Fuzzy Sets and Systems最新文献

In this paper, we want to use the idea of fuzzy topological space generated by classical topological space to study generated algebraic closure space and its applications. Firstly, we show that the generated $\text{Q}$-Scott open set monad induced by classical Scott open set monad is a submonad of $\text{Q}$-Scott open set monad if and only if the underlying partial order of the quantale $\text{Q}$ is a frame. Then, we give a reasonable explanation for constructing Scott algebraic closure system on a frame $\text{Q}$ since it plays a similar role as Scott topology in topology. Finally, by the Scott algebraic closure system, we construct a monad on the category of $T_0$ separated algebraic closure spaces and show that the Eilenberg-Moore algebras of this monad are precisely frames.

Because competitive neural networks (CNNs) can simulate the phenomena of lateral inhibition among neurons, their dynamics are attracting increasing attention, which motives us to investigate the global exponential synchronization issue of multiple time-delays fuzzy CNNs (MDFCNNs) with different time scales in this article. Firstly, to solve the significant resource wastage problem caused by the time-triggered mechanism previously adopted in CNNs, a novel intermittent dynamic event-triggered mechanism is proposed. It is worth mentioning that the fuzzy logic systems are also utilized in this model and controller, effectively handling the uncertainties and nonlinearities in practical problems. Secondly, by designing the intermittent static/dynamic event-triggered mechanism, we derive the global exponential synchronization conditions for MDFCNNs with different time scales under a simpler and more implementable controller composed of a linear negative feedback control term. We also utilize the reduction to absurdity to demonstrate the nonexistence of Zeno behavior for the error system of master-slave CNNs. Furthermore, we provide several corollaries to further indicate the generality of the model and the cost savings of the control mechanism. Finally, we provide an example and some comparisons to demonstrate the efficiency of the derived theoretical findings.

The purpose of this paper is to study antitone involutions on tensor products of complete lattices. A lattice with antitone involution is called an involution lattice. We show that if M is a completely distributive involution lattice, then for each complete involution lattice L there exists a unique antitone involution on the tensor product $M\otimes L$ such that the natural embeddings of M and L into $M\otimes L$ are involution-preserving. This is best possible, since the described property characterizes complete distributivity in the class of complete involution lattices. When M and L are completely distributive involution lattices, $M\otimes L$ with the aforementioned antitone involution is the codomain of a universal bimorphism in the sense of the category of all completely distributive de Morgan algebras and their join- and involution-preserving maps. The case that M and L are orthocomplemented is explored too.

We provide a direct formula for Ralescu's scalar cardinality. Unlike the original, iterative definition, the formula reveals intuitive shortcomings of this concept of cardinality. These are apparent from examples and reflected formally in that, as we show, the concept violates one of the axioms of cardinality of fuzzy sets. In addition, we provide a relationship of this concept to Ralescu's concept of fuzzy cardinality which unveils a tight link between the two concepts and points out another counterintuitive property of the concept of scalar cardinality. We argue that the discussed concept of fuzzy cardinality represents an interesting proposition, suggest its geometric interpretation, and provide preliminary observations as a basis for future considerations.

The wide usage of large-scale knowledge graphs (KGs) motivates the development of user-friendly interfaces so that knowledge graphs become more readily accessible to a larger population. Natural language-based question answering (QA) systems are widely investigated and developed in the context of KGs, which can provide users with a natural means to retrieve the information they need from KGs without expecting them to know the query language. It is very common that natural language contains linguistic terms (fuzzy terms), and fuzzy (flexible) query has been widely investigated in the context of databases. This paper contributes a QA system with fuzzy terms over KGs called f-KGQA. f-KGQA can deal with different types of questions, including simple questions, complex questions, and questions with fuzzy terms. More importantly, users are provided with a channel to flexibly define their fuzzy terms based on their understanding. Our experimental results demonstrate the effectiveness and applicability of f-KGQA in handling questions with fuzzy terms.

The purpose of the paper is to formulate Choquet integral representation theorems for a monotone functional on a collection of functions in such a way that the representing measures are simultaneously inner and outer continuous on appropriate collections of sets such as open, closed, compact, and measurable. This type of theorem is referred to as the continuous Choquet integral representation theorem and will be discussed in a setting general enough for practical use. The benefits of our results are as follows:

• (i)

  the representing measures are simultaneously inner and outer continuous,

• (ii)

  the collections of sets for which the representing measures are inner and outer continuous are larger than those in previous studies,

• (iii)

  the regularity of the representing measures is also considered, and

• (iv)

  it is possible to handle not only σ-continuous but also τ-continuous functionals.

The main goal of this paper is to introduce new local stability conditions for continuous-time Takagi-Sugeno (T-S) fuzzy systems. These stability conditions are based on linear matrix inequalities (LMIs) in combination with quadratic Lyapunov functions. Moreover, they integrate information on the membership functions at the origin and effectively leverage the linear structure of the underlying nonlinear system in the vicinity of the origin. As a result, the proposed conditions are proved to be less conservative compared to existing methods using fuzzy Lyapunov functions. Moreover, we establish that the proposed methods offer necessary and sufficient conditions for the local exponential stability of T-S fuzzy systems. Discussions on the inherent limitations associated with fuzzy Lyapunov approaches are also given. To illustrate the theoretical results, we provide comprehensive examples that demonstrate the core concepts and validate the efficacy of the proposed conditions.

This paper proposes a protocol-based secure guaranteed cost sampled-data controller design problem of Takagi-Sugeno (T-S) fuzzy system under denial-of-service (DoS) attack and input saturation. First, in the absence of an effective description for the characteristics of received signals on controller, a novel scheduling protocol is proposed according to the characteristics of the round-robin protocol and DoS attack, which can guarantee the specific sequence characteristic for control updates. Then, via introducing input delay approach and switched system modeling method, a time-delay switched system with fixed switching sequence is introduced to describe the considered system with DoS phenomenon. Moreover, some novel control criteria are presented to ensure the resulting closed-loop system reaches a required cost level under the obtained control law. And an optimization problem is proposed to compute the optimal upper of the specified cost level. Finally, a simulation example is presented to demonstrate the effectiveness of the algorithm.

Recently, De Miguel, Bustince and De Baets have conducted a systematic study on convolution lattices based on distributive lattices. There have been few reports on applying non-distributive lattices to a domain of functions. As a complement to their work, in this paper, we carry out an in-depth investigation of convolution operations of the functions between a non-distributive lattice (domain) and a frame (co-domain). We first present an equivalence characterization between non-distributive lattices and idempotent functions and further show that a subset of the set of idempotent functions is closed under convolution operations. We demonstrate that this subset also is a bisemilattice and satisfies the Birkhoff equation under join- and meet-convolution operations. Finally, we analyze and study the lattice structure related to the obtained algebraic structure.