Related papers: Measuring the Directional Distance Between Fuzzy S…
Distance measures are indispensable tools in quantum information processing and quantum computing. This since they can be used to quantify to what extent information is preserved, or altered, by quantum processes. In this paper we propose a…
We consider the directed Hausdorff distance between point sets in the plane, where one or both point sets consist of imprecise points. An imprecise point is modelled by a disc given by its centre and a radius. The actual position of an…
A time series is a sequence of data items; typical examples are videos, stock ticker data, or streams of temperature measurements. Quite some research has been devoted to comparing and indexing simple time series, i.e., time series where…
The concepts of similarity and distance are crucial in data mining. We consider the problem of defining the distance between two data sets by comparing summary statistics computed from the data sets. The initial definition of our distance…
Real-world phenomena often exhibit vagueness, partial truth, and incomplete information. To model such uncertainty in a mathematically rigorous way, many generalized set-theoretic frameworks have been introduced, including Fuzzy Sets [1],…
We investigate the size of the distance set determined by two subsets of finite dimensional vector spaces over finite fields. A lower bound of the size is given explicitly in terms of cardinalities of the two subsets. As a result, we…
While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the…
We propose simple schemes that can perfectly identify projective measurement apparatus secretly chosen from a finite set. Entanglements are used in these schemes both to make possible the perfect identification and to improve the efficiency…
In the paper we define the convergence of compact fuzzy sets as a convergence of alpha-cuts in the topology of compact subsets of a metric space. Furthermore we define typical convergences of fuzzy variables and show relations with…
Keeping in consideration the high demand for clustering, this paper focuses on understanding and implementing K-means clustering using two different similarity measures. We have tried to cluster the documents using two different measures…
Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories…
Fuzzy measures, also referred to as nonadditive measures, emerge from the foundational concept of additive measures by transforming additivity into monotonicity. In comparison to the expansive $2^n$ coefficients of fuzzy measures, additive…
This paper defines a distance function that measures the dissimilarity between planar geometric figures formed with straight lines. This function can in turn be used in partial matching of different geometric figures. For a given pair of…
Dynamical systems often exhibit the emergence of long-lived coherent sets, which are regions in state space that keep their geometric integrity to a high extent and thus play an important role in transport. In this article, we provide a…
On the basis of network analysis, and within the context of modeling imprecision or vague information with fuzzy sets, we propose an innovative way to analyze, aggregate and apply this uncertain knowledge into community detection of…
Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve…
Given two distinct datasets, an important question is if they have arisen from the the same data generating function or alternatively how their data generating functions diverge from one another. In this paper, we introduce an approach for…
This paper proposes a new approach to multi-sensor data fusion. It suggests that aggregation of data from multiple sensors can be done more efficiently when we consider information about sensors' different characteristics. Similar to most…
Understanding distance metrics in high-dimensional spaces is crucial for various fields such as data analysis, machine learning, and optimization. The Manhattan distance, a fundamental metric in multi-dimensional settings, measures the…
For a multi-attribute decision making (MADM) problem, the information of alternatives under different attributes is given in the form of intuitionistic fuzzy number(IFN). Intuitionistic fuzzy set (IFS) plays an important role in dealing…