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  • Further characterization of uninorms on bounded lattices
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2021-01-19
    Xiang-Rong Sun; Hua-Wen Liu

    Uninorms on bounded lattices have recently attracted widespread attention. In this study, we first propose the necessary structure for uninorms with Archimedean underlying t-norms and t-conorms on bounded lattices. We also discuss the characterization of more general classes of uninorms. We then study the necessity for a particular structure of uninorms that is required by many existing methods for

    更新日期:2021-01-19
  • Generalized fractional evolution equations driven by fuzzy variational inequalities
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2021-01-18
    Shengda Zeng; Jinxia Cen; Van Thien Nguyen

    The aim of this paper is to study a comprehensive dynamics system called fractional fuzzy differential variational inequality, which is composed of a nonlinear fractional differential equation with Atangana-Baleanu fractional derivative and a time-dependent fuzzy variational inequality. We explore an existence and uniqueness theorem for the dynamics system under consideration. Our proof is based on

    更新日期:2021-01-19
  • Semicopula based integrals
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2021-01-13
    LeSheng Jin; Anna Kolesárová; Radko Mesiar

    We define the notion of weak universal integral based on a semicopula, and introduce and discuss two particular classes of weak universal integrals based on semicopulas, which generalize the well-known Sugeno and Shilkret integrals. In special cases, when the considered semicopulas are bounded from above by the Łukasiewicz t-norm, all introduced integrals reduce to the corresponding smallest semicopula

    更新日期:2021-01-13
  • Fuzzy differential equations with Riemann-Liouville generalized fractional integrable impulses
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2021-01-12
    Truong Vinh An; Ngo Van Hoa

    We introduce a new class of fuzzy differential equations with noninstantaneous impulses represented by the Riemann-Liouville generalized fractional integral. We investigate the existence of the solution and two types of Hyers-Ulam-Rassias stability of the aforementioned problem via the Banach fixed-point theorem. Some illustrate examples are also presented.

    更新日期:2021-01-12
  • Incremental fuzzy clustering of time series
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2021-01-12
    Ling Wang; Peipei Xu; Qian Ma

    Clustering is one of the most popular data mining methods for analyzing the time series, not only due to its exploratory power, but also because it is often a preprocessing step or subroutine for other techniques. In this paper, an incremental fuzzy clustering algorithm of time series (IFCTS) is proposed, in which the clustering is divided into two stages: offline and online clustering. During the

    更新日期:2021-01-12
  • A new transformation of continuous unimodal asymmetric probability distributions into possibility distributions
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2021-01-06
    Laurent Foulloy; Gilles Mauris

    This paper deals with a new transformation, so-called two-sided normalized (TSN), of continuous unimodal asymmetric probability distributions into possibility distributions. Many properties are derived and interpretations are discussed. A comparison with the optimal transformation is provided. In particular, the respective positions of right or left branches relative to the resulting optimal and TSN

    更新日期:2021-01-06
  • Calculus of linear fuzzy-number-valued functions using the generalized derivative and the Riemann integral of fuzzy n-cell-number-valued functions
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2021-01-04
    Shexiang Hai; Zengtai Gong

    We study the differentiability, integral, and calculus of linear fuzzy-number-valued functions. Special emphasis is placed on the linear fuzzy-number-valued function F˜(t)=u˜1f1(t)+u˜2f2(t)+⋯+u˜mfm(t), where u˜1,u˜2,…,u˜m denote fuzzy n-cell numbers and f1,f2,…,fm represent real functions of a real variable. The concepts of the limit and continuity of fuzzy n-cell-number-valued functions are defined

    更新日期:2021-01-04
  • AE and EA robustness of interval circulant matrices in max-product algebra
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2021-01-04
    H. Myšková; J. Plavka

    Max-product algebra is defined as a linearly ordered set with two binary operations. Classical addition and multiplication are replaced by maximum and multiplication, respectively. A square matrix A is robust, if for each starting vector x, the orbit stabilizes. If this property holds only for starting vectors from an interval vector X, we say that A is X-robust. We shall deal with the matrices of

    更新日期:2021-01-04
  • A class of bivariate independence copula transformations
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2021-01-04
    Martynas Manstavičius; Gediminas Bagdonas

