145 research outputs found

    Pointwise construction of Lippschitz aggregation operators with specific properties

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    This paper describes an approach to pointwise construction of general aggregation operators, based on monotone Lipschitz approximation. The aggregation operators are constructed from a set of desired values at certain points, or from empirically collected data. It establishes tight upper and lower bounds on Lipschitz aggregation operators with a number of different properties, as well as the optimal aggregation operator, consistent with the given values. We consider conjunctive, disjunctive and idempotent n-ary aggregation operators; p-stable aggregation operators; various choices of the neutral element and annihilator; diagonal, opposite diagonal and marginal sections; bipolar and double aggregation operators. In all cases we provide either explicit formulas or deterministic numerical procedures to determine the bounds. The findings of this paper are useful for construction of aggregation operators with specified properties, especially using interpolation schemata.<br /

    Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms

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    This work studies the aggregation operators on the set of all possible membership degrees of typical hesitant fuzzy sets, which we refer to as H, as well as the action of H-automorphisms which are defined over the set of all finite non-empty subsets of the unitary interval. In order to do so, the partial order ≤H, based on α-normalization, is introduced, leading to a comparison based on selecting the greatest membership degrees of the related fuzzy sets. Additionally, the idea of interval representation is extended to the context of typical hesitant aggregation functions named as the H-representation. As main contribution, we consider the class of finite hesitant triangular norms, studying their properties and analyzing the H-conjugate functions over such operators. © 2013 Elsevier Inc. All rights reserved.Peer Reviewe

    Aggregation, non-contradiction ans excluded-middle

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    This paper investigates the satisfaction of the Non-Contradiction (NC) and Excluded-Middle (EM) laws within the domain of aggregation operators. It provides characterizations both for those aggregation operators that satisfy NC/EM with respect to (w.r.t.) some given strong negation, as well as for those satisfying them w.r.t. any strong negation. The results obtained are applied to some of the most important known classes of aggregation operators

    Whole and its Parts : Micro Foundations of Macro Behaviour

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    2-Increasing binary aggregation operators

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    In this work we investigate the class of binary aggregation operators (=agops) satisfying the 2-increasing property, obtaining some characterizations for agops having other special properties (e.g., quasi-arithmetic mean, Choquet-integral based, modularity) and presenting some construction methods. In particular, the notion of P-increasing function is used in order to characterize the composition of 2-increasing agops. The lattice structure (with respect to the pointwise order) of some subclasses of 2-increasing agops is presented. Finally, a method is given for constructing copulas beginning from 2- increasing and 1-Lipschitz agops

    Fuzzy Aggregators - an Overview

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    The article deals with mathematical formalism of the process of combining several inputs into a single output in fuzzy inteligent systems, the process known as aggregation. We are interested in logic aggregation operators. Such aggregators are present in most decision problems and in fuzzy expert systems. Fuzzy inteligent systems are equipped with aggregation operators (aggregators) with which reasoning models adapt well to human reasoning. A brief overview of the field of fuzzy aggregators is given. Attention is devoted to so called graded logic aggregators.. The role of fuzzy agregators in modelling reasoning and the way they are chosen in modelling are pointed out. The conclusions are given and research in the field is pointed out

    Aggregation functions: Means

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    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 reinforcement of uninorms and absorbing norms

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    DUKE_HCERES2020Aggregation operators Reinforcement ... We propose a n-ary extension of absorbing norms, defined with the help of generative functions, and its relationship with additive generating functions of uninorms. In this paper, we also present new aggregation operators, namely the k-uninorms and k-absorbing norms. These operators are a generalization of usual uninorms and absorbing norms for which a set combination of inputs is introduced. Their main ability is to provide reinforcement for contradictory inputs, as nullnorms and as opposed to uninorms. On the other hand it still provides full reinforcement for agreeing inputs, as uninorms and as opposed to nullnorms. Numerous examples are given in order to illustrate the behavior of the proposed operators
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