Related papers: Simplicial depths for fuzzy random variables
A fuzzy clustering algorithm for multidimensional data is proposed in this article. The data is described by vectors whose components are linguistic variables defined in an ordinal scale. The obtained results confirm the efficiency of the…
The treatment of both aleatory and epistemic uncertainty by recent methods often requires an high computational effort. In this abstract, we propose a numerical sampling method allowing to lighten the computational burden of treating the…
Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied…
Moved by the need increased for modeling of the fuzzy data, the success of the systems of exact generation of summary of data, we propose in this paper, a new approach of generation of summary from fuzzy data called Fuzzy-SaintEtiQ. This…
In this paper the author presents a kind of Soft Computing Technique, mainly an application of fuzzy set theory of Prof. Zadeh [16], on a problem of Medical Experts Systems. The choosen problem is on design of a physician's decision model…
Fuzzy implication functions are a key area of study in fuzzy logic, extending the classical logical conditional to handle truth degrees in the interval $[0,1]$. While existing literature often focuses on a limited number of families, in the…
In practical situations, interval-valued fuzzy sets are frequently encountered. In this paper, firstly, we present shadowed sets for interpreting and understanding interval fuzzy sets. We also provide an analytic solution to computing the…
The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…
A standard approach to building a fuzzy controller based on stochastic logic uses binary random signals with an average (expected value of a random variable) in the range [0, 1]. A different approach is presented, founded on a…
The notion of statistical depth has been extensively studied in multivariate and functional data over the past few decades. In contrast, the depth on temporal point process is still under-explored. The problem is challenging because a point…
An orthogonal approach to the fuzzification of both multisets and hybrid sets is presented. In particular, we introduce L-multi-fuzzy and L-fuzzy hybrid sets, which are general enough and in spirit with the basic concepts of fuzzy set…
The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth…
In this article, we combine the concept of a bipolar fuzzy set and a soft set. We introduce the notion of bipolar fuzzy soft set and study fundamental properties. We study basic operations on bipolar fuzzy soft set. We define exdended…
In this book we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), plithogenic logic (as generalization of classical, fuzzy, intuitionistic fuzzy, and neutrosophic logics),…
We propose a novel measure of statistical depth, the metric spatial depth, for data residing in an arbitrary metric space. The measure assigns high (low) values for points located near (far away from) the bulk of the data distribution,…
Concepts of graph theory have applications in many areas of computer science including data mining, image segmentation, clustering, image capturing, networks, etc . An interval-valued fuzzy set is a generalization of the notion of a fuzzy…
Using the concept of fuzzy field, we have considered the fuzzy field of real and complex numbers and thereafter we have established a few standard results of real and complex numbers with respect to a membership function.
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
Statistical depth functions provide measures of the outlyingness, or centrality, of the elements of a space with respect to a distribution. It is a nonparametric concept applicable to spaces of any dimension, for instance, multivariate and…
Motivated by the optimality principles for non-subdifferentiable optimization problems, we introduce new relative subdifferentials and examine some properties for relatively lower semicontinuous functions including $\epsilon$-regular…