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Continuity of the polytope generated by a set of matrices is dealt with in this paper. We have defined a norm for the polytope, and verified when these matrices belong to a compact set in Rn×n the norm is bounded and the polytope is compact. Moreover, we have verified if the polytope is treated as a set-valued mapping from Rn to Rn, it is continuous and with convex and compact values.
This paper considers the fundamental properties of polytopes in Banach space. A norm is defined for the polytopes and the preliminarily properties are then analyzed. It is proved that the linear summation of two polytopes is still a polytope. For a given compact set, its polytope is compact if and only if the supporting space is with finite dimension. If the dimension of its supporting space is infinite,...
In this paper we study different properties of continuity and regularity for the special fuzzy multimeasure induced by the set-valued integral of a Birkhoff weak real function with respect to a set multifunction taking values in the family of all nonempty subsets of a real Banach space.
This paper is held in the information technology services management environment, with a few ideas of information technology governance, and purposes to implement a hybrid model to manage the services of a database, based on the principles of information technology services management in a supplementary health operator. It is a hybrid model because utilizes fundamental nuances of services management...
This paper presents a methodology that defines the most suitable configurations to allocate reclosers in power distribution networks. The methodology is composed by two stages. At the first stage, optimal configurations to install reclosers in each feeder are established, considering the improvement promoted in continuity indexes. Each configuration corresponds to a previously fixed number of reclosers...
In this paper, we propose a natural way to define topologies by using fuzzy metrics; here the value of the distance between two points is a non-negative fuzzy number. With such topology, we also define notions like continuity, convergent sequence, Cauchy sequences and complete spaces. As an application, we provide a fixed point theorem quite similar to the classical Banach's theorem.
This paper tries to show some important properties of the single input rule modules (SIRMs) connected fuzzy inference systems (FIS), including both type-1 (T1) and interval type-2 (IT2) FISs. Three kinds of properties — continuity, monotonicity and robustness — are explored. First, conditions on the parameters are derived to ensure that the SIRMs connected FISs are continuous and monotonic. Then,...
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