The Experts below are selected from a list of 2331 Experts worldwide ranked by ideXlab platform

Joan Torrens - One of the best experts on this subject based on the ideXlab platform.

  • t operators and uninorms on a finite Totally Ordered Set
    International Journal of Intelligent Systems, 1999
    Co-Authors: Margarita Mas, Gaspar Mayor, Joan Torrens
    Abstract:

    This paper presents a detailed study of two classes of operators on a finite Totally Ordered Set of labels L: t-operators and uninorms. Both kinds of operators (on [0, 1]) are introduced as generalizations of t-norms and t-conorms. We characterize these operators on L as special combinations of operators of directed algebras in a similar way as they are characterized in the case of [0, 1] as special combinations of t-norms and t-conorms. We also study duality of these operators with respect to the only negation N on L, and we give the number of different t-operators and uninorms that exist on L, related to the number of elements in L. ©1999 John Wiley & Sons, Inc.

Morgan Weiler - One of the best experts on this subject based on the ideXlab platform.

  • pattern avoidance in poSet permutations
    Order, 2016
    Co-Authors: Sam Hopkins, Morgan Weiler
    Abstract:

    We extend the concept of pattern avoidance in permutations on a Totally Ordered Set to pattern avoidance in permutations on partially Ordered Sets. The number of permutations on P that avoid the pattern p is denoted A v P (p). We extend a proof of Simion and Schmidt to show that A v P (132)=A v P (123) for any poSet P, and we exactly classify the poSets for which equality holds.

  • pattern avoidance in permutations on the boolean lattice
    arXiv: Combinatorics, 2012
    Co-Authors: Sam Hopkins, Morgan Weiler
    Abstract:

    We extend the concept of pattern avoidance in permutations on a Totally Ordered Set to pattern avoidance in permutations on partially Ordered Sets. The number of permutations on P that avoid the pattern a is denoted Av_P(a). We extend a proof of Simion and Schmidt to show that Av_P(123) <= Av_P(132) for any poSet P, and we exactly classify the poSets for which equality holds. We also give asymptotically close bounds on the number of permutations on the Boolean lattice that avoid the pattern {1}{1,2}{2}.

  • pattern avoidance in poSet permutations
    arXiv: Combinatorics, 2012
    Co-Authors: Sam Hopkins, Morgan Weiler
    Abstract:

    We extend the concept of pattern avoidance in permutations on a Totally Ordered Set to pattern avoidance in permutations on partially Ordered Sets. The number of permutations on $P$ that avoid the pattern $\pi$ is denoted $Av_P(\pi)$. We extend a proof of Simion and Schmidt to show that $Av_P(132) \leq Av_P(123)$ for any poSet $P$, and we exactly classify the poSets for which equality holds.

Margarita Mas - One of the best experts on this subject based on the ideXlab platform.

  • t operators and uninorms on a finite Totally Ordered Set
    International Journal of Intelligent Systems, 1999
    Co-Authors: Margarita Mas, Gaspar Mayor, Joan Torrens
    Abstract:

    This paper presents a detailed study of two classes of operators on a finite Totally Ordered Set of labels L: t-operators and uninorms. Both kinds of operators (on [0, 1]) are introduced as generalizations of t-norms and t-conorms. We characterize these operators on L as special combinations of operators of directed algebras in a similar way as they are characterized in the case of [0, 1] as special combinations of t-norms and t-conorms. We also study duality of these operators with respect to the only negation N on L, and we give the number of different t-operators and uninorms that exist on L, related to the number of elements in L. ©1999 John Wiley & Sons, Inc.

Sam Hopkins - One of the best experts on this subject based on the ideXlab platform.

  • pattern avoidance in poSet permutations
    Order, 2016
    Co-Authors: Sam Hopkins, Morgan Weiler
    Abstract:

    We extend the concept of pattern avoidance in permutations on a Totally Ordered Set to pattern avoidance in permutations on partially Ordered Sets. The number of permutations on P that avoid the pattern p is denoted A v P (p). We extend a proof of Simion and Schmidt to show that A v P (132)=A v P (123) for any poSet P, and we exactly classify the poSets for which equality holds.

  • pattern avoidance in permutations on the boolean lattice
    arXiv: Combinatorics, 2012
    Co-Authors: Sam Hopkins, Morgan Weiler
    Abstract:

    We extend the concept of pattern avoidance in permutations on a Totally Ordered Set to pattern avoidance in permutations on partially Ordered Sets. The number of permutations on P that avoid the pattern a is denoted Av_P(a). We extend a proof of Simion and Schmidt to show that Av_P(123) <= Av_P(132) for any poSet P, and we exactly classify the poSets for which equality holds. We also give asymptotically close bounds on the number of permutations on the Boolean lattice that avoid the pattern {1}{1,2}{2}.

  • pattern avoidance in poSet permutations
    arXiv: Combinatorics, 2012
    Co-Authors: Sam Hopkins, Morgan Weiler
    Abstract:

    We extend the concept of pattern avoidance in permutations on a Totally Ordered Set to pattern avoidance in permutations on partially Ordered Sets. The number of permutations on $P$ that avoid the pattern $\pi$ is denoted $Av_P(\pi)$. We extend a proof of Simion and Schmidt to show that $Av_P(132) \leq Av_P(123)$ for any poSet $P$, and we exactly classify the poSets for which equality holds.

Siu Oyoung - One of the best experts on this subject based on the ideXlab platform.

  • a Totally Ordered Set of discrete abstractions for a given hybrid continuous system
    Lecture Notes in Computer Science, 1997
    Co-Authors: Jorg Raisch, Siu Oyoung
    Abstract:

    This contribution proposes a hierarchy of discrete abstractions for a given hybrid or continuous system with quantized measurements and symbolic control inputs. The continuous (or hybrid) base system and its discrete abstractions form a Totally Ordered Set of models; ordering is in the sense of Set inclusion of model behaviours or, equivalently, in terms of approximation accuracy. The ordering is shown to be invariant under feedback; this provides theoretical justification for designing feedback control for the underlying hybrid system on the basis of a discrete abstraction. Also, within this Ordered Set, the notion of a “least accurate” (and therefore least complex) model which allows a given Set of specifications to be met makes sense. The discrete abstractions are realized as nondeterministic automata; they are in observer-canonical form and hence, by construction, observable. Non-reachable states are also “weeded out” by construction, leaving a minimal state Set for each approximating automaton.