Computing fuzzy rough approximations in large scale information systems

Rough set theory is a popular and powerful machine learning tool. It is especially suitable for dealing with information systems that exhibit inconsistencies, i.e. objects that have the same values for the conditional attributes but a different value for the decision attribute. In line with the emerging granular computing paradigm, rough set theory groups objects together based on the indiscernibility of their attribute values. Fuzzy rough set theory extends rough set theory to data with continuous attributes, and detects degrees of inconsistency in the data. Key to this is turning the indiscernibility relation into a gradual relation, acknowledging that objects can be similar to a certain extent. In very large datasets with millions of objects, computing the gradual indiscernibility relation (or in other words, the soft granules) is very demanding, both in terms of runtime and in terms of memory. It is however required for the computation of the lower and upper approximations of concepts in the fuzzy rough set analysis pipeline. Current non-distributed implementations in R are limited by memory capacity. For example, we found that a state of the art non-distributed implementation in R could not handle 30,000 rows and 10 attributes on a node with 62GB of memory. This is clearly insufficient to scale fuzzy rough set analysis to massive datasets. In this paper we present a parallel and distributed solution based on Message Passing Interface (MPI) to compute fuzzy rough approximations in very large information systems. Our results show that our parallel approach scales with problem size to information systems with millions of objects. To the best of our knowledge, no other parallel and distributed solutions have been proposed so far in the literature for this problem

The Application of Dominance-based Rough Sets Theory to Evaluation of Transportation Systems

AbstractThe paper presents an original procedure of evaluation of a transportation system, resulting in its assignment into a predefined class, representing the overall standard of the considered system and the level of transportation service. The method relies on the application of the dominance-based rough set theory (DRST), allows for thorough data exploration, evaluation of informational content of the considered characteristics and generation of certain decision rules that support t he evaluation process. In the analysis different characteristics (criteria and attributes) describing various aspects of a transportation system operations are taken into account. The assignment of a transportation system to a specific quality class is performed based on the values of characteristics which are compared with the evaluation pattern, i.e. the set of decision rules generated through the analysis of customers’ opinions and expectations concerning a transportation system. The method is composed of three major steps, including: 1) identification of the most important characteristics, 2) generation of the evaluation pattern, and 3) assignment of the transportation system to the appropriate class. In the evaluation process five key components of a transportation system, including: transportation means, human resources, informational resources, transportation infrastructure and technical equipment as well as organizational rules are considered