    This paper deals with the problem of characterizing all functions f:[0,1]→R+ such that Cf(x,y)=xyf((1−x)(1−y)), x,y∈[0,1] is a bivariate copula. We provide a complete characterization for the two cases: (i) when Cf is, in addition, totally positive of order 2 (TP2) and (ii) when f is twice continuously differentiable. In general, the function f need only be twice differentiable Lebesgue almost everywhere

    更新日期:2021-01-04
  • A note to the finite T-sum of L − R fuzzy numbers and further considerations
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-30
    Michał K. Urbański; Kinga M. Wójcicka; Paweł M. Wójcicki

    In the first part of this paper we consider the α-cut of a sum of two fuzzy sets. We show that the α-cut of such a sum can be written as one closed interval determined by the minimum and maximum of some special functions, over a set uniquely determined by the considered t-norm. In the second part of the paper we show that not only α-cut of a sum of two fuzzy intervals has this property, but also α-cut

    更新日期:2020-12-31
  • Algebraic structure of fuzzy signatures
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-30
    László T. Kóczy; M. Eugenia Cornejo; Jesús Medina

    Fuzzy signatures have been used for various applications, including medical diagnosis, communication of robots based on intention guessing, and residential building evaluation. However, there exist many questions about this research topic which have not been addressed in the literature. One of the most important aims is to formally define a family of fuzzy signatures from which an algebraic structure

    更新日期:2020-12-30
  • Fuzzy complex numbers: representations, operations, and its analysis
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-30
    Zengtai Gong; Zhiyong Xiao

    As a key theoretical basis of fuzzy complex analysis, a new representation of fuzzy complex numbers is proposed in this paper which unifies the exponential form, trigonometric form and algebraic form of fuzzy complex numbers, and some arithmetic operations are investigated. The concepts of strong sum and strong difference are defined in order to simplify the addition and subtraction operations of complex

    更新日期:2020-12-30
  • A set of practical experiments to validate the fuzzy Kalman filter
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-29
    Víctor Jiménez; Biel P. Alvarado; Fernando Matía

    The Fuzzy Kalman Filter (FKF) was recently reformulated, with a number of basic examples included in order to demonstrate its applicability. We now look ahead to its practical implementation, introducing deep analysis which includes very detailed simulations and complete real applications. This will allow us to not only validate the FKF but also to draw important conclusions which will help users in

    更新日期:2020-12-29
  • Soft robust solutions to possibilistic optimization problems
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-29
    Adam Kasperski; Paweł Zieliński

    This paper discusses a class of uncertain optimization problems, in which unknown parameters are modeled by fuzzy intervals. The membership functions of the fuzzy intervals are interpreted as possibility distributions for the values of the uncertain parameters. It is shown how the known concepts of robustness and light robustness, for the traditional interval uncertainty representation of the parameters

    更新日期:2020-12-29
  • Adaptive neural asymptotic control for uncertain nonlinear multiagent systems with a fuzzy dead zone constraint
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-29
    Chengjie Huang; Zhi Liu; C.L. Philip Chen; Yun Zhang

    A consensus control scheme is developed for a class of leader-follower multiagent systems with a fuzzy dead zone constraint. Differently from previous work, the method developed implements a predefined convergence of tracking errors for multiagent systems; especially, the dynamic model for each follower has a fuzzy dead zone input. To solve the problem, not only a set of smooth functions are used within

    更新日期:2020-12-29
  • Characterization of idempotent n-uninorms
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-29
    Andrea Mesiarová-Zemánková

    The structure of idempotent n-uninorms is studied. We show that each idempotent 2-uninorm with the 2-neutral element {e1,e2}z1 can be expressed as an ordinal sum of an idempotent uninorm (possibly also of a countable number of idempotent semigroups with operations min and max) and a 2-uninorm such that U2(0,1)=z1 (possibly restricted to ]0,1[2, or [0,1[2, or ]0,1]2). Similar results are shown also

    更新日期:2020-12-29
  • More Relaxed Stability Analysis and Positivity Analysis for Positive Polynomial Fuzzy Systems via Membership Functions Dependent Method
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-29
    Meng Han; H.K. Lam; Fucai Liu; Yinggan Tang

    In this paper, the conservatism source of the positivity and stability analysis results of positive polynomial fuzzy-model-based (PPFMB) control system are studied. Also, in order to improve the flexibility of controller design, a fuzzy controller that does not depend on the membership functions of the fuzzy model is designed. In the existing literatures, it is proved that the LCLF can reduce the conservatism

