a straightforward idempotent rule leading to a unique result are those based on the conjunctive and disjunctive weight functions. In this article, we show that other partial orders can achieve a similar goal when the problem is slightly relaxed into a distance optimization one. Building upon previous work, this paper investigates the use of distances compatible with informative partial orders to determine a unique solution to the combination problem. The obtained operators are conjunctive/disjunctive, idempotent and commutative, but lack associativity. They are, however, quasi-associative allowing sequential combinations at no extra complexity. Some experiments demonstrate interesting discrepancies as compared to existing approaches, notably with the aforementioned rules relying on weight functions. [ABSTRACT FROM AUTHOR]

Due to legal reasons, faces on a given image may have to be blurred. This may be achieved by combining several information sources, which may provide information at different levels of granularity; for instance face detectors return bounding boxes corresponding to assumed positions of faces, whereas skin detectors may return pixel level information. A general, well-founded and efficient approach to combining box-based information sources was recently proposed in the context of pedestrian detection. This approach relies on evidence theory to calibrate and combine sources. In this paper, we apply this approach to combine face (rather than pedestrian) detectors, in order to obtain a state-of-the-art face blurring system based on multiple detectors. Then, we propose another approach to tackle the blurring problem, which consists essentially in applying at the pixel-level the central idea – combining evidentially calibrated information sources – of the preceding box-based approach. This shift of focus induces several conceptual advantages. In addition, the proposed approach shows better performances on a classical face dataset, as well as on a more challenging one. [ABSTRACT FROM AUTHOR]

Probabilistic rough set approximations are proposed based on a conditional probability to describe the desired levels of precision between the equivalence classes and an approximated set. This definition shows the detailed information on individuals satisfying some conditions but ignores the structural information. In this paper, applying the structured granules in a coarsened-grained universe, we introduce structured probabilistic rough set approximations between the power sets of the original universe and the coarsened-grained universe. By using the zooming-in and structured probabilistic rough approximation operators, two pairs of probabilistic rough lower and upper approximations on the same universe are investigated. Related properties and relationships of them are investigated. Furthermore, applying the Bayesian decision procedure, conditional probability and loss functions, three-way classifications in structured probabilistic rough set approximations are then proposed to classify the structured granules of the coarsened-grained universe into three disjoint structured probabilistic regions. This method gives the values of the pair of thresholds. Meanwhile, by using the minimum-risk decision rules, we also can construct the structured probabilistic rough lower and upper approximations. Finally, we discuss the monotonicity of structured probabilistic positive and negative regions. [ABSTRACT FROM AUTHOR]

Probabilistic Argumentation (PA) is a recent line of research in AI aiming to combine the strengths of argumentation and probabilistic reasoning. Though several models of PA have been proposed, the development of practical applications is still hindered by the lack of inference procedures and reasoning engines. In this paper, we present a reduction method to compute a recently proposed model of PA called PABA. Using the method we design inference procedures to compute the credulous semantics, the ideal semantics and the grounded semantics for a general class of PABA frameworks, that we refer to as Bayesian PABA frameworks. We also show that, though restricting to Bayesian PABA frameworks, the inference procedures can be used to compute other PA models thanks to simple translations. Finally, we implement the inference procedures to obtain a multi-semantics engine for probabilistic argumentation and demonstrate its usage. [ABSTRACT FROM AUTHOR]

In order to use fuzzy sets in real-world applications, an interpretation for the values of membership functions is needed. The history of fuzzy set theory shows that the interpretation in terms of statistical likelihood is very natural, although the connection between likelihood and probability can be misleading. In this paper, the likelihood interpretation of fuzzy sets is reviewed: it makes fuzzy data and fuzzy inferences perfectly compatible with standard statistical analyses, and sheds some light on the central role played by extension principle and α -cuts in fuzzy set theory. Furthermore, the likelihood interpretation justifies some of the combination rules of fuzzy set theory, including the product and minimum rules for the conjunction of fuzzy sets, as well as the probabilistic-sum and bounded-sum rules for the disjunction of fuzzy sets. [ABSTRACT FROM AUTHOR]

