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Fuzzy sets and systems
North-Holland Publishing Company
Fuzzy sets and systems

North-Holland Publishing Company

0165-0114

Fuzzy sets and systems/Journal Fuzzy sets and systemsSCI
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    n -ary associative functions

    Lai, Zhi-qiangWang, Xue-ping
    1.1-1.13页
    查看更多>>摘要：Let T* : [0,1]2-[0, 1] be an associative function with neutral element, f : [0,1]- [0, 1] be a monotone right continuous function and f(-1) : [0, 1]- [0, 1] be the pseudo-inverse of f. This article answers the question: what properties of the range of a generator f are sufficient and necessary for the corresponding generated function T : [0, 1]2-[0, 1] defined by T(x, y) = f(-1)(T*(f(x),f(y))) with property of T(...T(T(x1,x2),x3),...,xn) = f(-1)(T*(f(x1),...,f(xn))) forallnE {1, ...,n,...} withn >= 2 andforallx1,...,xn E [0, 1].
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Unima on [0,1]

    Gurdal, UtkuOgur, OmerCetin, Selim
    1.1-1.18页
    查看更多>>摘要：We propose the novel notion of a unimum, which is intended as a kind of logical quantifier, corresponding to the uninorms interpreted as logical connectives. We examine the relationships of this tools with uninorms, as well as certain special subclasses corresponding to t-norms, and t-conorms. We also provide examples and discuss some fundamental properties and aspects that will solidify the foundations of the theory.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Extracting business-relevance for the analysis of strategic patent portfolios from highly imprecise fuzzy estimates

    Collan, MikaelLuukka, Pasi
    1.1-1.13页
    查看更多>>摘要：Valuation of assets connected to forward-looking strategic investments and decision-making such as strategic patent-portfolios takes place in the presence of high uncertainty. Available information is typically in the form of vague signals and forecasts about the future and the tool that can be used to interpret it is the expert or a group of experts, because information about the structure of the future does not allow construction of models and historical data is not available. The expert estimates, from which fuzzy number estimates are constructed and aggregated, reflect the high imprecision, and extracting relevant information from them may be challenging. This paper presents how fuzzy expert estimates of strategic patent-portfolio value from multiple experts can be aggregated by using the lossless fuzzy weighted averaging without loss of relevant information and how business-relevant information can be extracted from seemingly worthlessly imprecise information, when a longitudinal set of estimates is available. A numerical case, in the context of real-world strategic patent valuation, is presented. New application of the lossless fuzzy weighted averaging and the recently introduced Luukka-Stoklasa defuzzification for general fuzzy sets is presented and results are compared with those obtained by using more traditional methods. The research offers a novel contribution to the literature on applying fuzzy logic to strategic decision-making
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Maxitive functions with respect to general orders

    Kupper, MichaelZapata, Jose M.
    1.1-1.21页
    查看更多>>摘要：In decision-making, maxitive functions are used for worst-case and best-case evaluations. Maxitivity gives rise to a rich structure that is well-studied in the context of the pointwise order. In this article, we investigate maxitivity with respect to general preorders and provide a representation theorem for such functions. The results are illustrated for different stochastic orders in the literature, including the usual stochastic order, the increasing convex/concave order, and the dispersive order.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    QFIG: A novel attribute reduction method using conditional entropy in quantified fuzzy approximation space

    Yang, LeiSang, BinbinXu, WeihuaChen, Hongmei...
    1.1-1.15页
    查看更多>>摘要：At present, attribute reduction based on different attribute importance measures is one of the hot topics in granular computing. Conditional entropy is a common measure to evaluate the importance of attributes in classification tasks. This paper proposes a conditional entropy based on quantified fuzzy information granular and constructs a novel attribute reduction method. First, a quantified fuzzy similarity relation is explored to overcome the instability of the existing parameterized fuzzy relations. The quantified fuzzy information granular (QFIG) induced by the defined relation and their related properties are also discussed. Second, a new QFIG-based fuzzy rough set model and its properties are proposed. Meanwhile, a general framework of the proposed fuzzy rough approximation operators is established. Third, we construct a QFIGbased conditional entropy for evaluating the importance of attributes in decision information systems. At the same time, the corresponding attribute reduction algorithm is designed based on heuristic reduction strategy. Finally, the performance of the proposed algorithm is demonstrated by numerical comparison experiments on twelve public datasets. Experimental results not only confirm the effectiveness of the proposed algorithm but also show that the performance of the proposed algorithm is better than that of some existing attribute reduction algorithms.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Uniform random fuzzy measures

