Some Applications Idempotent Probability Measures Space

Idempotent Probability Measures, I

The set of all idempotent probability measures (Maslov measures) on a compact Hausdorff space endowed with the weak* topology determines is functorial on the category Comp of compact Hausdorff spaces. We prove that the obtained functor is normal in the sense of E. Shchepin. Also, this functor is the functorial part of a monad on Comp. We prove that the idempotent probability measure monad conta...

Correspondence Principle for Idempotent Calculus and Some Computer Applications *

SOME SIMILARITY MEASURES FOR PICTURE FUZZY SETS AND THEIR APPLICATIONS

In this work, we shall present some novel process to measure the similarity between picture fuzzy sets. Firstly, we adopt the concept of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and picture fuzzy sets. Secondly, we develop some similarity measures between picture fuzzy sets, such as, cosine similarity measure, weighted cosine similarity measure, set-theoretic similar...

Idempotent Measures on Compact Semigroups

Throughout this paper, 5 will be a compact Hausdorff topological semigroup, 5 will denote the convolution semigroup of normalized non-negative regular Borel measures on 5, and H will be the carrier of a measure p in 5. The space of continuous complex valued functions on 5 will be denoted by C(S), while Cr(S) will be the subspace of C(S) of real valued functions. Standard terminology and definit...

Injective Hilbert Space Embeddings of Probability Measures

A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing and independence testing. This embedding represents any probability measure as a mean element in a reproducing kernel Hilbert space (RKHS). The embedding function has been proven to be injective when the reproducing kernel is universal. In this...