The Banzhaf index is a function determining the power or influence in the decision of a set of agents. The extension of this index to the family of the cooperative games is named Banzhaf value. The relationships of closeness among the agents should modify their power. Games with a priori unions study situations where the closeness relations among the agents are taken into account. In this model the agents are organized in an a priori partition where each element of the partition represents a group of agents with close interests or ideas. The power is determined in two steps, first as a problem among the unions and later, inside each one, the power of each agent is determined. Proximity relations extend this model considering leveled closeness among the agents. In this paper we analyze a version of the Banzhaf value for games with a proximity relation and we show the interest of this value by applying it to the allocation of the power of the political groups in the European Parliament. [ABSTRACT FROM AUTHOR]

Rough Cognitive Networks are granular classifiers stemming from the hybridization of Fuzzy Cognitive Maps and Rough Set Theory. Such cognitive neural networks attempt to quantify the impact of rough granular constructs (i.e., the positive, negative and boundary regions of a target concept) over each decision class for the problem at hand. In rough classifiers, determining the precise granularity level is crucial to compute high prediction rates. Regrettably, learning the similarity threshold parameter requires reconstructing the information granules, which may be time-consuming. In this paper, we put forth a new multiclassifier system classifier named Rough Cognitive Ensembles . The proposed ensemble employs a collection of Rough Cognitive Networks as base classifiers, each operating at a different granularity level. This allows suppressing the requirement of learning a similarity threshold. We evaluate the granular ensemble with 140 traditional classification datasets using different heterogeneous distance functions. After comparing the proposed model to 15 well-known classifiers, the experimental evidence confirms that our scheme yields very promising classification rates. [ABSTRACT FROM AUTHOR]

Answer set programming is a form of declarative programming that can be used to elegantly model various systems. When the available knowledge about these systems is imperfect, however, the resulting programs can be inconsistent. In such cases, it is of interest to find plausible repairs, i.e. plausible modifications to the original program that ensure the existence of at least one answer set. Although several approaches to this end have already been proposed, most of them merely find a repair which is in some sense minimal. In many applications, however, expert knowledge is available which could allow us to identify better repairs. In particular, we consider the scenario where this expert knowledge is formulated as rules of thumb, but no training data is available to learn how these rules of thumb interact. The main question we address in this paper is whether we can then still aggregate the rules of thumb in a useful way. In addition to standard aggregation techniques, we present a novel statistical approach that assigns weights to these rules of thumb, by sampling, in a particular way, from a pool of possible repairs. In particular, we evaluate how frequently each given rule of thumb is violated in the sample of repairs, and use the Z-score of this distribution to set the weight of that rule. We analyze the potential of using expert knowledge in this way, by focusing on a specific case study: Gene Regulatory Networks. We describe the rules of thumb that express available expert knowledge from the biological literature and explain how they can be encoded while repairing inconsistencies. Finally, we experimentally compare the proposed repair strategies using rules of thumb against the baseline strategy of identifying minimal repairs. [ABSTRACT FROM AUTHOR]

Rough sets have often been studied under a three-valued logic framework. In this paper, we attempt to extend the previous study in two ways. Firstly, we extend the previous study from single-granulation to multigranulation. Secondly, we study multigranulation rough set theory from the viewpoint of three-way decision. More precisely, we embody the idea of three-way decision theory in the definition of multigranulation rough set theory. This leads to an axiomatic definition of decision-oriented aggregation operators on 3 = { 0 , 1 2 , 1 } , which are quite different from those conjunctions proposed so far. Moreover, considering that a multigranulation rough set also divides the universe into five disjoint subsets, we present a five-valued semantics for multigranulation rough set model, and a kind of non-deterministic matrices is thus given. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method called 2-probabilities focused combination for combining information about user preferences on products or services in recommender systems based on Dempster–Shafer theory. Regarding this method, in focal sets of mass functions representing user preferences, focal elements with probabilities in top two highest ones are retained and the remaining focal elements are considered as noise and then transferred to the whole set element. To demonstrate the advantages of the new method, a baseline known as 2-points focused combination is selected for performance comparison in a range of experiments using Movielens and Flixster data sets. According to the results of experiments, the new method is more effective in accuracy of recommendations and comparable in computational time. Also, the new method is capable of overcoming the weakness of the baseline because of the ability to generate stable results. [ABSTRACT FROM AUTHOR]

