Strongly barycentrically associative and preassociative functions

We study the property of strong barycentric associativity, a stronger version of barycentric associativity for functions with indefinite arities. We introduce and discuss the more general property of strong barycentric preassociativity, a generalization of strong barycentric associativity which does not involve any composition of functions. We also provide a generalization of Kolmogoroff-Nagumo's characterization of the quasi-arithmetic mean functions to strongly barycentrically preassociative functions.Comment: arXiv admin note: text overlap with arXiv:1406.434

The Xeros data model: tracking interpretations of archaeological finds

At an archaeological dig, interpretations are built around discovered artifacts based on measurements and informed intuition. These interpretations are semi-structured and organic, yet existing tools do not capture their creation or evolution. Patina of Notes (PoN) is an application designed to tackle this, and is underpinned by the Xeros data model. Xeros is a graph structure and a set of operations that can deal with the addition, edition, and removal of interpretations. This data model is a specialisation of the W3C PROV provenance data model, tracking the evolution of interpretations. The model is presented, with operations defined formally, and characteristics of the representation that are beneficial to implementations are discussed

A classification of barycentrically associative polynomial functions

We describe the class of polynomial functions which are barycentrically associative over an infinite commutative integral domain

A computational approach to George Boole's discovery of mathematical logic

This paper reports a computational model of Boole's discovery of Logic as a part of Mathematics. George Boole (1815–1864) found that the symbols of Logic behaved as algebraic symbols, and he then rebuilt the whole contemporary theory of Logic by the use of methods such as the solution of algebraic equations. Study of the different historical factors that influenced this achievement has served as background for our two main contributions: a computational representation of Boole's Logic before it was mathematized; and a production system, BOOLE2, that rediscovers Logic as a science that behaves exactly as a branch of Mathematics, and that thus validates to some extent the historical explanation. The system's discovery methods are found to be general enough to handle three other cases: two versions of a Geometry due to a contemporary of Boole, and a small subset of the Differential Calculus.Publicad

Snapshot Semantics for Temporal Multiset Relations (Extended Version)

Snapshot semantics is widely used for evaluating queries over temporal data: temporal relations are seen as sequences of snapshot relations, and queries are evaluated at each snapshot. In this work, we demonstrate that current approaches for snapshot semantics over interval-timestamped multiset relations are subject to two bugs regarding snapshot aggregation and bag difference. We introduce a novel temporal data model based on K-relations that overcomes these bugs and prove it to correctly encode snapshot semantics. Furthermore, we present an efficient implementation of our model as a database middleware and demonstrate experimentally that our approach is competitive with native implementations and significantly outperforms such implementations on queries that involve aggregation.Comment: extended version of PVLDB pape

Use of idempotent functions in the aggregation of different filters for noise removal

The majority of existing denoising algorithms obtain good results for a specific noise model, and when it is known previously. Nonetheless, there is a lack in denoising algorithms that can deal with any unknown noisy images. Therefore, in this paper, we study the use of aggregation functions for denoising purposes, where the noise model is not necessary known in advance; and how these functions affect the visual and quantitative results of the resultant images

A Simple Proportional Conflict Redistribution Rule

One proposes a first alternative rule of combination to WAO (Weighted Average Operator) proposed recently by Josang, Daniel and Vannoorenberghe, called Proportional Conflict Redistribution rule (denoted PCR1). PCR1 and WAO are particular cases of WO (the Weighted Operator) because the conflicting mass is redistributed with respect to some weighting factors. In this first PCR rule, the proportionalization is done for each non-empty set with respect to the non-zero sum of its corresponding mass matrix - instead of its mass column average as in WAO, but the results are the same as Ph. Smets has pointed out. Also, we extend WAO (which herein gives no solution) for the degenerate case when all column sums of all non-empty sets are zero, and then the conflicting mass is transferred to the non-empty disjunctive form of all non-empty sets together; but if this disjunctive form happens to be empty, then one considers an open world (i.e. the frame of discernment might contain new hypotheses) and thus all conflicting mass is transferred to the empty set. In addition to WAO, we propose a general formula for PCR1 (WAO for non-degenerate cases).Comment: 21 page

Systematic approach to nonlinear filtering associated with aggregation operators. Part 1. SISO-filters

There are various methods to help restore an image from noisy distortions. Each technique has its advantages and disadvantages. Selecting the appropriate method plays a major role in getting the desired image. Noise removal or noise reduction can be done on an image by linear or nonlinear filtering. The more popular linear technique is based on average (on mean) linear operators. Denoising via linear filters normally does not perform satisfactorily since both noise and edges contain high frequencies. Therefore, any practical denoising model has to be nonlinear. In this work, we introduce and analyze a new class of nonlinear SISO-filters that have their roots in aggregation operator theory. We show that a large body of non-linear filters proposed to date constitute a proper subset of aggregation filters. (C) 2017 The Authors. Published by Elsevier Ltd.This work was supported by grants the RFBR No. 17-07-00886 and by Ural State Forest Engineering's Center of Excellence in "Quantum and Classical Information Technologies for Remote Sensing Systems"