| Summary: | We introduce and discuss the concept of <i>n</i>-ary <i>K</i>-increasing fusion functions and <i>n</i>-ary <i>K</i>-increasing aggregation functions, <i>K</i> being a subset of the index set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi><mo>}</mo></mrow></semantics></math></inline-formula> indicating in which variables a considered function is increasing. It is also assumed that this function is decreasing in all other variables. We show that each <i>n</i>-ary <i>K</i>-increasing aggregation function is generated by some aggregation function which enables us to introduce and study the properties of <i>n</i>-ary <i>K</i>-increasing aggregation functions related to the properties of their generating aggregation functions. In particular, we also discuss binary <i>K</i>-increasing aggregation functions, including fuzzy implication and complication functions, among others.
|
|---|