This paper explores the implications of integrating the so-called linear tracing procedure with uncertainty modeling using sets of probabilities for equilibrium refinements under strategic uncertainty. We first reexamine the linear tracing procedure [10] by studying the relationship between priors and Nash equilibria. A prior belongs to the source set of a Nash equilibrium if the linear tracing procedure based on this prior leads to that equilibrium. We show that the source set of any Nash equilibrium is always nonempty and closed, but not generally convex. We then motivate the idea of iteratively applying this procedure to the auxiliary games that are used to model hypothetical reasoning under the procedure. Based on this idea, we propose a notion of robustness for equilibria that allows for modeling of players' initial expectations in the linear tracing procedure through sets of probability distributions. By considering ϵ -contaminated classes for modeling uncertainty, we illustrate this concept with two examples, and then discuss the role of strategic uncertainty in coordination failure. [ABSTRACT FROM AUTHOR]

An important problem in knowledge-based systems is inconsistency handling. This problem has recently been attracting a lot of attention in AI community. In this paper, we tackle the problem of evaluating the amount of conflicts in knowledge bases, and provide a new fine grained inconsistency measure, denoted I MCC , based on maximal consistent sets (MCSes). The main idea consists in quantifying the inconsistency of a knowledge base by considering that all its consistent pieces of information are possible. Furthermore, we provide an epistemic interpretation of our inconsistency measure using the multimodal logic S5 . Then, we show that I MCC satisfies several state-of-the-art postulates. Moreover, we provide an encoding in integer linear programming for computing our inconsistency measure, which is defined from the set of MCSes. We also propose a Partial Max-SAT encoding, which allows us to avoid the computation of the MCSes. Finally, we provide a comparison between I MCC and two related existing inconsistency measures. [ABSTRACT FROM AUTHOR]

In this comment, several paragraphs from the paper "Statistical reasoning with set-valued information: Ontic vs. epistemic views" have been selected and discussed. The selection has been based, on one side, on a personal view of what can be considered the most clarifying points in the paper and, on the other side, on the aspects I am more familiar with and interested in and being quite unequivocally ontic-oriented. For sure, it is a biased selection, but the aim of these comments is that of sharing what I have found to be more appealing within the discussion and I would like to point out in connection with my own expertise. [ABSTRACT FROM AUTHOR]

When arbitrary sets are approximated by more structured sets, it may not be possible to obtain an exact approximation that is equivalent to a given set. Presented here, is a new proposal for a ‘metric’ approach to Rough Sets. We assume some finite measure space is defined on a given universe, and then use it to define various similarity indexes . A set of axioms and the concept of consistency for similarity indexes are also proposed. The core of the paper is a definition of the ‘ optimal ’ or ‘ best ’ approximation with respect to any particular similarity index, and an algorithm to find this optimal approximation by using the Marczewski–Steinhaus Index. This algorithm is also shown to hold for a class of similarity indexes that are consistent with the Marczewski–Steinhaus Index. [ABSTRACT FROM AUTHOR]

The Logic of Approximate Entailment ( LAE ) is a graded counterpart of classical propositional calculus, where conclusions that are only approximately correct can be drawn. This is achieved by equipping the underlying set of possible worlds with a similarity relation. When using this logic in applications, however, a disadvantage must be accepted; namely, in LAE it is not possible to combine conclusions in a conjunctive way. In order to overcome this drawback, we propose in this paper a modification of LAE where, at the semantic level, the underlying set of worlds is moreover endowed with an order structure. The chosen framework is designed in view of possible applications. [ABSTRACT FROM AUTHOR]

As an extension of Pawlak rough set model, decision-theoretic rough set model (DTRS) adopts the Bayesian decision theory to compute the required thresholds in probabilistic rough set models. It gives a new semantic interpretation of the positive, boundary and negative regions by using three-way decisions. DTRS has been widely discussed and applied in data mining and decision making. However, one limitation of DTRS is its lack of ability to deal with numerical data directly. In order to overcome this disadvantage and extend the theory of DTRS, this paper proposes a neighborhood based decision-theoretic rough set model (NDTRS) under the framework of DTRS. Basic concepts of NDTRS are introduced. A positive region related attribute reduct and a minimum cost attribute reduct in the proposed model are defined and analyzed. Experimental results show that our methods can get a short reduct. Furthermore, a new neighborhood classifier based on three-way decisions is constructed and compared with other classifiers. Comparison experiments show that the proposed classifier can get a high accuracy and a low misclassification cost. [ABSTRACT FROM AUTHOR]

