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

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.

D-quantification: A Japanese Variation

Determiner quantifiers like <em>every</em> and<em> most</em> are assumed to take common nouns phrases of type &lt;e,t&gt; to derive a generalized quantifier of type &lt;&lt;e,t&gt;,t&gt;. Matthewson 2001 subjects this standard assumption to crosslinguistic scruity, and based on St'at'imcets (Lillooet Salish), she proposes a two-step approach to create a QP; the first is the creation of a DP of type &lt;e&gt; and the second involves quantification over parts of the plural individual denoted by the DP. This paper discusses Japanese, which lacks D and has nouns of type &lt;e&gt; (cf. Chierchia 1998, Mizuguchi 2004). Japanese allows 'double quantification', which, I argue, is best explained if Japanese nouns remain of type &lt;e&gt; throughout the derivation.