Rough Set Models on Two universes

Catoptrical rough set model on two universes using granule-based definition and its variable precision extensions

“…Let R ⊆ U × V denote a given relation depending on the universe U and V . The triplet ( U , V , R ) is a generalized approximation space over dual universes [14,23,28,39] . With respect to R , the successor neighborhood of an element x in U can be denoted by…”

“…Some authors also study approximation structures or rough set model by algebraic methods [2,4,15,27,40] . Classic rough set model can also be generalized via two universes [14,22,23,28,39,41] . Rough set models over two universes can be applied into formal concept analysis and decision-making system [22,23,28,39] .…”

“…Rough set models over two universes can be applied into formal concept analysis and decision-making system [22,23,28,39] . Several scholars have studied rough set models based on two universes [14,23,28,39,41] . For example, Min et al introduced the concept of granular association rule on two universes [32] .…”

Interval sets and interval-set algebras

“…They are Iwiński rough sets, or interval sets, constructed based on two universes. Many authors, including, for example, Wong et al [37], Yao [44], Pei and Xu [28], Shu and He [31], Li [10], Li and Zhang [11], Gong and Sun [6], Mi et al [16] and Pei and Fan [27], studied rough sets and fuzzy rough sets over universes. The results can be easily related to interval sets and interval fuzzy sets [52].…”

Merger and Acquisition Target Selection Based on Interval Neutrosophic Multigranulation Rough Sets over Two Universes

“…Through extending a single universe to two universes, it is beneficial to express a complicated group decision making knowledge base. Hence, Pei and Xu [26] studied the concept of rough sets over two universes systematically. Since then, several scholars have researched rough sets over two universes widely according to numerous practical requirements [27][28][29][30][31][32][33].…”