Metrics and their weaker forms are used to measure the difference between two data. There are many metrics that are available but not desired by a practitioner. This paper recommends in a plausible reasoning manner an easy-to-understand method to construct desired distance-like measures: to fuse easy-to-obtain pseudo-semi-metrics, pseudo-metrics, or metrics by making full use of well-known t-norms, t-conorms, aggregation operators, and similar operators. The simple reason to do this is that data for a real world problem are sometimes from multiagents. (...) A distance-like notion, called weak interval-valued pseudo-metrics, is defined by using known notions of pseudo-semi-metrics, pseudo-metrics, and metrics; this notion is topologically good and shows precision, flexibility, and compatibility than single pseudo-semi-metrics, pseudo-metrics, or metrics. Propositions and detailed examples are given to illustrate how to fabricate an expected or demanded WIVP-metric in practical problems, and WIVP-metric and its special cases are characterized by using axioms. Moreover, some WIVP-metrics pertinent to quantitative logic theory or interval-valued fuzzy graphs are constructed, and fixed point theorems and common fixed point theorems in weak interval-valued metric spaces are also presented. Topics and strategies for further study are also put forward concretely and clearly. (shrink)

BackgroundBilateral cerebral palsy is the most common type of CP in children and is often accompanied by different degrees of communication impairment. Several studies have attempted to identify children at high risk for communication impairment. However, most prediction factors are qualitative and subjective and may be influenced by rater bias. Individualized objective diagnostic and/or prediction methods are still lacking, and an effective method is urgently needed to guide clinical diagnosis and treatment. The aim of this study is to develop and (...) validate an objective, individual-based model for the prediction of communication impairment in children with BCP by the time they enter school.MethodsA multicenter prospective cohort study will be conducted in four Chinese hospitals. A total of 178 children with BCP will undergo advanced brain magnetic resonance imaging at baseline. At school entry, communication performance will be assessed by a communication function classification system. Three-quarters of children with BCP will be allocated as a training cohort, whereas the remaining children will be allocated as a test cohort. Multivariate lesion- and connectome-based approaches, which have shown good predictive ability of language performance in stroke patients, will be applied to extract features from MR images for each child with BCP. Multiple machine learning models using extracted features to predict communication impairment for each child with BCP will be constructed using data from the training cohort and externally validated using data from the test cohort. Prediction accuracy across models in the test cohort will be statistically compared.DiscussionThe findings of the study may lead to the development of several translational tools that can individually predict communication impairment in children newly diagnosed with BCP to ensure that these children receive early, targeted therapeutic intervention before they begin school.Trial registrationThe study has been registered with the Chinese Clinical Trial Registry. (shrink)