background and objectives: identification of surgical instruments in laparoscopic video images has several biomedical applications. while several methods have been proposed for accurate detection of surgical instruments, the accuracy of these methods is still challenged high complexity of the laparoscopic video images. this paper introduces a surgical instrument detection framework (sidf) for a...

Background and Objectives: Identification of surgical instruments in laparoscopic video images has several biomedical applications. While several methods have been proposed for accurate detection of surgical instruments, the accuracy of these methods is still challenged high complexity of the laparoscopic video images. This paper introduces a Surgical Instrument Detection Framework (SIDF) for a...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  Ulrich Hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. Many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. Using Hohle's idea, we show that for a (universal) algebra $A$, th...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  ulrich hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. using hohle's idea, we show that for a (universal) algebra $a$, th...

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...