This paper is an investigation of the automorphisms of the algebra of truth values of type-2 fuzzy sets. This algebra contains isomorphic copies of the truth value algebras of type-1 and of interval-valued fuzzy sets. It is shown that these subalgebras are characteristic; that is, are carried onto themselves by automorphisms of the containing algebra of truth values of fuzzy sets. Some other re...

Certain three-dimensional images arising in medicine and astrophysics are modelled as a smooth random field, and experimenters are interested in the number of ‘peaks’ or ‘hot-spots’ present in such an image. This paper studies the Hadwiger characteristic of the excursion set of a random field; the excursion set is the set of points where the image exceeds a fixed threshold, and the Hadwiger cha...

I demonstrate the existence in protein domain sequences of sets of statistically significant periodic signals, characteristic of the architectures of those domains. It is shown that, although the frequencies of the signals characteristic of a particular architecture have definite wave numbers, they can occur in any physical property. The characteristic signals define sequence units, which may c...

The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov in 1989 as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this paper we first apply the concept of interval-valued intuitionistic fuzzy sets to K-algebras. Then we introduce the notion of interval-valued intuitionistic fuzzy ideals (IIFIs, in short) of K-al...

For any polynomial ideal I, let the minimal triangular set contained in the reduced Buchberger-Gröbner basis of I with respect to the purely lexicographical term order be called the W-characteristic set of I. In this paper, we establish a strong connection between Ritt’s characteristic sets and Buchberger’s Gröbner bases of polynomial ideals by showing that the W-characteristic set C of I is a ...

We collect certain useful lemmas concerning the characteristic map, GLninvariant sets of matrices, and the relative codimension. We provide a characterization of rank varieties in terms of the characteristic map as well as some necessary and some sufficient conditions for linear subspaces to allow the dominant restriction of the characteristic map.

In this paper, we introduce intuitionistic fuzzy semi pre open (closed) sets and intuitionistic fuzzy semi pre continuous mappings in intuitionistic fuzzy topological spaces in Sostak’s sense. Also we investigate the characteristic properties of these sets and mappings.

We calculate the universal Euler characteristic and universal dimension function on semilinear and semibounded sets and obtain some criteria for definable equivalence of semilinear and semibounded sets in terms of these invariants.