* Correspondence: [email protected] Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China Full list of author information is available at the end of the article Abstract In this article, we answer the question: For p, ω Î R with ω >0 and p(ω 2) ≠ 0, what are the greatest value r1 = r1(p, ω) and the least value r2 = r2(p, ω) such that the double inequality Mr1 (a, b) ...

For the aggregation problem of attributes with a correlation relationship, it is often necessary to take factor into account in order make decision results more objective and reasonable. The Heronian mean an operator which reflects interaction between attributes. It great theoretical practical significance study popularize multiple attribute decision-making methods based on operator. In this pa...

It is well known that primitive Pythagorean triangles have integer inradius and exradii. We investigate the generalization to primitive Heronian triangles. In particular, we study the special cases of isosceles triangles and triangles with sides in arithmetic progression. We also give two families of primitive Heronian triangles, one decomposable and one indecomposable, which have integer inrad...

Due to the complexity and uncertainty of objective things, interval-valued intuitionistic fuzzy (I-VIF) numbers are often used describe attribute values in multiple-attribute decision making (MADM). Sometimes, there correlations between attributes. In order make decision-making result more reasonable, it is necessary take correlation factors into account. Therefore, study MADM based on attribut...

Jensen-Shannon, J-divergence and Arithmetic-Geometric mean divergences are three classical divergence measures known in the information theory and statistics literature. These three divergence measures bear interesting inequality among the three non-logarithmic measures known as triangular discrimination, Hellingar’s divergence and symmetric chi-square divergence. However, in 2003, Eve studied ...

The Heronian mean provides an aggregation operator that considers the inter-dependent phenomena among the aggregated arguments. Nevertheless, it seems that the existing literatures only consider the HM for aggregating crisp numbers rather than any other types of arguments. In this paper, the HM under interval-valued intuitionistic fuzzy environments is studied. First, a generalized interval-val...