    Baz, JuanBeliakov, GlebDiaz, IreneMontes, Susana...
    1.1-1.15页
    查看更多>>摘要：Random generation of fuzzy measures is an important computational task in applied problems related to fuzzy integrals such as the Choquet, Sugeno or Shilkret integrals. In general, a desirable property is the uniformity over the set of fuzzy measures. However, testing this property is not an easy task. In this paper, properties of uniform random fuzzy measures are derived. Special attention is being paid to the families of balanced fuzzy measures, belief measures and possibilities measures. Then, based of such properties, statistical tests for the uniformity of random fuzzy measures are developed. Finally, the uniformity of the most used algorithms is tested using the proposed methods.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Ordinal sums of triangular norms on a bounded trellis

    Geng, JunChen, ZiwenWang, Rina
    1.1-1.13页
    查看更多>>摘要：In this paper, we present ordinal sums of triangular norms on bounded trellises with one summand firstly by taking a right-transitive element as the left endpoint and a boolean AND-associative element as the right endpoint of the given interval sub-trellis. Also, the corresponding recursive construction of triangular norms on bounded trellises is shown. Meanwhile, we extend the result to the ordinal sums of triangular norms on bounded trellises with more summands including two cases that the given interval sub-trellises are contiguous or not. Particularly, we can naturally obtain two classes of triangular norms which are different from others on bounded lattices. And some illustrative examples are added for clarity.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Fuzzy variational calculus in linearly correlated space: Part I

    Frederico, Gastao S. F.Esmi, EstevaoBarros, Laecio C.
    1.1-1.15页
    查看更多>>摘要：This article is the first part of series of articles that aim to present the foundations for fuzzy variational calculus for functions taking values in the space of linearly correlated fuzzy numbers RT(A). Recall that the space RT(A) is composed by all sums of a real number r and a fuzzy number qA, where A is a given asymmetric fuzzy number and q is an arbitrary real number. Two advantages of this space are that it can be equipped with a Banach space structure and, similar to additive models in Statistics, its elements can be interpreted as the sum of a deterministic expected/predictable value with an uncertain/noise component. The foundation of variational calculus theory requires the definition and establishment of many concepts and results. This article presents a total order relation on RT(A) for which the notions of local minimal and maximal of a RT(A)-valued function f can be derived. We present a fuzzy version of the first and second optimality conditions in terms of derivatives off. Finally, we present a generalized fuzzy version of du Bois-Reymond lemma which is essential in variational calculus theory.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Quantale-valued maps and partial maps

    Shen, LiliTang, Xiaoye
    1.1-1.18页
    查看更多>>摘要：Let Q be a commutative and unital quantale. By a Q-map we mean a left adjoint in the quantaloid of sets and Q-relations, and by a partial Q-map we refer to a Kleisli morphism with respect to the maybe monad on the category Q-Map of sets and Q-maps. It is shown that every Q-map is symmetric if and only if Q is weakly lean, and that every Q-map is exactly a map in Set if and only Q is lean. Moreover, assuming the axiom of choice, it is shown that the category of sets and partial Q-maps is monadic over Q-Map.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    The relationships between type-2 t-norms on normal convex fuzzy truth values

    Zhang, WeiHu, Bao QingWu, Xinxing
    1.1-1.15页
    查看更多>>摘要：Recent literature has mainly focused on four forms of type-2 t-norms on F-NC composed of all normal convex fuzzy truth values: t-norms defined on the complete lattice, t(ln)-norms defined by Hernandez et al., t(r)-norms defined by Harding et al., and t(lo)-norms defined by Wu et al. The paper studies the relationships among these four types of type-2 t-norms constructed by generalized extended t-norms that come from the generalization of Zadeh's extension principle. Firstly, we sequentially characterize the conditions under which generalized extended t-norms satisfy each restrictive axiom in the definitions of type-2 t-norms, particularly closure properties. Then, we prove that on F-NC, generalized extended t-norms being t(r)-norms (resp. t(lor)-norms) is equivalent to them being t(lo)-norms (resp. t(lor)-norms). Finally, through examples, we demonstrate that on F-NC, t(lo)-norms (resp. t(lor)-norms) are strictly stronger than t-norms (resp. t(r)-norms) even if all of them are constructed by generalized extended t-norms.
      原文链接:
    • NETL
    • NSTL
    • Elsevier