Interval graph is a very important subclass of intersection graphs and perfect graphs. It has many applications in different real life situations. The problems on interval graph are solved by using different data structures among them interval tree is very useful. During last decade this data structure is used to solve many problems on interval graphs due to its nice properties. Some of its imp...

it is firstly proved that the multi-input-single-output (miso) fuzzy systems based on interval-valued $r$- and $s$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  a formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

This paper studies how to conduct efficiency assessment using data envelopment analysis (DEA) in interval and/or fuzzy input–output environments. A new pair of interval DEA models is constructed on the basis of interval arithmetic, which differs from the existing DEA models handling interval data in that the former is a linear CCR model without the need of extra variable alternations and uses a...

The recording of multiple interval-censored failure times is common in dental research. Modeling multilevel data has been a difficult task. This paper aims to use the Bayesian approach to analyze a set of multilevel clustered interval-censored data from a clinical study to investigate the effectiveness of silver diamine fluoride and sodium fluoride varnish in arresting active dentin caries in C...

The existing image and data compression techniques try to minimize the mean square deviation between the original data f(x, y, z) and the compressed-decompressed data f̃(x, y, z). In many practical situations, reconstruction that only guaranteed mean square error over the data set is unacceptable. For example, if we use the meteorological data to plan a best trajectory for a plane, then what we ...

Interval data is attracting attention from the data analysis community due to its ability to describe complex concepts. Since clustering is an important data analysis tool, extending these techniques to interval data is important. Applying traditional clustering methods on interval data loses information inherited in this particular data type. This paper proposes a novel dissimilarity measure w...

The Fuzzy Kohonen Clustering Network combines the idea of fuzzy membership values for learning rates. It is a kind of self-organizing fuzzy neural network that can show great superiority in processing the ambiguity and the uncertainty of data sets or images. Symbolic data analysis provides suitable tools for managing aggregated data described by intervals. This paper introduces Fuzzy Kohonen Cl...

In a recent paper, Kooperberg, Stone, and Truong (1995a) introduced hazard regression (HARE), in which linear splines and their tensor products are used to estimate the conditional log-hazard function based on possibly censored, positive response data and one or more covariates. Model selection is carried out in an adaptive fashion using maximum likelihood estimation of the unknown coefficients...

This paper is devoted to the problem of fitting input-output data by a modeling function, linear in its parameters, in the presence of interval-bounded errors in output variable. A method for outlier detection is proposed. Another issue under consideration is the comparative simulation study of the well-known statistical point estimates (least squares, maximum likelihood) and point estimates ca...

Bivariate interval censored data arises in many applications. However, both theoretical and computational investigations for this type of data are limited because of the complicated structure of bivariate censoring. In this paper, we propose a two-stage spline-based sieve estimator for the association between two event times with bivariate case 2 interval censored data. A smooth and explicit es...