A refinement of various mean inequalities

Abstract

A new refinement of the classical arithmetic mean and geometric mean inequality is given. Moreover, a new interpretation of the classical mean is given and this refinement theorem is generalized.

The Location Selection for Roundabout Construction Using Rough BWM-Rough WASPAS Approach Based on a New Rough Hamy Aggregator

“…The Hamy mean (HM) [64] is used for aggregation of values while simultaneously including mutual correlations among multiple arguments and is defined in the following way: Definition 1. [64].…”

Interval type-2 fuzzy Hamy mean operators and their application in multiple criteria decision making

“…The Hamy mean (HM) (Hara et al 1998) is a very useful technique characterized by the ability to capture the…”

“…Definition 3 (Hara et al 1998) Let x j (j = 1, 2, … , n) be a collection of nonnegative real numbers, and parameter k = 1, 2, … , n. If then HM (k) is called the Hamy mean (HM), where (i 1 , i 2 , … , i k ) traverses all the k-tuple combination of (1, 2, … , n), n k , is the binomial coefficient, and…”

“…Lemma 1 (Hara et al 1998) Let x i (i = 1, 2, … , n) be a collection of nonnegative real numbers, and for k = 1, 2, … , n. Then with equality holding if and only if…”

“…Therefore, this assumption is not reasonable and also unrealistic in many practical situations. To deal with this issue, the motivation of this paper is to develop some new interval type-2 fuzzy aggregation operators based on Hamy mean (HM) (Hara et al 1998), which can capture the interactions among the aggregated decision information within the context of IT2FS. Hamy mean (HM), as a well-known aggregation technique, is widely used in information fusion.…”