    更新日期:2020-12-29
  • Inflationary BL-algebras obtained from 2-dimensional general overlap functions
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-28
    Rui Paiva; Regivan Santiago; Benjamín Bedregal; Umberto Rivieccio

    naBL-algebras are non-associative generalizations of BL-algebras obtained from non-associative t-norms (nat-norms). In the present paper we propose a further generalization of BL-algebras where associativity is not required. Such generalization is based on a subclass of bivariate general overlap functions called inflationary. We call this non-associative generalization inflationary BL-algebras, and

    更新日期:2020-12-28
  • On some classes of nullnorms and h-pseudo homogeneity
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-28
    Lucélia Lima; Benjamin Bedregal; Marcus Rocha; Aitor Castillo-Lopez; Javier Fernandez; Humberto Bustince

    Nullnorms are aggregation functions which generalize t-norms and t-conorms. For each nullnorm there exists an annihilator element such that, below it, the function behaves like a t-conorm, and, above it, like a t-norm. In this paper, we study some classes of nullnorms which naturally arise from well known classes of t-norms and t-conorms, such as idempotent, Archimedean, cancellative, positive and

    更新日期:2020-12-28
  • Fuzzy quantifiers defined over fuzzy domains
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-22
    Antonín Dvořák; Michal Holčapek

    In this paper, we introduce a generalization of the concept of fuzzy quantifier called fuzzy quantifiers over fuzzy domains. The development of this generalization is motivated by the impossibility to satisfactorily define the important operation of relativization for standard fuzzy quantifiers. We provide basic examples of these quantifiers and define and investigate also several semantic properties

    更新日期:2020-12-23
  • Random generation of k-interactive capacities
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-22
    Gleb Beliakov; Francisco Javier Cabrerizo; Enrique Herrera-Viedma; Jian-Zhang Wu

    The theory of capacities provides powerful formal methodology to account for criteria dependencies in multiple criteria decision problems. The discrete Choquet and Sugeno integrals aggregate criteria valuations accounting for criteria synergies and redundancies. We address an important problem of randomly generating capacities of special classes for simulation studies and for capacity learning through

    更新日期:2020-12-23
  • An auxiliary system discretization approach to Takagi-Sugeno fuzzy models
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-22
    Víctor C. da S. Campos; Márcio F. Braga; Luciano Frezzatto

    This paper proposes a new procedure for discretizing nonlinear systems described by Takagi-Sugeno fuzzy models. The discretization procedure consists of obtaining a linear auxiliary system that approximates the Takagi-Sugeno model over a sampling instant. By discretizing this auxiliary system, a norm bounded uncertain linear discrete-time system is found, which is capable of representing the fuzzy

    更新日期:2020-12-23
  • Integer interval DEA: An axiomatic derivation of the technology and an additive, slacks-based model
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-22
    Manuel Arana-Jiménez; M. Carmen Sánchez-Gil; Atefeh Younesi; Sebastián Lozano

    The present paper studies the efficiency assessment of Decision-Making Units (DMUs) when their inputs and outputs are described under uncertainty of the type of integer interval data. An axiomatic derivation of the production possibility set (PPS) is presented. An additive, slacks-based data envelopment analysis (DEA) model is formulated, consisting of two phases. This has required the use of adequate

    更新日期:2020-12-23
  • Strictly join irreducible varieties of BL-algebras: The missing pieces
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-18
    Stefano Aguzzoli; Matteo Bianchi

    Let L be a variety of MTL-algebras, and let L(L) be its lattice of subvarieties, ordered by inclusion. L is called strictly join irreducible (SJI) if, whenever L is the join of a set of elements S⊆L(MTL), then L∈S. Every variety in L(L) is obtained as join of SJI varieties, which may be considered as the building blocks of all the varieties in L(L). In a previous work by the second author, a partial

    更新日期:2020-12-18
  • Extreme semilinear copulas
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-18
    Fabrizio Durante; Juan Fernández-Sánchez; Manuel Úbeda-Flores

    We study the extreme points (in the Krein-Milman sense) of the class of semilinear copulas and provide their characterization. Related results into the more general setting of conjunctive aggregation functions (i.e., semi–copulas and quasi–copulas) are also presented.

