New Model of Heteroasociative min Memory Robust to Acquisition Noise

Associative memories in min and max algebra are of great interest for pattern recognition. One property of these is that they are one-shot, that is, in an attempt they converge to the solution without having to iterate. These memories have proven to be very efficient, but they manifest some weakness with mixed noise. If an appropriate kernel is not used, that is, a subset of the pattern to be recalled that is not affected by noise, memories fail noticeably. A possible problem for building kernels with sufficient conditions, using binary and gray-scale images, is not knowing how the noise is registered in these images. A solution to this problem is presented by analyzing the behavior of the acquisition noise. What is new about this analysis is that, noise can be mapped to a distance obtained by a distance transform. Furthermore, this analysis provides the basis for a new model of min heteroassociative memory that is robust to the acquisition/mixed noise. The proposed model is novel because min associative memories are typically inoperative to mixed noise. The new model of heteroassocitative memory obtains very interesting results with this type of noise.

An Asymptotic Cyclicity Analysis of Live Autonomous Timed Event Graphs

Designing a discrete event system converging to steady temporal patterns is an essential issue of a system with time window constraints. Until now, to analyze asymptotic stability, we have modeled a timed event graph’s dynamic behavior, transformed it into the matrix form of (max,+) algebra, and then constructed a precedence graph. This article’s aim is to provide a theoretical basis for analyzing the stability and cyclicity of timed event graphs without using (max,+) algebra. In this article, we propose converting one timed event graph to another with a dynamic behavior equivalent to that of the original without going through the conversion process. This paper also guarantees that the derived final timed event graph has the properties of a precedence graph. It then investigates the relationship between the properties of the derived precedence graph and that of the original timed event graph. Finally, we propose a method to analyze asymptotic cyclicity and stability for a given timed event graph by itself. The analysis this article provides makes it easy to analyze and improve asymptotic time patterns of tasks in a given discrete event system modeled with a live autonomous timed event graph such as repetitive production scheduling.

Factor rank preservers of matrices over additively-idempotent multiplicatively-cancellative semirings

Here, we characterize the linear operators that preserve factor rank of matrices over additively-idempotent multiplicatively-cancellative semirings. The main results in this paper generalize the corresponding results on the two element Boolean algebra [L. B. Beasley and N. J. Pullman, Boolean-rank-preserving opeartors and Boolean-rank-1 spaces, Linear Algebra Appl. 59 (1984) 55–77] and on the max algebra [R. B. Bapat, S. Pati and S.-Z. Song, Rank preservers of matrices over max algebra, Linear Multilinear Algebra 48(2) (2000) 149–164]; and hold on max-plus algebra and some other tropical semirings.

Strong Tolerance and Strong Universality of Interval Eigenvectors in a Max-Łukasiewicz Algebra

The Łukasiewicz conjunction (sometimes also considered to be a logic of absolute comparison), which is used in multivalued logic and in fuzzy set theory, is one of the most important t-norms. In combination with the binary operation ‘maximum’, the Łukasiewicz t-norm forms the basis for the so-called max-Łuk algebra, with applications to the investigation of systems working in discrete steps (discrete events systems; DES, in short). Similar algebras describing the work of DES’s are based on other pairs of operations, such as max-min algebra, max-plus algebra, or max-T algebra (with a given t-norm, T). The investigation of the steady states in a DES leads to the study of the eigenvectors of the transition matrix in the corresponding max-algebra. In real systems, the input values are usually taken to be in some interval. Various types of interval eigenvectors of interval matrices in max-min and max-plus algebras have been described. This paper is oriented to the investigation of strong, strongly tolerable, and strongly universal interval eigenvectors in a max-Łuk algebra. The main method used in this paper is based on max-Ł linear combinations of matrices and vectors. Necessary and sufficient conditions for the recognition of strong, strongly tolerable, and strongly universal eigenvectors have been found. The theoretical results are illustrated by numerical examples.

Rough interval Max Plus Algebra for Transportation Problems

The traffic problem is an important problem which has been broadly learnt in Operations Research domain. This paper presents a new Rough Interval Max Algebra Approach (RIMAA) for solving the traffic problem with Rough Interval data. The proposed approach is simple and able to give a suitable solution to this problem. Finally, a descriptive example is given to evaluate performance of the proposed approach.

Rough interval Max Plus Algebra for Transportation Problems

The traffic problem is an important problem which has been broadly learnt in Operations Research domain. This paper presents a new Rough Interval Max Algebra Approach (RIMAA) for solving the traffic problem with Rough Interval data. The proposed approach is simple and able to give a suitable solution to this problem. Finally, a descriptive example is given to evaluate performance of the proposed approach.