Variable Precision Fuzzy Rough Sets

Abstract

Abstract. In this paper the variable precision fuzzy rough sets (VPFRS) concept will be considered. The notions of the fuzzy inclusion set and the α-inclusion error based on the residual implicators will be introduced. The level of misclassification will be expressed by means of α-cuts of the fuzzy inclusion set. Next, the use of the mean fuzzy rough approximations will be postulated and discussed. The concept of VPFRS will be defined using the extended version of the variable precision rough sets (VPRS) model, which utilises a general allowance for levels of misclassification expressed by two parameters: lower (l) and upper (u) limit. Remarks concerning the variable precision rough fuzzy sets (VPRFS) idea will be given. An example will illustrate the proposed VPFRS model.

A comprehensive study of implicator–conjunctor-based and noise-tolerant fuzzy rough sets: Definitions, properties and robustness analysis

“…There are models which are frequency-based, analogous to the VPRS model of Ziarko [5,24,25,42,43,65]. Another model adjusts the set which is approximated [69].…”

“…Models of this type are the Variable Precision Fuzzy Rough Set model of Mieskowicz-Rolka and Rolka [42,43], the Vaguely Quantified Fuzzy Rough Set model of Cornelis et al [5], the Soft Fuzzy Rough Set model of Hu et al [24,25] and the Variable Precision Fuzzy Rough Set model based on Fuzzy Granules of Yao et al [65]. The idea behind this type of robust models is that only a subset of the R-foreset of an object x is taken into account when computing the lower and upper approximation in x, which is similar to the Variable Precision Rough Set model of Ziarko [70].…”

“…To mitigate this problem in the crisp case, Ziarko [70] proposed the Variable Precision Rough Set (VPRS) model in 1993. This model also served as a starting point for the design of several noise-tolerant fuzzy rough set approaches, such as [5,7,17,18,24,25,42,43,65,69], which will be discussed in detail in Section 4.…”

“…We also establish sufficient conditions under which its approximations satisfy the same theoretical properties as Pawlak's model. In Section 4, we review the seven most important noise-tolerant fuzzy rough set models introduced in the literature: Mieszkowicz-Rolka and Rolka's Variable Precision Fuzzy Rough Set model (VPFRS [42,43] [69]), Fernández-Salido and Murakami's β-Precision Fuzzy Rough Set model (β-PREC, [17,18]) and Cornelis et al's Ordered Weighted Average based Fuzzy Rough Set model (OWA, [7]). In Section 5, we test the robustness of these proposals and the IC model in the presence of class and attribute noise, and in Section 6, we conclude and state future work.…”

A Variable Precision Fuzzy Rough Group Decision-making Model for IT Outsourcing Risk Evaluation in Nuclear Power Industry

“…This paper proposes a new model called Variable Precision Fuzzy Rough Group Decision-making (VPFRGDM) to evaluate IT outsourcing risk in the nuclear industry. Firstly, historical knowledge is represented in a fuzzy decision table(FDT) based on TCT; Then, based on VPFRS [3] and fuzzy TOPSIS approach [4], it evaluates the risk under a certain admissible inclusion error βand the whole error interval. The model further reduces the bias in fuzzy group decision-making (FGDM), improves the efficiency in IT outsourcing risk decision-making.…”