China
Africa
Explore chapters and articles related to this topic
Fuzzy-Genetic Approach to Epidemiology
Published in Jyoti Mishra, Ritu Agarwal, Abdon Atangana, Mathematical Modeling and Soft Computing in Epidemiology, 2020
Minakshi Biswas Hathiwala, Jignesh Pravin Chauhan, Gautam Suresh Hathiwala
In mathematics, general topology, viz., point set topology or ordinary topology, deals with the characteristics of a space that are preserved under continuous distortions, such as stretching and bending, but not tearing or gluing. General topology, which is based on the crisp set, establishes the foundational aspects of other branches of topology. Pretopological spaces are the generalization of topological spaces. Two elements may be close to a third element via some relation; however, there is not sufficient structure to say which one of them is closer or nearer. Such a space is called a topological space. It has a suitable structure to embrace the concept of boundary. If we remove the underlying behavior of boundary from this structure, the weakest notion of nearness is uncovered, and thus, we obtain a pretopological space [7]. It is customary to define topology on a set through a class of open sets or a class of closed sets [8]. However, the concept of topology on a set can also be presented through operators such as closures, neighborhoods, and interiors instead of the conventional class of open or closed sets [9].
An alternative construction of uninorms on bounded lattices
Published in International Journal of General Systems, 2023
In a general topology, by considering a nonempty set A and the set of all subsets of A, the closure operator (resp. interior operator) in is defined as an expansive, isotone and idempotent map (resp. a contractive, isotone and idempotent map ). Both of these operators can be used for constructing topologies in A in a general topology (Engelking 1989). More precisely, a one-to-one correspondence from the set of all topologies in A to the set of all closure (interior) operators in . That is, any topology in a nonempty set can induce the closure (interior) operator on its underlying powerset. It should be pointed out that closure and interior operators can be defined in a lattice of all subsets of a set A with the set union as the join and the set intersection as the meet. Hence, Everett (1944) extended the closure operator (resp. interior operator) in to a general lattice where the condition (resp. ) is omitted.
Lightweight design process considering assembly connection and non-probabilistic uncertainty with its application to machine structural design
Published in Engineering Optimization, 2023
Bobin Guan, Min Wan, Xiangdong Wu, Xuexi Cui, Yisheng Zhang
To ensure the optimization space, first, a sufficient design domain should be provided in topology optimization. According to this principle, the initial design model is constructed as a square structure with joint holes of the columns. In addition, a fixed stepped hole is designed at the middle of the upper beam, as the space reserved for the deformation of the blank and for the non-contact measurement device. Following the division of the design and non-design domains, a general topology optimization is conducted. Figure 10 shows the optimization results, and indicates that the obtained structure remains centrally symmetrical; however, manufacturing certain areas is challenging. For example, the upper and lower surfaces of the upper beam are retained, while the materials between them are removed. In addition, the microstructure is exposed at the interface of the design and non-design domains. Thus, manufacturing constraints need to be introduced in topology optimization.
H 2 input load disturbance rejection controller design for synchronised output regulation of time-delayed multi-agent systems with frequency domain method
Published in International Journal of Control, 2019
For a general topology, V is still a unitary matrix and Λ is an upper triangular matrix. Let and , then the transfer matrix H(s) can be diagonalised: and where Since Λ is upper triangular and both and are diagonal, we get It is worth noting that Equation (17) is composed of N isolated systems. System (17) is asymptotically internally stable if and only if all the transfer matrices Hi(s) of N subsystems can achieve internally stable simultaneously.