Feature Selection (FS) is an important pre-processing step in data mining and classification tasks. The aim of FS is to select a small subset of most important and discriminative features. All the traditional feature selection methods assume that the entire input feature set is available from the beginning. However, online streaming features (OSF) are an integral part of many real-world applications. In OSF, the number of training examples is fixed while the number of features grows with time as new features stream in. A critical challenge for online streaming feature selection (OSFS) is the unavailability of the entire feature set before learning starts. Several efforts have been made to address the OSFS problem, however they all need some prior knowledge about the entire feature space to select informative features. In this paper, the OSFS problem is considered from the rough sets (RS) perspective and a new OSFS algorithm, called OS-NRRSAR-SA, is proposed. The main motivation for this consideration is that RS-based data mining does not require any domain knowledge other than the given dataset. The proposed algorithm uses the classical significance analysis concepts in RS theory to control the unknown feature space in OSFS problems. This algorithm is evaluated extensively on several high-dimensional datasets in terms of compactness, classification accuracy, run-time, and robustness against noises. Experimental results demonstrate that the algorithm achieves better results than existing OSFS algorithms, in every way. [ABSTRACT FROM AUTHOR]

Interpretability is one of the key concepts in many of the applications using the fuzzy rule-based approach. It is well known that there are many different criteria around this concept, the complexity being one of them. In this paper, we focus our efforts in reducing the complexity of the fuzzy rule sets. One of the most interesting approaches for learning fuzzy rules is the iterative rule learning approach. It is mainly characterized by obtaining rules covering few examples in final stages, being in most cases useless to represent the knowledge. This behavior is due to the specificity of the extracted rules, which eventually creates more complex set of rules. Thus, we propose a modified version of the iterative rule learning algorithm in order to extract simple rules relaxing this natural trend. The main idea is to change the rule extraction process to be able to obtain more general rules, using pruned searching spaces together with a knowledge simplification scheme able to replace learned rules. The experimental results prove that this purpose is achieved. The new proposal reduces the complexity at both, the rule and rule base levels, maintaining the accuracy regarding to previous versions of the algorithm. [ABSTRACT FROM AUTHOR]

The notion of preference is crucial in many fields. This justifies the development of many formalisms for preferences representation such as CP-nets, qualitative choice logic and its extensions. Preferences help to choose the best option in decision making, to compare between arguments in argumentation theory, etc. In this paper, we establish a link between a preference formalism, called Prioritized Qualitative Choice Logic ( PQCL ) and argumentation theory. We show that for any set of preferences expressed using PQCL (called PQCL theory), a Value-based Argumentation Framework ( VAF ) can be built. However, we point out some problems related to the evaluation of arguments which does not guarantee the correspondence between elements of PQCL theory and those of its associated VAF . We show that the major problem is due to the evaluation of arguments defined in existing argumentation frameworks, where an absolute status is assigned to each argument: objectively (or skeptically) accepted if it belongs to every extension, subjectively (or credulously) accepted if it is in some extensions and not in others and rejected if it does not belong to any extension. To deal with this problem, we propose to revise the evaluation of arguments in the corresponding VAF . As a result, there is a direct relationship between preferred extensions of the corresponding VAF and preferred models of a set of preferences expressed using PQCL . In addition, rank ordering the set of arguments is possible. The relationship between the two formalisms is interesting since on the one hand, it points out that one should be careful in using argumentation theory for decision making purposes or in formalizing a given problem as an argumentation framework and on the other hand, it makes it possible to use an argumentation framework for preference elicitation. [ABSTRACT FROM AUTHOR]

When looking for a propositional abductive explanation of a given set of manifestations, an ordering between possible solutions is often assumed. While the complexity of computing optimal solutions is already known, in this paper we consider second-best solutions with respect to different orderings, and different definitions of what a second-best solution is: an optimal solution not already found, or a solution that is optimal among the ones not previously found. [ABSTRACT FROM AUTHOR]

It is desirable to identify the degree of responsibility of each part of a knowledge base for the inconsistency of that base to make some necessary trade-off decisions on restoring the consistency of that base. In this paper, we propose a measurement for the degree of responsibility of each formula in a knowledge base for the inconsistency of that base. This measurement is given in terms of minimal inconsistent subsets of a knowledge base. Moreover, it can be well explained in the context of causality and responsibility presented by Chockler and Halpern [1] . [ABSTRACT FROM AUTHOR]