    更新日期:2020-12-18
  • Expansive properties of induced dynamical systems
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-16
    Daniel Jardón; Iván Sánchez

    For a given metric space X, we consider the set of all normal fuzzy sets on X, denoted by F(X). In this work, we study expanding, positively expansive and weakly positively expansive dynamical systems (X,f) and how they are reflected in the dynamical system (F(X),fˆ), where fˆ is the Zadeh's extension of f and F(X) has one of the following metrics: the levelwise metric, the endograph metric, the sendograph

    更新日期:2020-12-16
  • Aggregation for linearly ordered fuzzy preference relations based on consistency
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-15
    T. Calvo; P. Fuster-Parra; J. Martín; G. Mayor

    The study of consistency in decision-making models is of great importance. Our proposal deals with a special type of extended aggregation functions to guarantee consistency that is based on T-S consistency of linearly ordered fuzzy preference relations (fuzzy ranking for preferences). Necessary conditions to ensure consistency in the aggregation process are provided. Moreover, sufficient conditions

    更新日期:2020-12-16
  • Pseudo-integral and generalized Choquet integral
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-10
    Deli Zhang; Radko Mesiar; Endre Pap

    Due to many applications, the Choquet integral as a powerful tool for modeling non-deterministic problems needs to be further extended. Therefore the paper is devoted to a generalization of the Choquet integral. As a basis, the pseudo-integral for bounded integrand is extended to the case for nonnegative integrands at first, and then the generalized Choquet integral is defined. As special cases, pseudo-Choquet

    更新日期:2020-12-10
  • Fuzzy importance sampling method for estimating failure possibility
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-10
    Kaixuan Feng; Zhenzhou Lu; Chunyan Ling; Lu Wang

    To improve the computational efficiency of the fuzzy simulation in estimating failure possibility of the structure containing fuzzy uncertainty, a fuzzy importance sampling method is proposed in this paper. In the proposed method, the optimal importance sampling density for estimating failure possibility is deduced as the product of the indicator function related to failure domain and the joint membership

    更新日期:2020-12-10
  • Multivariate imprecise Sklar type theorems
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-10
    Matjaž Omladič; Nik Stopar

    The omnipotent instrument for modeling multivariate dependence of random variables in standard probability theory has become copulas discovered by A. Sklar in 1959. Only recently Omladič and Stopar prove that in the bivariate case an analogous role is played by exactly the same copulas for random variables coming from finitely additive probability spaces. One of the main results of this paper is that

    更新日期:2020-12-10
  • Belief functions induced by random fuzzy sets: A general framework for representing uncertain and fuzzy evidence
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-09
    Thierry Denœux

    We revisit Zadeh's notion of “evidence of the second kind” and show that it provides the foundation for a general theory of epistemic random fuzzy sets, which generalizes both the Dempster-Shafer theory of belief functions and possibility theory. In this perspective, Dempster-Shafer theory deals with belief functions generated by random sets, while possibility theory deals with belief functions induced

    更新日期:2020-12-09
  • Characterizing idempotent nullnorms on a special class of bounded lattices
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-04
    Xinxing Wu; Shudi Liang; Gül Deniz Çaylı

    Nullnorms with a zero element being at any point of a bounded lattice are an important generalization of triangular norms and triangular conorms. This paper obtains an equivalent characterization for the existence of idempotent nullnorms with the zero element a on any bounded lattice containing only two distinct elements incomparable with a. Furthermore, some basic properties for the bounded lattice

    更新日期:2020-12-04
  • An Advanced Interpretable Fuzzy Neural Network Model based a Uni-Nullneuron constructed from N-uninorms
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-03
    Paulo Vitor de Campos Souza; Edwin Lughofer

    This paper formulates a fuzzy logic neuron that uses n-uninorms to construct uni-nullneurons. A fuzzy neural network (FNN) composed of these neurons is easy to operate with nullnorms and uninorms at different times, which results in high accuracy of the model outputs and increases the flexibility in connecting the rule antecedents (enabling AND and OR connections within one rule). This, in turn, may

    更新日期:2020-12-03
  • Deriving priority vector from pairwise comparisons matrix with fuzzy elements
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-02
    Jaroslav Ramík

    This paper deals with the pairwise comparisons matrix with fuzzy elements (FPCM). Fuzzy elements of the FPCM are applied whenever the decision maker is not sure about the value of his/her evaluation of the relative importance of elements in question. We investigate the pairwise comparisons matrices with elements from abelian linearly ordered group (alo-group) over a real interval, introduce the concept

