module over a ring is a general mathematical concept for many examples of mathematicalobjects that can be added to each other and multiplied by scalar numbers.in this paper, we consider a module over a ring as a universe and by using the notion of reference points, we provide local approximations for  subsets of the universe.

Since the early 1990s, many authors have studied fuzzy rough set models and their application in machine learning and data reduction. In this work, we adjust the β-precision and the ordered weighted average based fuzzy rough set models in such a way that the number of theoretical properties increases. Furthermore, we evaluate the robustness of the new models a-β-PREC and a-OWA to noisy data and...

decision support systems (dsss) are prevalent information systems for decision making in many competitive business environments. in a dss, decision making process is intimately related to some factors which determine the quality of information systems and their related products. traditional approaches to data analysis usually cannot be implemented in sophisticated companies, where managers need...

decision support systems (dsss) are prevalent information systems for decision making in many competitive business environments. in a dss, decision making process is intimately related to some factors which determine the quality of information systems and their related products. traditional approaches to data analysis usually cannot be implemented in sophisticated companies, where managers nee...

In this paper, three types of (philosophical, optimistic and pessimistic) multigranulation single valued neutrosophic (SVN) covering-based rough set models are presented, and these three models are applied to the problem of multi-criteria group decision making (MCGDM).Firstly, a type of SVN covering-based rough set model is proposed.Based on this rough set model, three types of mult...

We study multigranulation decision-theoretic rough sets in incomplete information systems. Based on Bayesian decision procedure, we propose the notions of weighted mean multigranulation decision-theoretic rough sets, optimistic multigranulation decision-theoretic rough sets, and pessimistic multigranulation decision-theoretic rough sets in an incomplete information system. We investigate the re...

We present a parameter free and monotonic alternative to the parametric variable precision model of rough set data analysis, based on the well known PRE index λ of Goodman and Kruskal. Using weighted (parametric) λ models we show how expert knowledge can be integrated without losing the monotonic property of the index. Based on a weighted λ index we present a polynomial algorithm to determine a...

In this paper, we take a GL-quantale as the truth value table to study a new rough set model—L-valued fuzzy rough sets. The three key components of this model are: an L-fuzzy set A as the universal set, an L-valued relation of A and an L-fuzzy set of A (a fuzzy subset of fuzzy sets). Then L-valued fuzzy rough sets are completely characterized via both constructive and axiomatic approaches. 

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...

We present a parameter free and monotonic alternative to the parametric variable precision model of rough set data analysis. The proposed model is based on the well known PRE index λ of Goodman and Kruskal. Using a weighted λ model it is possible to define a two dimensional space based on (Rough) sensitivity and (Rough) specificity, for which the monotonicity of sensitivity in a chain of sets i...