Given a coloring of Z+, we call a monochromatic set A = {a1 < a2 < · · · < am} an m-set. The diameter of A is am a1. Given two m-sets A and B, we say that they are non-overlapping if max(A) < min(B) or max(B) < min(A). The original study of non-overlapping m-sets, done by Bialostocki, Erdős, and Lefmann, concerned non-decreasing diameters. We investigate an “intermingling” of certain subset dia...

In this paper, we introduce some properties of an intuitionistic normal fuzzy m-subgroup of m- group with m-homomorphism and isomorphism. We study he image, the pre-image and the inverse mapping of the intuitionistic normal fuzzy m-‎subgroups.‎

The $3k-4$ conjecture in groups $\mathbb{Z}/p\mathbb{Z}$ for $p$ prime states that if $A$ is a nonempty subset of satisfying $2A\neq \mathbb{Z}/p\mathbb{Z}$ and $|2A|=2|A|+r \leq \min\{3|A|-4,\;p-r-4\}$, then covered by an arithmetic progression size at most $|A|+r+1$. A theorem Serra Zemor proves the provided $r\leq 0.0001|A|$, without any additional constraint on $|A|$. Subject to mild $|2A|\...

We provide an extension of the notion of chain-valued frame introduced by Pultr and Rodabaugh in [Category theoretic aspects of chain-valued frames: parts I and II, Fuzzy Sets and Systems 159 (2008) 501–528 and 529–558] by relaxing the assumption that L be a complete chain. As a result of this investigation we formulate the category L-Frm of L-frames under the weaker assumption that L is a comp...

In this state-of-the-art paper, important advances that have been made during the past five years for both general and interval type-2 fuzzy sets and systems are described. Interest in type-2 subjects is worldwide and touches on a broad range of applications and many interesting theoretical topics. The main focus of this paper is on the theoretical topics, with descriptions of what they are, wh...