Nonlinear dimensionality reduction aims at providing lowdimensional representions of high-dimensional data sets. Many new methods have been proposed in the recent years, but the question of their assessment and comparison remains open. This paper reviews some of the existing quality measures that are based on distance ranking and K-ary neighborhoods. Many quality criteria actually rely on the a...

We introduce the basic concepts on intuitionistic fuzzy subalgebras on n-ary groupoids, i.e., on algebras containing one fundamental n-ary operation. We describe some similarities and differences between the n-ary and binary case. In the case of n-ary quasigroups and groups we suggest the common method of investigations based on some methods used in the universal algebra.

In this paper from q-ary perfect codes a new completely regular q-ary codes are constructed. In particular two new ternary completely regular codes are obtained from the ternary Golay [11,6,5] code and new families of q-ary completely regular codes are obtained from q-ary 1-perfect codes.

This article investigates numerous integer sequences derived from two special balanced k-ary trees. Main contributions of this article are two fold. The first one is building a taxonomy of various balanced trees. The other pertains to discovering new integer sequences and generalizing existing integer sequences to balanced k-ary trees. The generalized integer sequence formulae for the sum of he...

The well-known connection between hyperidentities of an algebra and identities satisfied by the clone of this algebra is studied here in a restricted setting, that of n-ary strongly full hyperidentities and identities of the n-ary clone of term operations of an algebra induced by strongly full terms, both of a type consisting only of n-ary operation symbols. We call such a type an n-ary type. U...

A q-ary maximum distance separable (MDS) code C with length n, dimension k over an alphabet A of size q is a set of qk codewords that are elements of An, such that the Hamming distance between two distinct codewords in C is at least n− k+1. Sets of mutually orthogonal Latin squares of orders q ≤ 9, corresponding to two-dimensional q-ary MDS codes, and q-ary one-error-correcting MDS codes for q ...