In this study, comparison of two intuitionistic fuzzy sets is focused. From the viewpoint of set optimization, eight types of intuitionistic fuzzy-set relations based on set relations in a vector space are proposed as a new comparison criteria of intuitionistic fuzzy sets. Moreover, an evaluation measure of the difference between two intuitionistic fuzzy sets are introduced and related properties are investigated.

This paper studies the basic invariants, constructed by Conway and Sloane, of the complex reflection group numbered as 34 in the list of Shephard-Todd [14].

Let $H$ be a Hilbert space. In this paper we show among others that, if $A$ and $B$ are positive invertible operators with $0<m\le A,B\le M$ for some constants $m<M,$ then for all $\nu \in \left[0,1\right],$

where is Kantorovich constant and $R:=\max \left\{1-\nu ,\nu \right\}$. We also have the following inequalities for the Hadamard product

where $\nu \in \left[0,1\right]$.

Some extensions for sequences $A_i$ and $B_i$ of selfadjoint operators with $0<m\le A_i, B_i\le M,$ and $p_i\ge 0$ for $i\in \left\{1,...,n\right\}$ with $\sum _{i=1}^n{p}_i=1$ are also given.