The Order-Preserving SubMatrices (OPSMs) capture consensus trends over columns shared by rows in a data matrix. Mining OPSM patterns discovers important and interesting local correlations in many real applications, such as those involving biological data or sensor data. The prevalence of uncertain data in various applications, however, poses new challenges for OPSM mining, since data uncertaint...

A new approach to define the similarity measure betweeninterval-valued fuzzy sets is presented. The proposed approach isbased on a weighted measure in which the normalized similaritiesbetween lower functions and also between upper functions arecombined by a weight parameter. The properties of this similaritymeasure are investigated. It is shown that, the proposed measurehas some advantages in c...

Fuzzy valued measure ([7], [10], [3], [5]) is a natural generalization of a set valued measure ([6]). Infinite addition is defined ([12]) as a Zadeh’s extension principle of continuity. In [9], using an additive fuzzy valued measure, an integral of single valued function is defined and some basic properties are given. In this paper we proceed to investigate specific properties of integrals in f...

Given a constraint set with k constraints in the framework of Optimality Theory (OT), what is its capacity as a classification scheme for linguistic data? One useful measure of this capacity is the size of the largest data set of which each subset is consistent with a different grammar hypothesis. This measure is known as the Vapnik-Chervonenkis dimension (VCD) and is a standard complexity meas...

Inter alia, Lebesgue-style integration plays a major role in advanced probability. We formalize a significant part of its theory in Higher Order Logic using the generic interactive theorem prover Isabelle/Isar. This involves concepts of elementary measure theory, real-valued random variables as Borelmeasurable functions, and a stepwise inductive definition of the integral itself. Building on pr...