    更新日期:2020-12-02
  • Fuzzy fractional differential equations with the generalized Atangana-Baleanu fractional derivative
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-02
    Ho Vu; Behzad Ghanbari; Ngo Van Hoa

    In this paper, we introduce a generalization of Atangana-Baleanu type fractional calculus with respect to the generalized Mittag-Leffler kernel which has been named as the generalized Atangana-Baleanu (GAB) type fractional calculus. Existence and uniqueness results for the initial value problems of fuzzy differential equations involving a GAB fractional derivative in the Caputo sense are established

    更新日期:2020-12-02
  • Measuring variability and association for categorical data
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-02
    Erindi Allaj

    The quantification of the variability of the categorical data is an important topic not only in statistics, but also in many other disciplines. We suggest different variability measures to describe the variability of categorical data. In our approach, any set of categorical data for a determinate categorical variable is treated as a fuzzy set. Therefore, measuring the variability of categorical data

    更新日期:2020-12-02
  • New family of triangular norms for decreasing generators in the form of a logarithm of a linear fractional function
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-02
    T.M. Ledeneva

    The purpose of this paper is to establish restrictions on the parameters under which a function in the form of a natural logarithm of a linear fractional function is a decreasing generator. In addition to the general case, all special cases of generators of this type are considered. A triangular norm is constructed for each generator. In fact, a new parametric class of decreasing generators that generalizes

    更新日期:2020-12-02
  • On fuzzy monotone convergence Q-cotopological spaces
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-12-02
    Zhongxi Zhang; Fu-Gui Shi; Qingguo Li; Kai Wang

    In this paper, we generalize the concept of a monotone convergence space (also called a d-space) to the setting of a Q-cotopological space, where Q is a commutative and integral quantale. We establish a D-completion for every stratified Q-cotopological space, which is a category reflection of the category SQ-CTop of stratified Q-cotopological spaces onto the full subcategory SQ-DCTop of monotone convergence

    更新日期:2020-12-02
  • Some new results on the migrativity of uninorms over overlap and grouping functions
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-27
    Kuanyun Zhu; Jingru Wang; Yongwei Yang

    In 2018, Qiao and Hu [48] studied the α-migrativity of uninorms over overlap and grouping functions when the uninorm U belongs to one certain class (e.g., Umin, Umax, the family of idempotent uninorms, representable uninorms or uninorms continuous on ]0,1[2). In addition, they obtained some equivalent characterizations of them. This paper will continue to consider the characterizations of this kind

    更新日期:2020-11-27
  • The aggregation of transitive fuzzy relations revisited
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-26
    T. Calvo Sánchez; P. Fuster-Parra; O. Valero

    In this paper, we consider the problem of aggregating a collection of transitive fuzzy binary relations in such a way that the aggregation process preserves transitivity. Specifically, we focus our efforts on the characterization of those functions that aggregate a collection of fuzzy binary relations which are transitive with respect to a collection of t-norms preserving the transitivity. We characterize

    更新日期:2020-11-27
  • Topological stability for fuzzy expansive maps
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-25
    L. Badilla; D. Carrasco-Olivera; V.F. Sirvent; H. Villavicencio

    We introduce the definitions of expansivity and topological stability for homeomorphisms on fuzzy metric spaces. We show some basic properties of fuzzy expansive homeomorphisms. Moreover we prove Walters's theorem in the context of fuzzy metric spaces, i.e., a fuzzy expansive system with the fuzzy shadowing property is fuzzy topologically stable.

    更新日期:2020-11-26
  • Three types of fuzzy covering-based rough set models
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-24
    Junli Zhou; Fasheng Xu; Yanyong Guan; Hongkai Wang

    In this paper, three new types of fuzzy covering-based rough set models are proposed. First, the membership-degree-based fuzzy covering rough set is defined in the fuzzy covering approximation space by separately comparing the membership degree of each object belonging to the approximated fuzzy set with those of the component fuzzy sets in the fuzzy covering for the same object. Second, the membership-function-based

    更新日期:2020-11-25
  • First-order linear fuzzy differential equations on the space of linearly correlated fuzzy numbers
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-23
    Yonghong Shen

    The present paper is concerned with the solutions of first-order linear fuzzy differential equations under the condition of LC-differentiability. Motivated by the fact that the structure of the space of linearly correlated fuzzy numbers strongly depends on the symmetry of the basic fuzzy number, here we address first-order linear fuzzy differential equations by distinguishing whether the basic fuzzy

