Rough set and rule-based multicriteria decision aiding

Abstract

ABSTRACT. 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.

Integrating agricultural sustainability into policy planning: A geo-referenced framework based on Rough Set theory

“…Elementary sets Decision class es follows Pawlak et al (1995), Stefanowski (2007) and Slowinski et al (2012). Researchers who would like to further investigate the formal characteristics of the method, and its early applications and developments, refer to Pawlak (1982), Kryszkiewicz (1998), Yao (1998), and Pawlak and Skowron (2007 }, and they remain singleton if Age is removed by S. All the attributes that behave like the attribute Age can be considered redundant; the remaining subset of S with no redundant attributes P = {Size, Type} is called a minimal set.…”

Multicriteria Evaluation of Managerial Competences: An Application of the Dominance Principle and the Rough Set Theory

“…In addition to this, it is not possible to identify inconsistencies which violate the Dominance principle: "objects which have a better evaluation or which have at least the same evaluation (class decision) cannot be associated with a worse decision class, having considered all the decision criteria". RST ignores not only the preference order in the value sets of attributes but the monotonic relationship between evaluations of objects on such attributes ("criteria") and the preference ordered value of decision (classification decision or degree of preference) [7], [17]. This question is treated by the extension of RST: DRSA is applied [17].…”

“…RST ignores not only the preference order in the value sets of attributes but the monotonic relationship between evaluations of objects on such attributes ("criteria") and the preference ordered value of decision (classification decision or degree of preference) [7], [17]. This question is treated by the extension of RST: DRSA is applied [17]. By this principle, indiscernibility relations are substituted by relations of Dominance in the approximations of the decision classes.…”

Generation of rough sets reducts and constructs based on inter-class and intra-class information

“…It is worth stressing that the classic reducts [20] have rich research history and have been the subject of many studies, in both classic [18,22,25] and extended forms [2,[14][15][16]38,41]. They have also been considered in numerous papers on various aspects of information systems analysis [21,24,26,42], including the Dominance-based Rough Set Approach (DRSA) [7,21,28,29], a rapidly developing [4,12] branch of the theory, having a strong impact on the domain of multicriteria decision aiding [23].…”