Fuzzy Sets and Systems最新文献

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.

This paper investigates the fuzzy prescribed-time self-triggered consensus control for nonlinear multi-agent systems (MASs) with dead-zone output. First, by proposing a dead-zone output approximation model and utilizing Nussbaum-type functions, an adaptive compensation mechanism is developed to alleviate the effect of unknown dead-zone output. Meanwhile, the fuzzy logic systems are incorporated to approximate the unknown functions of the nonlinear MASs. Next, by adopting a time-varying scaling function, a consensus control method is recursively established to steer the consensus errors into a small range within the prescribed time. Furthermore, a self-triggered scheme is established to conserve communication resources while avoiding continuously monitoring trigger conditions. It is illustrated that boundedness of all signals and practical prescribed-time leader-following consensus can be achieved. Finally, the simulation results show the effectiveness of the proposed method.

This paper studies the admissibility analysis for Takagi-Sugeno (T-S) fuzzy singular systems with a time-varying delay. A novel Lyapunov-Krasovskii functional (LKF) approach, named a delay-interval-based piecewise Lyapunov functional, is first introduced. This LKF enables the use of distinct delay-dependent matrices for each partitioned delay subinterval, thereby providing additional information on the delay and its derivative. Secondly, a zero equation approach with delay-variation-dependent free matrices is presented to avoid the appearance of the delay-dependent quadratic function after the LKF's derivative. Subsequently, a cluster of admissibility criteria for the considered systems is derived by incorporating the Bessel-Legendre integral inequality. These criteria exhibit hierarchy, which means that the larger the number of delay-interval partitions, the less conservatism. Finally, the efficacy of the proposed methods is validated through numerical examples.

This article focuses on minimax programming problems subject to addition-Łukasiewicz fuzzy relational inequalities. We first establish two necessary and sufficient conditions for a solution of the fuzzy relational inequalities being a minimal one and explore the existence condition of the unique minimal solution. We then supply an algorithm for obtaining some minimal solutions starting from a given one and apply minimal solutions to the minimax programming problems for searching optimal solutions. We also provide two algorithms for solving a kind of single variable optimization problems and get the greatest optimal solution. The algorithm for finding some minimal solutions of a given one is also used for searching some minimal optimal solutions.

This article researches the admissibility analysis problem for T-S fuzzy Markovian jump singular systems (MJSSs) with time-varying delays. First, based on the new state decomposition vectors, an extended Lyapunov-Krasovskii functional (LKF) is formulated, which allows that the involved matrices are not all positive definite. And, this LKF not only considers the state integral variable, but also makes full use of the time derivative information of membership function, which undoubtedly provides an advantage to the results. Then, based on free matrix integral inequality, a modified version is derived to estimate the value of integral term generated during the derivation of LKF. Based on extended LKF and modified integral inequality, the admissibility criterion with less conservative is obtained for T-S fuzzy MJSSs. Finally, two simulation examples are offered to demonstrate the effectiveness of proposed method.

It is well known that every bivariate copula induces a positive measure on the Borel σ-algebra on ${[0,1]}^2$, but there exist bivariate quasi-copulas that do not induce a signed measure on the same σ-algebra. In this paper we show that a signed measure induced by a bivariate quasi-copula can always be expressed as an infinite combination of measures induced by copulas. With this we are able to give the first characterization of measure-inducing quasi-copulas in the bivariate setting.

Extended multi-adjoint logic programming is a non-monotonic logic programming framework whose semantics is defined in terms of stable models. This paper will focus on the theoretical development of a syntactical sufficient condition for the existence and uniqueness of stable models in extended multi-adjoint logic programming, through the notion of stratification. Namely, we will detail a constructive method for the computation of the unique stable model of a given stratified extended multi-adjoint logic program. As a consequence, this study will be an interesting alternative to the semantical sufficient conditions for the existence and the uniqueness of stable models, given in the literature for multi-adjoint normal logic and extended multi-adjoint logic programs.

This article deals with a class of interval-valued multiobjective optimization problems (abbreviated as, IVMOP). We employ the notions of generalized Hukuhara (abbreviated as, gH) derivative and q-gH-Hessian to introduce the descent direction of the objective function of IVMOP at a noncritical point. Using this descent direction, we propose a new variant of Newton's method for solving IVMOP, employing an Armijo-like rule coupled with a backtracking technique to find the step length. Moreover, we establish that our proposed algorithm converges to a weak effective solution of IVMOP under certain suitable assumptions on the components of the objective function of IVMOP. A non-trivial example has been furnished to demonstrate the effectiveness of the proposed algorithm. To the best of our knowledge, this is the first time that a variant of Newton's method has been introduced to solve IVMOP, that does not involve the approach of scalarization of the objective function.

The (extended) homogeneity plays important, and often crucial role in economics, decision making and image processing. When studying the quasi-homogeneity equation, the multiplicative Cauchy equation on $[0,1]$ naturally appears. However, after a detailed analysis of its existing solutions it turned out that some solution of (extended) homogeneity equation was missing. The aim of the paper is to present a complete list of solutions of the multiplicative Cauchy equation and then to give the missing solution of quasi-homogeneity equation from the previous work. For a triangular norm T, we introduce a new concept of T-quasi-homogeneity and, for a strict t-norm T, we clarify the link between the quasi-homogeneity and the T-quasi-homogeneity.

For L being a completely distributive lattice, we introduce a notion of L-coarse spaces, which can be regarded as a large-scale analogue of probabilistic uniform spaces. The main goal of this paper is to investigate the properties of L-coarse spaces that can induce L-valued coarse proximity spaces. First of all, we introduce a notion of L-valued coarse neighborhood systems, and show that the resulting category is isomorphic to that of L-valued coarse proximity spaces. Then we study the normality of coarsely connected L-coarse spaces and of asymptotically connected L-valued asymptotic resemblance spaces, and show that these two normality properties are coincident. More importantly, we show that a coarsely connected L-coarse space induces an L-valued coarse proximity if and only if it is coarsely normal. We conclude with noting that the previous result are also valid for asymptotically connected L-valued asymptotic resemblance spaces.