Ordinal classification problems with monotonicity constraints (also referred to as multicriteria classification problems) often appear in real-life applications, however, they are considered relatively less frequently in theoretical studies than regular classification problems. We introduce a rule induction algorithm based on the statistical learning approach that is tailored for this type of p...

Scientific analysis of decision problems aims at giving the decision maker (DM) a recommendation concerning a set of objects (called also alternatives, solutions, acts, actions, cases, candidates) evaluated from the point of view of a plurality of their characteristics considered relevant for the problem at hand, and called attributes. For example, a decision can regard: 1) diagnosis of patholo...

Lower and upper approximations of upward (downward) union of decision classes in Variable Consistency Dominance-Based Rough Set Approach (VC-DRSA) are the basis for extraction of decision rules, so computations of approximations is a necessary step in knowledge representing and reduction based on VCDRSA. In this paper, a matrix-based method for computing lower approximations of upward and downw...

Set-valued information systems are generalized models of single-valued information systems. Its semantic interpretation can be classified into two categories: disjunctive and conjunctive. We focus on the former in this paper. By introducing four types of dominance relations to the disjunctive set-valued information systems, we establish a dominance-based rough sets approach, which is mainly bas...

We consider decision under uncertainty as a multi-attribute classification problem where a set of acts is described by outcomes gained with given probabilities. The Decision Maker (DM) provides desired classification for a small subset of reference acts. Such preference information is structured using Dominance-based Rough Set Approach (DRSA), and the resulting lower approximations of the quali...

Modelling of the contact between moving rough surfaces allows a better understanding of friction and wear mechanisms, which can be used in engineering solutions. This issue has been examined using a number of approaches. The statistical type of a contact model is still the most popularmodel used in rough surfaces contact.This statement does not mean that it is the best solution of contact rough...

Dominance-based Rough Set Approach (DRSA) has been proposed for multi-criteria classification problems in order to handle inconsistencies in the input information with respect to the dominance principle. The end result of DRSA is a decision rule model of Decision Maker preferences. In this paper, we consider an additive function model resulting from dominance-based rough approximations. The pre...

We present a methodology for non-statistical preference learning in multicriteria ranking based on Variable Consistency Dominance-based Rough Set Approach (VC-DRSA). A finite set of objects to be ranked is evaluated by a set of criteria, which are real-valued functions with ordinal or cardinal scales. Given the statement of a multicriteria ranking problem, the only objective information one can...

The paper proposes a two-phase methodology to support groups in multicriteria classification problems. The first phase, which relies on dominance-based rough set approach, takes as input a set of assignment examples, and generates as output a set of collective decision rules representing a generalized description of the preference information of the decision makers. The second phase then applie...

Consideration of preference-orders requires the use of an extended rough set model called Dominance-based Rough Set Approach (DRSA). The rough approximations defined within DRSA are based on consistency in the sense of dominance principle. It requires that objects having not-worse evaluation with respect to a set of considered criteria than a referent object cannot be assigned to a worse class ...