Double-Quantitative Generalized Multi-Granulation Set-Pair Dominance Rough Sets in Incomplete Ordered Information System

Abstract

Since the rough sets theory based on the double quantification method was proposed, it has attracted wide attention in decision-making. This paper studies the decision-making approach in Incomplete Ordered Information System (IOIS). Firstly, to better extract the effective information in IOIS, combined with the advantages of set-pair dominance relation and generalized multi-granulation, the generalized multi-granulation set-pair dominance variable precision rough sets (GM-SPD-VPRS) and the generalized multi-granulation set-pair dominance graded rough sets (GM-SPD-GRS) are proposed. Moreover, we discuss their related properties. Secondly, considering the GM-SPD-VPRS and the GM-SPD-GRS describe information from relative view and absolute view, respectively, we further combine the two rough sets to obtain six double-quantitative generalized multi-granulation set-pair dominance rough sets (GM-SPD-RS) models. Among them, the first two models fuse the approximation operators of two rough sets, and investigate the extreme cases of optimistic and pessimistic. The last four models combine the two rough sets by the logical disjunction operator and the logical conjunction operator. Then, we discuss relevant properties and derive the corresponding decision rules. According to the decision rules, an associated algorithm is constructed for one of the models to calculate the rough regions. Finally, we validate the effectiveness of these models with a medical example. The results indicate that the model is effective for dealing with practical problems.

A Composite Service Provisioning Mechanism in Edge Computing

“…Composite service is composed of component services according to a certain composite structure to realize users' complex functional requirements. is paper adopts the key concepts and definitions of composite services from our previous work [14][15][16][17][18][19][20][21][22][23][24].…”

Object-First Incremental Algorithms for Updating Approximations in Multi-Granulation Fuzzy Probabilistic Rough Sets Over Two Universes

“…RS theory is a mathematical tool for depicting imperfection and imprecision. To apply RS theory to various complex application fields, such as pattern recognition [2], [3], machine learning [4], [5], image processing [6], and data mining [7], [8], some scholars did in-depth research on RS theory and proposed many extension RS models, such as fuzzy rough set model [9], fuzzy probabilistic rough set model [10]. In 1995, Yao et al [11] proposed a twodomain RS model based on precise binary relations, which extended the RS theory to the information system over two universes.…”