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.