Related papers: A Fuzzy Directional Distance Measure
In this paper, a similarity-driven cluster merging method is proposed for unsuper-vised fuzzy clustering. The cluster merging method is used to resolve the problem of cluster validation. Starting with an overspecified number of clusters in…
We introduce the so--called doubling metric on the collection of non--empty bounded open subsets of a metric space. Given a subset $U$ of a metric space $X$, the predecessor $U_{*}$ of $U$ is defined by doubling the radii of all open balls…
The paper proposes another extension of the extremal principle. A new extremality model involving collections of arbitrary families of sets is studied. It generalizes the conventional model based on linear translations of given sets as well…
Fuzzy metric spaces, grounded in t-norms and membership functions, have been widely proposed to model uncertainty in machine learning, decision systems, and artificial intelligence. Yet these frameworks treat uncertainty as an external…
Following the definition of intuitionistic fuzzy n-norm [ 3 ], we have introduced the definition of intuitionistic fuzzy norm (in short IFN) over a linear space and there after a few results on intuitionistic fuzzy normed linear space and…
The concept of a fuzzy number is generalized to the case of a finite carrier set of partially ordered elements, more precisely, a lattice, when a membership function also takes values in a partially ordered set (a lattice). Zadeh's…
The choice of a point set, to be used in numerical integration, determines, to a large extent, the error estimate of the integral. Point sets can be characterized by their discrepancy, which is a measure of its non-uniformity. Point sets…
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…
Traditional finite element method is a well-established method to solve various problems of science and engineering. Different authors have used various methods to solve governing differential equation of heat conduction problem. In this…
To deal with uncertainty in reasoning, interval-valued logic has been developed. But uniform intervals cannot capture the difference in degrees of belief for different values in the interval. To salvage the problem triangular and…
In this paper a fuzzy clustering model for fuzzy data with outliers is proposed. The model is based on Wasserstein distance between interval valued data which is generalized to fuzzy data. In addition, Keller's approach is used to identify…
Red and blue galaxies are traditionally classified using some specific cuts in colour or other galaxy properties, which are supported by empirical arguments. The vagueness associated with such cuts are likely to introduce a significant…
A smartphone is a powerful learning aid in the hands of a large section of students around the world. The camera of the phone can be used for several learning purposes apart from its obvious purpose of photographing. If the focal length of…
It is shown that an aspect of the process of individuation may be thought of as a fuzzy set. The process of individuation has been interpreted as a two-valued problem in the history of philosophy. In this work, I intend to show that such a…
The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
Wasserstein distances provide a powerful framework for comparing data distributions. They can be used to analyze processes over time or to detect inhomogeneities within data. However, simply calculating the Wasserstein distance or analyzing…
Simulations and bisimulations are well-established notions in crisp/fuzzy automata theory and are widely used to compare the behaviors of automata. Their main drawback is that they compare the behaviors of fuzzy automata in a crisp manner.…
Alternative novel measures of the distance between any two partitions of a n-set are proposed and compared, together with a main existing one, namely 'partition-distance' D(.,.). The comparison achieves by checking their restriction to…
We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…