Fuzzy Sets and Systems最新文献

This paper considers the nonlinear fuzzy stochastic Volterra integral equations with constant delay, which are general and include many fuzzy stochastic integral and differential equations discussed in literature. Since Doob's martingale inequality is no longer applicable to such equations, a new maximum inequality is obtained. Combining with the Picard approximation method, the existence and uniqueness of solutions to nonlinear fuzzy stochastic Volterra integral equations with constant delay are given. Moreover we prove that the solution behaves stably in the case of small changes of initial values, kernels and nonlinearities. We further develop a Euler-Maruyama (EM) scheme and prove the strong convergence of the scheme. It is shown that the strong convergence order of the EM method is 0.5 under Lipschitz condition. Moreover, the strong superconvergence order is 1 if further, the kernel $h(t,s)$ of the stochastic term satisfies $h(t,t)=0$. Numerical examples demonstrated that the numerical results are consistent with the theoretical research conclusions. Furthermore, the application model of the fuzzy stochastic Volterra integral equation with constant delay in population dynamics is considered, and the exact solution of the numerical example is given in explicit form.

We introduce and study aggregation functions based on extremal values, namely extended $(l,u)$-aggregation functions whose outputs only depend on a fixed number l of extremal lower input values and a fixed number u of extremal upper input values, independently of the arity of the input n-tuples ($n\ge l+u$). We discuss several general properties of $(l,u)$-aggregation functions and we study special $(l,u)$-aggregation functions with neutral element, including t-conorms, t-norms and uninorms. We also study $(l,u)$-aggregation functions defined by means of integrals with respect to discrete fuzzy measures, as well as $(l,u)$-ordered weighted quasi-arithmetic means based on appropriate weighting vectors. We also stress some generalizations based on recently introduced new types of monotonicity. Some possible applications are sketched, too.

In this note we continue the work of Chon, as well as Mezzomo, Bedregal, and Santiago, by studying algebraic operations on fuzzy posets and bounded fuzzy lattices. We first prove that fuzzy posets are closed under finite direct products whenever the triangular norm realizing the product construction has no zero divisors. This result is then extended to the case of bounded fuzzy lattices. Some immediate consequences are then obtained within the setting of direct products realized by triangular norms with no nilpotent elements as well as strictly monotone and cancellative triangular norms. We then introduce a triangular norm based construction of ordinal products and similarly show that fuzzy posets are closed under ordinal products whenever the triangular norm realizing the product construction has no zero divisors.

Uncertainty theory was founded by Baoding Liu for modeling belief degrees about human uncertainty. And chance theory was pioneered by Yuhan Liu based on probability theory and uncertainty theory. In many cases, imprecise risk situation in subjective or objective setting and human uncertainty simultaneously appear in a complex system. To measure uncertain random events in this system, this paper combines uncertainty space with convex non-additive probability space into a new kind of two-dimensional chance space called U-C chance space. Moreover, a new framework for uncertain random variables combining uncertainty theory with convex non-additive probability theory is provided. For applications of this new framework, it can be applied to characterize some kinds of phenomena which possess the characteristics of both imprecise risk situations and belief degrees about human uncertainty in situations of great events, such as financial crisis, major natural disaster, etc. The main contribution of this paper is to derive the types of Kolmogorov and Marcinkiewicz-Zygmund LLNs for uncertain random variables satisfying some conditions under U-C chance space, where the convex non-additive probability is totally monotone. Furthermore, several examples are stated and explained.

This article is concerned with the dynamic sum-based event-triggered $H_{\infty }$ filtering issue for networked wind turbine systems subject to deception attacks and communication delays. By considering the time-varying wind power case rather than the existing maximum power case, a more general T-S fuzzy system with two premise variables is modeled for nonlinear wind turbine system. In order to save the communication cost, a novel dynamic sum-based event-triggered scheme is proposed, which has the following three merits. First, some past sampled measurements are utilized to reduce redundant transmissions. Second, an auxiliary dynamic variable based on the past sampled measurements is introduced in the triggering condition to further enlarge the triggering intervals. Third, a dynamic triggering threshold is designed, which can be regulated adaptively along with the system evolution. With the help of Lyapunov method and linear matrix inequality technique, some sufficient co-design conditions of $H_{\infty }$ filter and triggering matrices are derived for the T-S fuzzy filtering error system with deception attacks and communication delays. Lastly, some simulations are carried out to illustrate the advantages of the proposed strategy.

