γ‐Agregation operators and some aspects of generalized aggregation problem

Abstract

We explore questions related to the aggregation operators and aggregation of fuzzy sets. No preliminary knowledge of the aggregation operators theory and of the fuzzy sets theory are required, because all necessary information is given in Section 2. Later we introduce a new class of γ‐aggregation operators, which “ignore” arguments less than γ. Due to this property γ‐aggregation operators simplify the aggregation process and extend the area of possible applications. The second part of the paper is devoted to the generalized aggregation problem. We use the definition of generalized aggregation operator, introduced by A. Takaci in [7], and study the pointwise extension of a γ‐agop.

Keywords:

• aggregation operator
• γ‐aggregation operator
• pointwise extension
• generalized aggregation
• order relation

Notes

I express my gratitude to prof. A. Shostaks for his support and valuable remarks that have improved the quality of the paper. Financial support by project 09.1061 of Latvian Science Foundation is acknowledged.