Abstract. In this paper, we develop the idea of a generalized upper set in a BE-algebra. Furthermore, these sets are considered in the context of transitive and self distributive BE-algebras and their ideals, providing characterizations of one type, the generalized upper sets, in terms of the other type, ideals.

The notions of ð2; 2 _ qÞ-fuzzy p-ideals and fuzzy p-ideals with thresholds related to soft set theory are discussed. Relations between ð2; 2 _ qÞ-fuzzy ideals and ð2; 2 _ qÞ-fuzzy p-ideals are investigated. Characterizations of an ð2; 2 _ qÞ-fuzzy p-ideal and a fuzzy p-ideal with thresholds are displayed. Implication-based fuzzy p-ideals are discussed.

We report a method of preoperatively calculating resected and ischemic volume with a novel formula. This method has superior correlation with the absolute and percent change in estimated glomerular filtration rate compared to current nephrometry systems. The predictive model achieved a strong correlation for the absolute and percent change in estimated glomerular filtration rate.

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In this paper, we introduce the notion of generalized Fibonacci sequences over a groupoid and discuss it in particular for the case where the groupoid contains idempotents and pre-idempotents. Using the notion of Smarandache-type P-algebra, we obtain several relations on groupoids which are derived from generalized Fibonacci sequences. MSC: 11B39; 20N02; 06F35