    更新日期:2020-11-23
  • Best-possible bounds on the set of copulas with a given value of Spearman's footrule
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-20
    Gleb Beliakov; Enrique de Amo; Juan Fernández-Sánchez; Manuel Úbeda-Flores

    In this paper we find pointwise best-possible bounds on the set of copulas with a given value of the Spearman's footrule coefficient. We show that the lower bound is always a copula but, unlike the bounds on sets of copulas with a given value of other measures, such as Kendall's tau, Spearman's rho and Blonqvist's beta, the upper bound can be a copula or a proper quasi-copula. We characterised both

    更新日期:2020-11-21
  • The impact on the properties of the EFGM copulas when extending this family
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-17
    Susanne Saminger-Platz; Anna Kolesárová; Adam Šeliga; Radko Mesiar; Erich Peter Klement

    Several extensions of the family of (bivariate) Eyraud-Farlie-Gumbel-Morgenstern copulas (EFGM copulas) are considered. Some of them are well-known from the literature, others have recently been suggested (copulas based on quadratic constructions, based on some forms of convexity, and polynomial copulas). For each of these extensions we analyze which properties of EFGM copulas are preserved (or even

    更新日期:2020-11-17
  • Relational, closure and partition powerset theories
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-16
    Jiří Močkoř

    For general powerset theories in categories, new notions of relational, closure, or partition powerset theories in these categories are introduced. These new types of powerset theories are defined as categories whose objects are the original powerset objects with relational, closure, or partition structures defined on these objects. This construction generalizes classical constructions realized on

    更新日期:2020-11-16
  • A copula transformation in multivariate mixed discrete-continuous models
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-13
    Jae Youn Ahn; Sebastian Fuchs; Rosy Oh

    Copulas allow a flexible and simultaneous modeling of complicated dependence structures together with various marginal distributions. Especially if the density function can be represented as the product of the marginal density functions and the copula density function, this leads to both an intuitive interpretation of the conditional distribution and convenient estimation procedures. However, this

    更新日期:2020-11-13
  • Fractional calculus of linear correlated fuzzy-valued functions related to Fréchet differentiability
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-13
    Nguyen Thi Kim Son; Hoang Thi Phuong Thao; Nguyen Phuong Dong; Hoang Viet Long

    In this paper, we will introduce some types of Fréchet fractional derivative defined on the class of linear correlated fuzzy-valued functions. Firstly, we study Fréchet derivative and R-derivative of integer order and investigate their relationship with the well-known generalized Hukuhara derivatives in fuzzy metric space. Secondly, the Riemann-Liouville fractional integral of linear correlated fuzzy-valued

    更新日期:2020-11-13
  • A critical note on inverse fuzzy time series algorithms
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-13
    S. Askari

    Inverse fuzzy time series algorithms forecast a data point as a function of itself and previous observations. They cancel impact of previous observations by a predefined small parameter and return observed value of the data point as its predicted value. The present study shows that these algorithms, which are devised to predict fuzzy time series, cannot be used as forecasting tools in practice.

    更新日期:2020-11-13
  • Uninorms on bounded lattices constructed by t-norms and t-subconorms
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-12
    Xiu-juan Hua; Wei Ji

    The construction of uninorms on bounded lattices has been a attractive research area. In this paper, we introduce some new classes of uninorms on bounded lattices via t-subnorms and t-subconorms with a neutral element e under some constraints. We also give some illustrative examples to help understand the structure of these new uninorms. Moreover, we provide an answer to the open problem raised by

    更新日期:2020-11-12
  • A representation of nullnorms on a bounded lattice in terms of beam operations
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-12
    Hua-Peng Zhang; Zhudeng Wang; Yao Ouyang; Bernard De Baets

    We introduce three broad classes of nullnorms on a bounded lattice and lay bare the structure of their members. For that purpose, we introduce particular subsets of a bounded lattice, called upper (resp. lower) beams, and appropriate associative operations on them, called beam (resp. dual beam) operations, which conveniently generalize triangular norms (resp. triangular conorms). It is shown that nullnorms

    更新日期:2020-11-12
  • Conditions on marginals and copula of component lifetimes for signature representation of system lifetime
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-12
    Jorge Navarro; Tomasz Rychlik; Fabio Spizzichino

    The signature of a system is a probability vector that depends only on the system structure. Under the classic IID (independent and identically distributed) assumption on the component lifetimes, the system lifetime distribution is the convex combination of consecutive component failure times, and the signature coordinates constitute the mixture coefficients. In this case the signature representations

