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We investigate nonparametric regression methods based on spatial depth and quantiles when the response and the covariate are both functions. As in classical quantile regression for finite dimensional data, regression techniques developed…
We give an introduction to discrete functional analysis techniques for stationary and transient diffusion equations. We show how these techniques are used to establish the convergence of various numerical schemes without assuming…
This paper proposes a new fuzzy assessing procedure with application in management decision making. The proposed fuzzy approach build the membership functions for system characteristics of a standby repairable system. This method is used to…
Estimating the expectation of a real-valued function of a random variable from sample data is a critical aspect of statistical analysis, with far-reaching implications in various applications. Current methodologies typically assume…
Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…
Fuzzy numbers are commonly represented with fuzzy sets. Their objective is to better represent imprecise data. However, operations on fuzzy numbers are not as straightforward as maths on crisp numbers. Commonly, the Zadeh's extension rule…
In the most accessible terms this paper presents a convex-geometric approach to the study of fuzzy vectors. Motivated by several key results from the theory of convex bodies, we establish a representation theorem of fuzzy vectors through…
Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…
We develop a new method to locally cluster curves and discover functional motifs, i.e.~typical ``shapes'' that may recur several times along and across the curves capturing important local characteristics. In order to identify these shared…
In Internet of things (IoT), data is continuously recorded from different data sources and devices can suffer faults in their embedded electronics, thus leading to a high-dimensional data sets and concept drift events. Therefore, methods…
Fuzzing is a popular dynamic program analysis technique used to find vulnerabilities in complex software. Fuzzing involves presenting a target program with crafted malicious input designed to cause crashes, buffer overflows, memory errors,…
In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…
A model's interpretability is essential to many practical applications such as clinical decision support systems. In this paper, a novel interpretable machine learning method is presented, which can model the relationship between input…
We use princiles of fuzzy logic to develop a general model representing several processes in a system's operation characterized by a degree of vagueness and/or uncertainy. Further, we introduce three altenative measures of a fuzzy system's…
Fuzzy logic is an alternate approach for quantifying uncertainty relating to activity duration. The fuzzy version of the backward recursion has been shown to produce results that incorrectly amplify the level of uncertainty. However, the…
In this paper, notion of p - norm generalized trapezoidal intuitionistic fuzzy numbers is introduced. A new ranking method is introduced for p - norm generalized trapezoidal intuitionistic fuzzy numbers. Also we consider linear programming…
A functional data depth provides a center-outward ordering criterion which allows the definition of measures such as median, trimmed means, central regions or ranks in a functional framework. A functional data depth can be global or local.…
In this paper, we first study the arithmetic properties of intuitionistic fuzzy number, the monotonicity of intuitionistic fuzzy function and the derivative of intuitionistic fuzzy functions and then we study the fundamental properties on…
Most of the research related to Non Functional Requirements (NFRs) have presented NFRs frameworks by integrating non functional requirements with functional requirements while we proposed that measurement of NFRs is possible e.g. cost and…
We consider the problem of constructing nonparametric undirected graphical models for high-dimensional functional data. Most existing statistical methods in this context assume either a Gaussian distribution on the vertices or linear…