The individual ergodic theorem on the IF-events with product

The ergodic theory and particularly the individual ergodic theorem were studied in many structures. Recently the individual ergodic theorem has been proved for MV-algebras of fuzzy sets (Riečan in Czech Math J 50(125):673–680, 2000; Riečan and Neubrunn in Integral, measure, and ordering. Kluwer, Dordrecht, 1997) and even in general MV-algebras (Jurečková in Int J Theor Phys 39:757–764, 2000). The notion of almost everywhere equality of observables was introduced by Riečan and Jurečková (Int J Theor Phys 44:1587–1597, 2005). They proved that the limit of Cesaro means is an invariant observable for P-observables. In Lendelová (Int J Theor Phys 45(5):915–923, 2006c) showed that the assumption of P-observable can be omitted. In this paper we prove the individual ergodic theorem on family of IF-events and show that each P {\mathcal{P}} -preserving transformation in this family can be expressed by two corresponding P^\flat,P^\sharp {\mathcal{P}}^\flat,{\mathcal{P}}^\sharp -preserving transformations in tribe T. {\mathcal{T}}.     

Convex combinations of strict t-norms

Alsina, Frank, and Schweizer posed a question whether a non-trivial convex combination of triangular norms can ever be a triangular norm. In this paper we deal with the class of strict t-norms with well-defined first partial derivatives along their zero borders. We show that the answer to the question is negative for certain couples of such t-norms and we state out possible further research.     

A multi-granular linguistic model for management decision-making in performance appraisal

The performance appraisal is a relevant process to keep and improve the competitiveness of companies in nowadays. In spite of this relevance, the current performance appraisal models are not sufficiently well-defined either designed for the evaluation framework in which they are defined. This paper proposes a performance appraisal model where the assessments are modelled by means of linguistic information provided by different sets of reviewers in order to manage the uncertainty and subjectivity of such assessments. Therefore, the reviewers could express their assessments in different linguistic scales according to their knowledge about the evaluated employees, defining a multi-granular linguistic evaluation framework. Additionally, the proposed model will manage the multi-granular linguistic labels provided by appraisers in order to compute collective assessments about the employees that will be used by the management team to make the final decision about them.     

A new fast prototype selection method based on clustering

In supervised classification, a training set T is given to a classifier for classifying new prototypes. In practice, not all information in T is useful for classifiers, therefore, it is convenient to discard irrelevant prototypes from T. This process is known as prototype selection, which is an important task for classifiers since through this process the time for classification or training could be reduced. In this work, we propose a new fast prototype selection method for large datasets, based on clustering, which selects border prototypes and some interior prototypes. Experimental results showing the performance of our method and comparing accuracy and runtimes against other prototype selection methods are reported.     

Interoperability results for Semantic Web technologies using OWL as the interchange language

Using Semantic Web technologies in complex scenarios requires that such technologies correctly interoperate by interchanging ontologies using the RDF(S) and OWL languages. This interoperability is not straightforward because of the high heterogeneity in Semantic Web technologies and, while the number of such technologies grows, affordable mechanisms for evaluating Semantic Web technology interoperability are needed to comprehend the current and future interoperability of Semantic Web technologies.This paper presents the OWL Interoperability Benchmarking, an international benchmarking activity that involved the evaluation of the interoperability of different Semantic Web technologies using OWL as the interchange language. It describes the evaluation resources used in this benchmarking activity, the OWL Lite Import Benchmark Suite and the IBSE tool, and presents how to use them for evaluating the OWL interoperability of Semantic Web technologies. Moreover, the paper offers an overview of the OWL interoperability results of the eight tools participating in the benchmarking: one ontology-based annotation tool (GATE), three ontology frameworks (Jena, KAON2, and SWI-Prolog), and four ontology development tools (Protégé Frames, Protégé OWL, SemTalk, and WebODE).     

APROMORE: An advanced process model repository

Business process models are becoming available in large numbers due to their widespread use in many industrial applications such as enterprise and quality engineering projects. On the one hand, this raises a challenge as to their proper management: how can it be ensured that the proper process model is always available to the interested stakeholder? On the other hand, the richness of a large set of process models also offers opportunities, for example with respect to the re-use of existing model parts for new models. This paper describes the functionality and architecture of an advanced process model repository, named APROMORE. This tool brings together a rich set of features for the analysis, management and usage of large sets of process models, drawing from state-of-the art research in the field of process modeling. A prototype of the platform is presented in this paper, demonstrating its feasibility, as well as an outlook on the further development of APROMORE.     

A proposal for student modeling based on ontologies and diagnosis rules

The advances in the educational field and the high complexity of student modeling have provoked it to be one of the aspects more investigated in Intelligent Tutoring Systems (ITSs). The Student Models (SMs) should not only represent the student’s knowledge, but rather they should reflect, as faithfully as possible, the student’s reasoning process. To facilitate this goal, in this article a new approach to student modeling is proposed that benefits from the advantages of Ontological Engineering, advancing in the pursue of a more granular and complete knowledge representation. It’s focused, mainly, on the SM cognitive diagnosis process, and we present a method providing a rich diagnosis about the student’s knowledge state – especially, about the state of learning objectives reached or not. The main goal is to achieve SMs with a good adaptability to the student’s features and a high flexibility for its integration in varied ITSs.