Generation of Exhaustive Set of Rules within Dominance-based Rough Set Approach

AbstractThe rough sets theory has proved to be a useful mathematical tool for the analysis of a vague description of objects. One of extensions of the classic theory is the Dominance-based Set Approach (DRSA) that allows analysing preference-ordered data. The analysis ends with a set of decision rules induced from rough approximations of decision classes. The role of the decision rules is to explain the analysed phenomena, but they may also be applied in classifying new, unseen objects. There are several strategies of decision rule induction. One of them consists in generating the exhaustive set of minimal rules. In this paper we present an algorithm based on Boolean reasoning techniques that follows this strategy with in DRSA

Discretisation of conditions in decision rules induced for continuous

Typically discretisation procedures are implemented as a part of initial pre-processing of data, before knowledge mining is employed. It means that conclusions and observations are based on reduced data, as usually by discretisation some information is discarded. The paper presents a different approach, with taking advantage of discretisation executed after data mining. In the described study firstly decision rules were induced from real-valued features. Secondly, data sets were discretised. Using categories found for attributes, in the third step conditions included in inferred rules were translated into discrete domain. The properties and performance of rule classifiers were tested in the domain of stylometric analysis of texts, where writing styles were defined through quantitative attributes of continuous nature. The performed experiments show that the proposed processing leads to sets of rules with significantly reduced sizes while maintaining quality of predictions, and allows to test many data discretisation methods at the acceptable computational costs

Rough Set Applied to Air Pollution: A New Approach to Manage Pollutions in High Risk Rate Industrial Areas

This study presents a rough set application, using together the ideas of classical rough set approach, based on the indiscernibility relation and the dominance-based rough set approach (DRSA), to air micro-pollution management in an industrial site with a high environmental risk rate, such as the industrial area of Syracuse, located in the South of Italy (Sicily). This new data analysis tool has been applied to different decision problems in various fields with considerable success, since it is able to deal both with quantitative and with qualitative data and the results are expressed in terms of decision rules understandable by the decision-maker. In this chapter, some issue related to multi-attribute sorting (i.e. preference-ordered classification) of air pollution risk is presented, considering some meteorological variables, both qualitative and quantitative as attributes, and criteria describing the different objects (pollution occurrences) to be classified, that is, different levels of sulfur oxides (SOx), nitrogen oxides (NOx), and methane (CH4) as pollution indicators. The most significant results obtained from this particular application are presented and discussed: examples of ‘if, … then’ decision rules, attribute relevance as output of the data analysis also in terms of exchangeable or indispensable attributes/criteria, of qualitative substitution effect and interaction between them

Evolutionary approaches to optimisation in rough machining

This thesis concerns the use of Evolutionary Computation to optimise the sequence and selection of tools and machining parameters in rough milling applications. These processes are not automated in current Computer-Aided Manufacturing (CAM) software and this work, undertaken in collaboration with an industrial partner, aims to address this. Related research has mainly approached tool sequence optimisation using only a single tool type, and machining parameter optimisation of a single-tool sequence. In a real world industrial setting, tools with different geometrical profiles are commonly used in combination on rough machining tasks in order to produce components with complex sculptured surfaces. This work introduces a new representation scheme and search operators to support the use of the three most commonly used tool types: end mill, ball nose and toroidal. Using these operators, single-objective metaheuristic algorithms are shown to find near-optimal solutions, while surveying only a small number of tool sequences. For the first time, a multi-objective approach is taken to tool sequence optimisation. The process of ‘multi objectivisation’ is shown to offer two benefits: escaping local optima on deceptive multimodal search spaces and providing a selection of tool sequence alternatives to a machinist. The multi-objective approach is also used to produce a varied set of near-Pareto optimal solutions, offering different trade-offs between total machining time and total tooling costs, simultaneously optimising tool sequences and the cutting speeds of individual tools. A challenge for using computationally expensive CAM software, important for real world machining, is the time cost of evaluations. An asynchronous parallel evolutionary optimisation system is presented that can provide a significant speed up, even in the presence of heterogeneous evaluation times produced by variable length tool sequences. This system uses a distributed network of processors that could be easily and inexpensively implemented on existing commercial hardware, and accessible to even small workshops

Rough set and rule-based multicriteria decision aiding

The aim of multicriteria decision aiding is to give the decision maker a recommendation concerning a set of objects evaluated from multiple points of view called criteria. Since a rational decision maker acts with respect to his/her value system, in order to recommend the most-preferred decision, one must identify decision maker's preferences. In this paper, we focus on preference discovery from data concerning some past decisions of the decision maker. We consider the preference model in the form of a set of "if..., then..." decision rules discovered from the data by inductive learning. To structure the data prior to induction of rules, we use the Dominance-based Rough Set Approach (DRSA). DRSA is a methodology for reasoning about data, which handles ordinal evaluations of objects on considered criteria and monotonic relationships between these evaluations and the decision. We review applications of DRSA to a large variety of multicriteria decision problems

Robust ordinal regression for value functions handling interacting criteria

International audienceWe present a new method called UTAGMS–INT for ranking a finite set of alternatives evaluated on multiple criteria. It belongs to the family of Robust Ordinal Regression (ROR) methods which build a set of preference models compatible with preference information elicited by the Decision Maker (DM). The preference model used by UTAGMS–INT is a general additive value function augmented by two types of components corresponding to ‘‘bonus’’ or ‘‘penalty’’ values for positively or negatively interacting pairs of criteria, respectively. When calculating value of a particular alternative, a bonus is added to the additive component of the value function if a given pair of criteria is in a positive synergy for performances of this alternative on the two criteria. Similarly, a penalty is subtracted from the additive component of the value function if a given pair of criteria is in a negative synergy for performances of the considered alternative on the two criteria. The preference information elicited by the DM is composed of pairwise comparisons of some reference alternatives, as well as of comparisons of some pairs of reference alternatives with respect to intensity of preference, either comprehensively or on a particular criterion. In UTAGMS–INT, ROR starts with identification of pairs of interacting criteria for given preference information by solving a mixed-integer linear program. Once the interacting pairs are validated by the DM, ROR continues calculations with the whole set of compatible value functions handling the interacting criteria, to get necessary and possible preference relations in the considered set of alternatives. A single representative value function can be calculated to attribute specific scores to alternatives. It also gives values to bonuses and penalties. UTAGMS–INT handles quite general interactions among criteria and provides an interesting alternative to the Choquet integral