In recent years, many nearest neighbor algorithms based on fuzzy sets theory have been developed. These methods form a field, known as fuzzy nearest neighbor classification, which is the source of many proposals for the enhancement of the k nearest neighbor classifier. Fuzzy sets theory and several extensions, including fuzzy rough sets, intuitionistic fuzzy sets, type-2 fuzzy sets and possibil...

Locality sensitive hashing (LSH) has been used extensively as a basis for many data retrieval applications. However, previous approaches, such as random projection and multi-probe hashing, may exhibit high query complexity of up to Θ(n) when the underlying data distribution is highly skewed. This is due to the imbalance in the number of data stored per each bucket, which leads to slow query tim...

Fishburn, P. A subset S of N " = { 1,2,. , N} " is a discrete set of uniqueness if it is the only subset of N " with projections P,, Sets of uniqueness and additive sets are characterized by the absence of certain configurations in the lattice N ". The characterization shows that every additive set is a set of uniqueness. If n = 2, every set of uniqueness is also additive. However, when II 3 3,...

Traditional Adomian decomposition method (ADM) usually fails to solve singular initial value problems of Emden-Fowler type. To overcome this shortcoming, a new and effective modification of ADM that only requires calculation of the first Adomian polynomial is formally proposed in the present paper. Three singular initial value problems of Emden-Fowler type with , 1 α  , 2 and , 2  and have be...

Set based recognition (i.e, using a set of instances together for recognition) has been attracting more and more attention in recent years, benefitting from two facts: the difficulty of collecting sets of images for recognition fades quickly, and set based recognition models generally outperform the ones for single instance based recognition. In the past few years various approaches have been p...

Let X and Y be uncountable Polish spaces. A ⊂ X×Y represents a family of sets C provided each set in C occurs as an x-section of A. We say A uniquely represents C provided each set in C occurs exactly once as an xsection of A. A is universal for C if A represents C and every x-section of A is in C. A is uniquely universal for C if it is universal and uniquely represents C. We show that there is...