On weighted quasi-arithmetic means which are convex

On Hadamard Type Inequalities for Generalized Weighted Quasi-arithmetic Means

In the present paper we establish some integral inequalities analogous to the wellknown Hadamard inequality for a class of generalized weighted quasi-arithmetic means in integral form.

Weighted Quasi-Arithmetic Means: Utility Functions and Weighting Functions

Some Results on Lipschitz Quasi-Arithmetic Means

We present in this paper some properties of k-Lipschitz quasi-arithmetic means. The Lipschitz aggregation operations are stable with respect to input inaccuracies, what is a very important property for applications. Moreover, we provide sufficient conditions to determine when a quasi–arithemetic mean holds the k-Lipschitz property and allow us to calculate the Lipschitz constant k. Keywords— k-...

Clustering Methods Based on Weighted Quasi-Arithmetic Means of T-Transitive Fuzzy Relations

In this paper we propose clustering methods based on weighted quasiarithmetic means of T -transitive fuzzy relations. We first generate a T -transitive closure R from a proximity relation R based on a max-T composition and produce a T -transitive lower approximation or opening RT from the proximity relation R through the residuation operator. We then aggregate a new T -indistinguishability fuzz...

Concavity of weighted arithmetic means with applications

We prove that the following three conditions together imply the concavity of the sequence Pn iˆ0 aibi= Pn iˆ0 ai : concavity of fbng, log-concavity of fang and nonincreasing of f…bn ÿ bnÿ1†=…anÿ1=an ÿ anÿ2=anÿ1†g. As a consequence we get necessary and sufficient conditions for the concavity of the sequences fSnÿ1…x†=Sn…x†g and fSn…x†=Sn…x†g for any nonnegative x, where Sn…x† is the nth partial ...