    更新日期:2020-11-12
  • An online gradient-based parameter identification algorithm for the neuro-fuzzy systems
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-11
    Long Li; Zuqiang Long; Hao Ying; Zhijun Qiao

    Online gradient descent method has been widely applied for parameter learning in neuro-fuzzy systems. The success of the application relies on the convergence of the learning procedure. However, there barely have been convergence analyses on the online learning procedure for neuro-fuzzy systems. In this paper, an online gradient learning algorithm with adaptive learning rate is proposed to identify

    更新日期:2020-11-12
  • Multi-level adaptive neuro-fuzzy inference system-based reconstruction of 1D ISOMAP representations
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-10
    Honggui Li; Dimitri Galayko; Maria Trocan

    This paper addresses the inverse problem of isometric feature mapping (ISOMAP) via multi-level adaptive neuro-fuzzy inference system (ML-ANFIS). ISOMAP is a conventional nonlinear dimensionality reduction (NLDR) method, which prospects for low dimensional interior structure embedded in high dimensional data space. The inverse problem of ISOMAP reconstructs the original high dimensional data from the

    更新日期:2020-11-12
  • Fuzzy information entropy-based adaptive approach for hybrid feature outlier detection
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-04
    Zhong Yuan; Hongmei Chen; Tianrui Li; Jia Liu; Shu Wang

    Fuzzy information entropy based on fuzzy relation in fuzzy rough set is an important metric of uncertainty. However, the research of fuzzy information entropy for hybrid feature outlier detection has not been reported. On this basis, this paper constructs a hybrid feature outlier detection method based on fuzzy information entropy by using fuzzy approximate space with fuzzy similarity relation. Firstly

    更新日期:2020-11-06
  • Fixed-time stabilization of fuzzy neutral-type inertial neural networks with time-varying delay
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-04
    Chaouki Aouiti; Qing Hui; Hediene Jallouli; Emmanuel Moulay

    This paper addresses the problem of fixed-time stabilization for a class of fuzzy neutral-type inertial neural networks (FNTINNs) with time-varying delay. By using a novel fixed-time stability theorem for dynamical systems, two different feedback control laws are designed to ensure the fixed-time stabilization of FNTINNs with time-varying delay. The proposed theoretical results can lead to a better

    更新日期:2020-11-06
  • A characterization of the classes Umin and Umax of uninorms on a bounded lattice
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-04
    Hua-Peng Zhang; Mingxiu Wu; Zhudeng Wang; Yao Ouyang; Bernard De Baets

    As generalizations of the classes Umin and Umax of uninorms on the real unit interval, we introduce the classes Umin and Umax of uninorms on a bounded lattice and lay bare the structure of their members. It is shown that uninorms in Umin (resp. Umax) are characterized by a triangular conorm (resp. triangular norm) and a triangular subnorm (resp. triangular superconorm). The characterization theorems

    更新日期:2020-11-04
  • Diagonals between Q-distributors
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-11-03
    Lili Shen

    For a small quantaloid Q, it is shown that the category of Q-distributors and diagonals is equivalent to a quotient category of the category of Q-interior spaces and continuous Q-distributors. Kan adjunctions induced by Q-distributors play a crucial role in establishing this equivalence.

    更新日期:2020-11-03
  • On n-Polygonal Interval-Value Fuzzy Sets and Numbers
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-10-27
    Chunfeng Suo; Yongming Li; Zhihui Li

    The structure of interval-valued fuzzy sets is complex in regard to their arithmetic operations. To reduce the computational complexity of arithmetic operations on interval-valued fuzzy sets, we propose the notion of an n-polygonal interval-valued fuzzy set considering two 2n+2-tuple ordered real numbers. Complete representation of n-polygonal interval-valued fuzzy sets and numbers is provided. Moreover

    更新日期:2020-10-30
  • The interval eigenvalue problem using constraint interval analysis with an application to linear differential equations
    Fuzzy Set. Syst. (IF 3.305) Pub Date : 2020-10-26
    Marina T. Mizukoshi; Weldon A. Lodwick

    We study the interval eigenvalue problem and its application to stability theory of interval linear differential equations. The interval eigenvalue problem is studied from a constraint interval representation affording advantages not found in previous approaches.

    更新日期:2020-10-30
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