Rough set decision algorithms for modeling with uncertainty

Decision Making in Fuzzy Rough Set Theory

“…In this section, important notions of FRST [5,13] are recalled. First of all, the multiadjoint framework [5] allows us to set preferences among the objects and attributes of the decision table in order to give them more or less importance.…”

“…Thanks to the reflexivity of tolerance relations, we can conclude that a separable tolerance relation T a satisfies that T a (v, w) = 1 if and only if v = w for all v, w ∈ V a . Now, we recall the notions related to decision rules in the fuzzy framework [13] required for this paper. The first one presents the formulas, which are indispensable to express the information contained in decision tables in logical terms.…”

“…This data set was introduced in [30] and is represented in Table 7, where every unit corresponds to 10,000 yuan. This data set was analyzed from an RST perspective in [30] and was studied in the fuzzy framework in [13]. Now, we use that study to obtain the decision rules considered to decide on the investment in a new project.…”

“…Decision rules, together with their relevance indicators, that is, the support, the certainty, the credibility, etc., have been widely studied from a Boolean perspective, such as in the classical framework [8,9], in incomplete decision contexts [10], taking into account bireducts [11], and in three-way rough set theory [12]. However, the use of relevance indicators on decision rules in FRST is really limited [13]. In this paper, we are interested in exploiting the powerful advantages provided by decision rules in FRST for decisionmaking methods.…”

“…Specifically, this paper presents four different original methods to classify new objects, after a previous analysis of the data set from a FRST perspective. The two first methods are supported by the notions introduced in [13], which are the (1) degree of satisfiability, to measure how much the new object resembles the antecedent of decision rules extracted from the decision table, and the (2) support in the fuzzy setting, to take into account the representativeness of the rules whose antecedents are more similar to the new object. A third method, based on the notion of credibility [23,25], and a fourth one, consisting of a combination of the three previous ones, are also proposed.…”