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Fuzzy Switch Graphs (FSG s) are reactive fuzzy graphs that model systems in which accessibility relations and fuzzy values are changed whenever an edge is crossed [19]. Reversal Fuzzy Switch Graphs (R F S G s) were presented in [6] and model fuzzy reactive systems which provide the activation and deactivation of resources, a functionality that FSG s do not offer [19]. Activation and deactivation of arrows in a switch graph makes its applicability wider in fields like computer science and engineering. In this sense, the definition of operations for R F S G s is an important issue, since it enables to understand the algebraic structure of these graphs and allows to generate new model of systems from the previous one. This paper introduces some aggregation-based operations: union, intersection and extension for R F S G s. For each operation, the paper verify some properties. It ends with an application for engineering. [ABSTRACT FROM AUTHOR]

Lazy evaluations are playing important roles in various fields of computer science including hardware design, programming, decision making. In this paper one of the most known and used fuzzy logic system, the Łukasiewicz logic is considered. Pruning algorithms are presented to quicken the evaluations of logical formulae in Łukasiewicz logic by cutting out those branches of the formula tree that have no influence on the final result for some reasons. Correctness of the algorithm is also proven. [ABSTRACT FROM AUTHOR]

Abstract: The paper describes a logical framework for handling uncertain spatial information, and merging it when it comes from multiple sources. For this purpose, we use a simple logical formalization for spatial ontologies and for property ontologies relative to different universes of discourse (these ontologies only involve subsumption and mutual exclusiveness relations), since spatial information typically associates properties to sets of parcels that are themselves described in terms of the spatial and/or property vocabularies appearing in the ontologies. Apart from the ontological information describing relations between vocabulary labels, we propose to represent a piece of spatial information as a pair, called “attributive formula”, associating a property formula to a set of parcels (represented by a spatial formula). A set of inference rules is given in order to be able to reason from these attributive pairs. Then, we examine how uncertainty can be encoded in attributive information, using possibilistic logic in a reified manner with respect to parcels. Another important issue pointed out in this paper is that there are two ways to link a property to an area. A first meaning is that the property is true everywhere in the area, a second meaning is that the property is at least true somewhere in the area. This distinction is necessary in order to be able to use both ontological information (which can be encoded by “everywhere” attributive-formulas) and attributive information (which contain the two kinds of attributive-formulas). Lastly, the paper studies how information fusion problems can be handled in the context of spatial data. The problems encountered do not come only from the uncertainty and the possible inconsistency of information as in any information fusion situations, but also from the fact that sources may use different space partitions and may not explicitly specify the somewhere or everywhere reading associated to the information. [Copyright &y& Elsevier]

Abstract: The problem of how to merge, by means of a function, a family of metrics into a single one was studied deeply by J. Borsík and J. Doboš [On a product of metric spaces, Math. Slovaca 31 (1981) 193–205]. Motivated by the utility of quasi-metrics in Computer Science, the Borsík and Doboš study was extended to the quasi-metric context in such a way that a general description of how to combine through a function a family of quasi-metrics in order to obtain a single one as output was provided by G. Mayor and O. Valero [Aggregation of asymmetric distances in Computer Science, Inform. Sci. 180 (2010) 803–812]. In this paper, inspired by the fact that fixed point theory provides an efficient tool in many fields of applied sciences, we have proved fixed point theorems for a new type of contractions, that we have called projective -contractions, defined between quasi-metric spaces that have been obtained via the so-called quasi-metric aggregation functions. Moreover, we show that the new fixed point results are useful to discuss, on the one hand, the complexity of a collection of recursive programs whose running times of computing hold a coupled system of recurrence equations and, on the other hand, to analyze simultaneously the complexity and the correctness of recursive algorithms that perform a computation by means of a recursive denotational specification. [Copyright &y& Elsevier]

Abstract: Recently, Durante and Jaworski (2008) [6] have proved that the class of absolutely continuous copulas with a given diagonal section is non-empty in case that the diagonal function is such that the set of points where this coincides with the identity function has null-measure. In this paper, we show that if we consider sub-diagonals (or super-diagonals), then the framework changes. Concretely, for each sub-diagonal function there exists an absolutely continuous copula having this function as sub-diagonal section. [Copyright &y& Elsevier]

