A type-1 OWA operator for Extended Comparative Linguistic Expressions with Symbolic Translation

Abstract

Recently, a new representation model has been proposed to improve the interpretability and accuracy of Computing with Words (CW) processes, the so-called Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT). It extends the concept of comparative linguistic expressions based on hesitant fuzzy linguistic term sets into a continuous domain by means of the symbolic translation used in the linguistic 2-tuple model. The aggregation of this kind of information is vital when solving decision making problems, but as the field of ELICIT information is still quite new, not many aggregation operators have been defined for it. Therefore, taking into account the need to deal with the fuzzy representation of ELICIT information for its aggregation, we propose the ELICIT type-1 OWA (ELICIT-t1-OWA) operator based on the equivalent α−level type-1 OWA operator to simplify the CW processes by using ELICIT trapezoidal fuzzy representations. The ELICIT-t1-OWA operator will use interval weights induced by an interval-valued linguistic quantifier to aggregate ELICIT expressions and then its properties will be studied. Additionally, a way to deal with both the weights and arguments of the ELICIT-t1-OWA operator is provided in the form of fuzzy numbers. Finally, a decision making model dealing with ELICIT information that carries out the aggregation by using the proposed ELICIT-t1-OWA operator is developed and a numerical example to show its effectiveness is introduced.