This paper studies the structure of qualitative capacities, that is, monotonic set-functions, when they range on a finite totally ordered scale equipped with an order-reversing map. These set-functions correspond to general representations of uncertainty, as well as importance levels of groups of criteria in multiple-criteria decision-making. We show that any capacity or fuzzy measure ranging on a qualitative scale can be viewed both as the lower bound of a set of possibility measures and the upper bound of a set of necessity measures (a situation somewhat similar to the one of quantitative capacities with respect to imprecise probability theory). We show that any capacity is characterized by a non-empty class of possibility measures having the structure of an upper semi-lattice. The lower bounds of this class are enough to reconstruct the capacity, and the number of them is characteristic of its complexity. An algorithm is provided to compute the minimal set of possibility measures dominating a given capacity. This algorithm relies on the representation of the capacity by means of its qualitative Möbius transform, and the use of selection functions of the corresponding focal sets. We provide the connection between Sugeno integrals and lower possibility measures. We introduce a sequence of axioms generalizing the maxitivity property of possibility measures, and related to the number of possibility measures needed for this reconstruction. In the Boolean case, capacities are closely related to non-regular modal logics and their neighborhood semantics can be described in terms of qualitative Möbius transforms. [ABSTRACT FROM AUTHOR]

Fuzzy answer set programming (FASP) is a generalization of answer set programming (ASP) in which propositions are allowed to be graded. Little is known about the computational complexity of FASP and almost no techniques are available to compute the answer sets of a FASP program. In this paper, we analyze the computational complexity of FASP under Łukasiewicz semantics. In particular we show that the complexity of the main reasoning tasks is located at the first level of the polynomial hierarchy, even for disjunctive FASP programs for which reasoning is classically located at the second level. Moreover, we show a reduction from reasoning with such FASP programs to bilevel linear programming, thus opening the door to practical applications. For definite FASP programs we can show P-membership. Surprisingly, when allowing disjunctions to occur in the body of rules – a syntactic generalization which does not affect the expressivity of ASP in the classical case – the picture changes drastically. In particular, reasoning tasks are then located at the second level of the polynomial hierarchy, while for simple FASP programs, we can only show that the unique answer set can be found in pseudo-polynomial time. Moreover, the connection to an existing open problem about integer equations suggests that the problem of fully characterizing the complexity of FASP in this more general setting is not likely to have an easy solution. [ABSTRACT FROM AUTHOR]

There is extensive theoretical work on measures of inconsistency for arbitrary formulae in knowledge bases. Many of these are defined in terms of the set of minimal inconsistent subsets (MISes) of the base. However, few have been implemented or experimentally evaluated to support their viability, since computing all MISes is intractable in the worst case. Fortunately, recent work on a related problem of minimal unsatisfiable sets of clauses (MUSes) offers a viable solution in many cases. In this paper, we begin by drawing connections between MISes and MUSes through algorithms based on a MUS generalization approach and a new optimized MUS transformation approach to finding MISes. We implement these algorithms, along with a selection of existing measures for flat and stratified knowledge bases, in a tool called mimus . We then carry out an extensive experimental evaluation of mimus using randomly generated arbitrary knowledge bases. We conclude that these measures are viable for many large and complex random instances. Moreover, they represent a practical and intuitive tool for inconsistency handling. [ABSTRACT FROM AUTHOR]

Traditional c-means clustering partitions a group of objects into a number of non-overlapping sets. Rough sets provide more flexible and objective representation than classical sets with hard partition and fuzzy sets with subjective membership function for a given dataset. Rough c-means clustering and its extensions were introduced and successfully applied in many real life applications in recent years. Each cluster is represented by a reasonable pair of lower and upper approximations. However, the most available algorithms pay no attention to the influence of the imbalanced spatial distribution within a cluster. The limitation of the mean iterative calculation function, with the same weight for all the data objects in a lower or upper approximation, is analyzed. A hybrid imbalanced measure of distance and density for the rough c-means clustering is defined, and a modified rough c-means clustering algorithm is presented in this paper. To evaluate the proposed algorithm, it has been applied to several real world data sets from UCI. The validity of this algorithm is demonstrated by the results of comparative experiments. [ABSTRACT FROM AUTHOR]

This note is a rejoinder on our paper in this issue. It attempts to provide some clarifications and thoughts in connection with the discussions/comments made about it by Didier Dubois and Sébastien Destercke. We hope our comments are at the level of the discussants'. [ABSTRACT FROM AUTHOR]

