18 research outputs found

    Bandler–Kohout Subproduct With Yager’s Classes of Fuzzy Implications

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    The Bandler-Kohout subproduct (BKS) inference mechanism is one of the two established fuzzy relational inference (FRI) mechanisms; the other one being Zadeh's compositional rule of inference (CRI). Both these FRIs are known to possess many desirable properties. It can be seen that many of these desirable properties are due to the rich underlying structure, viz., the residuated algebra, from which the employed operations come. In this study, we discuss the BKS relational inference system, with the fuzzy implication interpreted as Yager's classes of implications, which do not form a residuated structure on [0,1] . We show that many of the desirable properties, viz., interpolativity, continuity, robustness, which are known for the BKS with residuated implications, are also available under this framework, thus expanding the choice of operations available to practitioners. Note that, to the best of the authors' knowledge, this is the first attempt at studying the suitability of an FRI where the operations come from a nonresiduated structure

    Bandler-Kohout Subproduct with Yager’s Families of Fuzzy Implications: A Comprehensive Study

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    Approximate reasoning schemes involving fuzzy sets are one of the best known applications of fuzzy logic in the wider sense. Fuzzy Inference Systems (FIS) or Fuzzy Inference Mechanisms (FIM) have many degrees of freedom, viz., the underlying fuzzy partition of the input and output spaces, the fuzzy logic operations employed, the fuzzification and defuzzification mechanism used, etc. This freedom gives rise to a variety of FIS with differing capabilities

    Lower Approximations by Fuzzy Consequence Operators

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    Peer ReviewedPostprint (author's final draft

    Bornological structures on many-valued sets

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    We introduce an approach to the concept of bornology in the framework of many-valued mathematical structures and develop the basics of the theory of many-valued bornological spaces and initiate the study of the category of many-valued bornological spaces and appropriately defined bounded "mappings" of such spaces. A scheme for constructing many-valued bornologies with prescribed properties is worked out. In particular, this scheme allows to extend an ordinary bornology of a metric space to a many-valued bornology on it

    Fifty years of similarity relations: a survey of foundations and applications

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    On the occasion of the 50th anniversary of the publication of Zadeh's significant paper Similarity Relations and Fuzzy Orderings, an account of the development of similarity relations during this time will be given. Moreover, the main topics related to these fuzzy relations will be reviewed.Peer ReviewedPostprint (author's final draft

    Bisimulations for Kripke models of Fuzzy Multimodal Logics

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    The main objective of the dissertation is to provide a detailed study of several different types of simulations and bisimulations for Kripke models of fuzzy multimodal logics. Two types of simulations (forward and backward) and five types of bisimulations (forward, backward, forward-backward, backward-forward and regular) are presented hereby. For each type of simulation and bisimulation, an algorithm is created to test the existence of the simulation or bisimulation and, if it exists, the algorithm computes the greatest one. The dissertation presents the application of bisimulations in the state reduction of fuzzy Kripke models, while preserving their semantic properties. Next, weak simulations and bisimulations were considered and the Hennessy-Milner property was examined. Finally, an algorithm was created to compute weak simulations and bisimulations for fuzzy Kripke models over locally finite algebras

    On similarity in fuzzy description logics

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    This paper is a contribution to the study of similarity relations between objects represented as attribute-value pairs in Fuzzy Description Logics . For this purpose we use concrete domains in the fuzzy description logic IALCEF(D)IALCEF(D) associated either with a left-continuous or with a finite t-norm. We propose to expand this fuzzy description logic by adding a Similarity Box (SBox) including axioms expressing properties of fuzzy equalities. We also define a global similarity between objects from similarities between the values of each object attribute (local similarities) and we prove that the global similarity defined using a t-norm inherits the usual properties of the local similarities (reflexivity, symmetry or transitivity). We also prove a result relative to global similarities expressing that, in the context of the logic MTL∀, similar objects have similar properties, being these properties expressed by predicate formulas evaluated in these object

    Application of fuzzy techniques to biomedical images

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    The main goal of this work is to bring together Fuzzy Logic techniques and Biomedical images analysis, linking this two fields through an image segmentation problem approached by a Fuzzy c-Means algorithm. This work has two main cores. The first one is a formal structural analysis of some Fuzzy Logic concepts within the theory of Indistinguishabilitty Operators. The main actors of this part will be indistinguishability operators, sets of extensional fuzzy subsets, upper approximation operators and lower approximation operators. All these concepts will be explained in depth further in this work. The second core is a practical application of the Fuzzy c-Means algorithm to segmentate biomedical images of mammographies and bone marrow microscopical captures

    Fitting aggregation operators to data

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    Theoretical advances in modelling aggregation of information produced a wide range of aggregation operators, applicable to almost every practical problem. The most important classes of aggregation operators include triangular norms, uninorms, generalised means and OWA operators.With such a variety, an important practical problem has emerged: how to fit the parameters/ weights of these families of aggregation operators to observed data? How to estimate quantitatively whether a given class of operators is suitable as a model in a given practical setting? Aggregation operators are rather special classes of functions, and thus they require specialised regression techniques, which would enforce important theoretical properties, like commutativity or associativity. My presentation will address this issue in detail, and will discuss various regression methods applicable specifically to t-norms, uninorms and generalised means. I will also demonstrate software implementing these regression techniques, which would allow practitioners to paste their data and obtain optimal parameters of the chosen family of operators.<br /
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