18 research outputs found

    On the distributivity equation for uni-nullnorms

    Get PDF
    summary:A uni-nullnorm is a special case of 2-uninorms obtained by letting a uninorm and a nullnorm share the same underlying t-conorm. This paper is mainly devoted to solving the distributivity equation between uni-nullnorms with continuous Archimedean underlying t-norms and t-conorms and some binary operators, such as, continuous t-norms, continuous t-conorms, uninorms, and nullnorms. The new results differ from the previous ones about the distributivity in the class of 2-uninorms, which have not yet been fully characterized

    An extension of the ordering based on nullnorms

    Get PDF
    summary:In this paper, we generally study an order induced by nullnorms on bounded lattices. We investigate monotonicity property of nullnorms on bounded lattices with respect to the FF-partial order. Also, we introduce the set of incomparable elements with respect to the F-partial order for any nullnorm on a bounded lattice. Finally, we investigate the relationship between the order induced by a nullnorm and the distributivity property for nullnorms

    Migrativity properties of 2-uninorms over semi-t-operators

    Get PDF
    summary:In this paper, we analyze and characterize all solutions about α\alpha-migrativity properties of the five subclasses of 2-uninorms, i. e. CkC^{k}, Ck0C^{0}_{k}, Ck1C^{1}_{k}, C10C^{0}_{1}, C01C^{1}_{0}, over semi-t-operators. We give the sufficient and necessary conditions that make these α\alpha-migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for GCkG\in C^{k}, the α\alpha-migrativity of GG over a semi-t-operator Fμ,νF_{\mu,\nu} is closely related to the α\alpha-section of Fμ,νF_{\mu,\nu} or the ordinal sum representation of t-norm and t-conorm corresponding to Fμ,νF_{\mu,\nu}. But for the other four categories, the α\alpha-migrativity over a semi-t-operator Fμ,νF_{\mu,\nu} is fully determined by the α\alpha-section of Fμ,νF_{\mu,\nu}

    Distributivity of ordinal sum implications over overlap and grouping functions

    Get PDF
    summary:In 2015, a new class of fuzzy implications, called ordinal sum implications, was proposed by Su et al. They then discussed the distributivity of such ordinal sum implications with respect to t-norms and t-conorms. In this paper, we continue the study of distributivity of such ordinal sum implications over two newly-born classes of aggregation operators, namely overlap and grouping functions, respectively. The main results of this paper are characterizations of the overlap and/or grouping function solutions to the four usual distributive equations of ordinal sum fuzzy implications. And then sufficient and necessary conditions for ordinal sum implications distributing over overlap and grouping functions are given

    On triangular norms and uninorms definable in ŁΠ12

    Get PDF
    AbstractIn this paper, we investigate the definability of classes of t-norms and uninorms in the logic ŁΠ12. In particular we provide a complete characterization of definable continuous t-norms, weak nilpotent minimum t-norms, conjunctive uninorms continuous on [0,1), and idempotent conjunctive uninorms, and give both positive and negative results concerning definability of left-continuous t-norms (and uninorms). We show that the class of definable uninorms is closed under construction methods as annihilation, rotation and rotation–annihilation. Moreover, we prove that every logic based on a definable uninorm is in PSPACE, and that any finitely axiomatizable logic based on a class of definable uninorms is decidable. Finally we show that the Uninorm Mingle Logic (UML) and the Basic Uninorm Logic (BUL) are finitely strongly standard complete w.r.t. the related class of definable left-continuous conjunctive uninorms

    Fitting aggregation operators to data

    Full text link
    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 /

    Aggregation functions: Means

    Get PDF
    The two-parts state-of-art overview of aggregation theory summarizes the essential information concerning aggregation issues. Overview of aggregation properties is given, including the basic classification of aggregation functions. In this first part, the stress is put on means, i.e., averaging aggregation functions, both with fixed arity (n-ary means) and with open arity (extended means).

    On the distributivity of T-power based implications

    Get PDF
    Due to the fact that Zadeh's quantifiers constitute the usual method to modify fuzzy propositions, the so-called family of T-power based implications was proposed. In this paper, the four basic distributive laws related to T-power based fuzzy implications and fuzzy logic operations (t-norms and t-conorms) are deeply studied. This study shows that two of the four distributive laws of the T-power based implications have a unique solution, while the other two have multiple solutions
    corecore