This short paper discusses the contributions made to the featured section on Low Quality Data. We further refine the distinction between the ontic and epistemic views of imprecise data in statistics. We also question the extent to which likelihood functions can be viewed as belief functions. Finally we comment on the data disambiguation effect of learning methods, relating it to data reconciliation problems. [ABSTRACT FROM AUTHOR]

This paper considers the problem of learning multinomial distributions from a sample of independent observations. The Bayesian approach usually assumes a prior Dirichlet distribution about the probabilities of the different possible values. However, there is no consensus on the parameters of this Dirichlet distribution. Here, it will be shown that this is not a simple problem, providing examples in which different selection criteria are reasonable. To solve it the Imprecise Dirichlet Model (IDM) was introduced. But this model has important drawbacks, as the problems associated to learning from indirect observations. As an alternative approach, the Imprecise Sample Size Dirichlet Model (ISSDM) is introduced and its properties are studied. The prior distribution over the parameters of a multinomial distribution is the basis to learn Bayesian networks using Bayesian scores. Here, we will show that the ISSDM can be used to learn imprecise Bayesian networks, also called credal networks when all the distributions share a common graphical structure. Some experiments are reported on the use of the ISSDM to learn the structure of a graphical model and to build supervised classifiers. [ABSTRACT FROM AUTHOR]

In information processing tasks, sets may have a conjunctive or a disjunctive reading. In the conjunctive reading, a set represents an object of interest and its elements are subparts of the object, forming a composite description. In the disjunctive reading, a set contains mutually exclusive elements and refers to the representation of incomplete knowledge. It does not model an actual object or quantity, but partial information about an underlying object or a precise quantity. This distinction between what we call ontic vs. epistemic sets remains valid for fuzzy sets, whose membership functions, in the disjunctive reading are possibility distributions, over deterministic or random values. This paper examines the impact of this distinction in statistics. We show its importance because there is a risk of misusing basic notions and tools, such as conditioning, distance between sets, variance, regression, etc. when data are set-valued. We discuss several examples where the ontic and epistemic points of view yield different approaches to these concepts. [ABSTRACT FROM AUTHOR]

Abstract: Recently, much attention has been given to multi-granulation rough sets (MGRS) and different kinds of multi-granulation rough set models have been developed from various viewpoints. In this paper, we propose four types of multi-granulation covering rough set (MGCRS) models under covering approximation space, where a target concept is approximated by employing the maximal or minimal descriptors of objects in a given universe of discourse U. And then, we investigate a number of basic properties of the four types of MGCRS models, and discuss the relationships and differences among the classical MGRS model and our MGCRS models. Moreover, the conditions for two distinct MGCRS models which produce identical lower and upper approximations of a target concept in a covering approximation space are also studied. Finally, the relationships among the four types of MGCRS models are explored. We find that for any subset , the lower approximations of X and the upper approximations of X under the four types of MGCRS models can construct a lattice, if we consider the binary relation of inclusion. [Copyright &y& Elsevier]

Abstract: In this paper, we address the problem of identifying the potential sources of conflict between information sources in the framework of belief function theory. To this aim, we propose a decomposition of the global measure of conflict as a function defined over the power set of the discernment frame. This decomposition, which associates a part of the conflict to some hypotheses, allows identifying the origin of conflict, which is hence considered as “local” to some hypotheses. This is more informative than usual global measures of conflict or disagreement between sources. Having shown the unicity of this decomposition, we illustrate its use on two examples. The first one is a toy example where the fact that conflict is mainly brought by one hypothesis allows identifying its origin. The second example is a real application, namely robot localization, where we show that focusing the conflict measure on the “favored” hypothesis (the one that would be decided) helps us to robustify the fusion process. [Copyright &y& Elsevier]

This paper is a fine review of various aspects related to the statistical handling of "ontic" random fuzzy sets by the means of appropriate distances. It is quite comprehensive and helpful, as it clarifies the status of fuzzy sets in such methods, explains the advantages of using a distance-based approach, specifies the pitfalls in which one should not fall when dealing with "ontic" random fuzzy sets and provides some illustration of practical computations. Not being a statistician but an occasional user of statistics, my discussion will mainly focus on this more practical aspect. [ABSTRACT FROM AUTHOR]