Abstract: The -migrative triangular subnorms, where T stands for the three prototype triangular norms (namely the product, the Łukasiewicz t-norm and the minimum), are investigated in detail. The paper gives necessary and sufficient conditions under which a triangular subnorm with a continuous additive generator is -migrative with respect to any of the three prototype triangular norms. [Copyright &y& Elsevier]

Abstract: The main purpose of this paper is to solve the functional equation , for and a pair of a t-norm T and a t-conorm S. This equation arises when we consider a convex linear combination of a t-norm and a t-conorm, and set out the problem of finding the intersection of the segments determined by the pairs and . [Copyright &y& Elsevier]

Abstract: In recent years, some new construction methods of fuzzy implications from other given ones have been proposed. One of them, the so-called threshold generation method, preserves important properties such as the exchange principle or the law of importation under some minimal conditions. This method is based on an adequate scaling on the second variable of the two initial fuzzy implications. In this paper, we propose a new method to generate fuzzy implications from two given ones in the same spirit of the threshold generation method but now through an adequate scaling on the first variable of the given fuzzy implications. The new implications, called vertical threshold generated implications, are deeply studied focusing on the preservation of the most common properties of fuzzy implications from the initial ones to the generated implication. Moreover, they are fully characterized by means of the -vertical section of the implication. [Copyright &y& Elsevier]

Abstract: Fuzzy interpolation enhances the robustness of fuzzy systems and helps to reduce systems complexity. Although a number of important fuzzy rule interpolation approaches have been proposed in the literature, most of these approaches cannot be expressed in a closed form. This is usually caused by the effort to avoid possible invalid interpolated results. This paper proposes a different fuzzy rule interpolation approach. It not only can be represented in a closed form but also guarantees that the interpolated results are valid fuzzy sets. This approach is based on a direct use of the extension principle which has been widely utilised for the development of a variety of fuzzy systems. The mathematical properties of the proposed approach are analysed by taking the advantage of the closed form representation. This approach has been applied to a practical problem of predicting diarrhoeal disease rates in remote villages. The results demonstrate the potential of the proposed work in enhancing the robustness of fuzzy interpolation. [Copyright &y& Elsevier]

Abstract: The inherently multidimensional problem of evaluating the complexity of an image is of a certain relevance in both computer science and cognitive psychology. Computer scientists usually analyze spatial dimensions in order to deal with automatic vision problems, such as feature extraction. Psychologists seem more interested in the temporal dimension of complexity, as a means to explore attentional models. Is it possible to define, by merging both approaches, a more general index of visual complexity? The aim of this paper is the definition of objective measures of image complexity that fits with the so named perceived time. Towards the end we have defined a fuzzy mathematical model of visual complexity, based on fuzzy measures of entropy; the results obtained by applying this model to a set of pictorial images present a strong correlation with the outcomes of an experiment with human subjects, based on variation of subjective temporal estimations associated with changes in visual attentional load, which is also described herein. [Copyright &y& Elsevier]

Abstract: Traditionally, flexible querying systems are supported by a logical framework that is based on satisfaction degrees. Alternatively, certainty about query satisfaction can also be modelled by possibility and necessity measures. This approach was extended by our group in order to handle the cases of missing information more adequately. In this paper, it is presented how our extended logical framework can be used to support flexible querying on conventional relational databases. The handling of preferences, both inside elementary query conditions and between query conditions, is presented, as well as the extension of the traditional selection, projection and join operators. Motivated examples are provided to illustrate the used concepts. [Copyright &y& Elsevier]

Abstract: Object-relational systems combine the robustness of the relational data model with the powerful modeling capabilities of the object-oriented paradigm. Object-relational database management systems (ORDBMS) allow us to implement a set of relations to store and retrieve objects coming from a hierarchy of classes. If we want to manipulate imprecise objects in this kind of systems, we have to properly extend them. In this paper we introduce pOSTgRESQL Fuzzy Object Relational DataBase (pg4DB), a framework that supports the management of fuzzy objects in ORDBMS such as PostgreSQL. As we will see pg4DB allows users to create imprecise objects and operate with them using object-relational SQL compliant sentences. [Copyright &y& Elsevier]