A linear order and OWA operator for discrete gradual real numbers

Abstract

In this paper we introduce a class of linear orders for discrete gradual real numbers. Based on the linear orders we propose an OWA operator on the set of discrete gradual numbers and discuss some its properties. This is a first step of our intentions to introduce a class of linear orders, and consequently also OWA operator, for the set of discrete gradual intervals. Because the set of all fuzzy intervals is included in the set of all gradual intervals, proposed linear orders and OWA operators would be applicable in the settings of fuzzy intervals too.

OWA operator for discrete gradual intervals: implications to fuzzy intervals and multi-expert decision making

“…Algorithm 1 is a generalization of algorithm given in [27] where only weighted averages were used in step 2 (Comparison). For more detailed explanation of algorithm see above mentioned paper.…”