Quantum mechanics

Endomorphism

Pure mathematics

Discrete mathematics

Statistics

Idempotence

Complete lattice

Power (physics)

Universality (dynamical systems)

Physics

Mathematics

Combinatorics

Generator (circuit theory)

Homomorphism

Homogeneity (statistics)

Fuzzy Sets and Systems

In this paper, construction methods of overlap and grouping functions on complete lattices via complete homomorphisms and complete 0L,1L-endomorphisms are investigated. At first, we propose the notion of O-generator triple of overlap functions. Then, properties such as (α,B,C)-migrativity, (B,C)-homogeneity, idempotency and cancellation law for the overlap functions obtained by such generator triples are discussed. Finally, we give an analogous discussion on grouping functions on complete lattices.

Constructing overlap and grouping functions on complete lattices by means of complete homomorphisms