By analyzing the behaviour of uninorms on the boundary of the unit square, we present decomposition theorems for uninorms, showing that a conjunctive (resp. disjunctive) uninorm can be decomposed into a disjunctive (resp. conjunctive) uninorm on an upper set (resp. a lower set) and a triangular subnorm (resp. superconorm) on a lower set (resp. an upper set). As an application of the decomposition theorems, we propose several construction methods for uninorms that are not internal on the boundary.

This paper considers the fixed-time stability of Filippov systems and discontinuous networks described by the Filippov systems. Firstly, the more generalized and economical inequality condition on Lyapunov function is proposed, which can not only improve the previous negative definite conditions, but also the indefinite conditions. Based on the definition of the Lyapunov stability and finite-time convergence, new fixed-time stability lemmas are proposed and the settling-time is also estimated. In order to apply the new fixed-time stability lemmas to the neural networks, fixed-time stabilization of a class of fuzzy leakage-delayed neural networks with discontinuous activations is considered which is rarely studied since the delay is leakage and activations are discontinuous and they are not easy to deal with simultaneously. By means of the Filippov regularization and differential inclusions theory, new criteria on the stabilization of the considered networks are derived via the new modified non-chattering controller, which can improve the previous ones with parameter and symbolic function. Finally, example and numerical simulations further examine the correctness of the main results.

This paper aims to highlight certain limitations in the study of fuzzy fractional discrete equations (FFDEs) based on the generalized Hukuhara difference (gH-difference) in the previous papers. In general, the equivalence between FFDEs and the associated fuzzy discrete fractional sum equations (FDFSEs) is not achieved, requiring the introduction of an appropriate hypothesis to establish this equivalence. Furthermore, this paper introduces the fundamental theory of fuzzy fractional discrete calculus through granular arithmetic operations between fuzzy intervals to address restrictions in the formerly mentioned approaches involving the generalized Hukuhara difference. These operations are constructed based on the concept of the horizontal membership function (HMF) utilized in multidimensional fuzzy arithmetic (MFA). Additionally, the paper proposes the application of fractional discrete calculus to two types of time-discretization diffusion equations with non-zero right-hand sides. Finally, several numerical examples are provided to validate the main results.

This paper describes a set of proposed additions to the recently introduced possibilistic fuzzy pay-off method for real option valuation that enhances the practical usability of the method. The additions are focused on the practical usability of the method and concentrate on emphasizing the consideration of the downside-risk found in projects. Technically the additions are based on using a novel interpretation of the possibilistic mean as a proxy respectively for the weight of the downside and the upside of a possibility distribution in the context of project profitability. This interpretation of the possibilistic mean is a new theoretical contribution.

The proposed new method-variant, called the “practical possibilistic fuzzy pay-off method for real option valuation”, can effectively distinguish between projects with an identical upside and non-identical downsides and allows for a more finance-theoretically comprehensive consideration of situations, where the circumstances surrounding the downside risk of a project change. Changes in the downside are reflected in the real option value. The proposed changes constitute the first variant of the possibilistic fuzzy pay-off method for real option valuation and they remarkably increase the practical usability of the method.

In this paper, we develop some connections between pointwise quasi-metric spaces and Scott spaces in domain theory. The main results include (i) the category of Scott quasi-metrics with S-morphisms is equivalent to that of pointwise quasi-metrics in the sense of Shi; (ii) a topological space $(X,T)$ is quasi-metrizable if and only if the topologically generated space $(I^X,{\omega }_I(T\left)\right)$ (where ${\omega }_I\left(T\right)$ denotes the family of all lower semi-continuous mappings from X to the unit interval I) can be induced by a pointwise quasi-metric with a property M; (iii) the notion of Scott quasi-uniformity is presented, and it is shown that d-spaces of domain theory are exactly the Scott quasi-uniformizable spaces; (iv) the relationship between Scott quasi-metrics (introduced by the first and second authors) and Scott quasi-uniformities is established. In specific, the Scott quasi-metrics are exactly the Scott quasi-uniformities that has a countable base.