New Aggregation Operator for Triangular Fuzzy Numbers based on the Geometric Means of the Slopes of the L- and R- Membership Functions

Abstract

In recent work authors have proposed four new aggregation operators for triangular and trapezoidal fuzzy numbers based on means of apex angles [1][2][3][4]. Subsequently authors have proposed [5] a new aggregation operator for TFNs based on the arithmetic mean of slopes of the L- and R- membership lines. In this paper the work is extended and a new aggregation operator for TFNs is proposed in which the L- and R- membership function lines of the aggregate TFN have slopes which are the geometric means of the corresponding L- and R- slopes of the individual TFNs. Computation of the aggregate is demonstrated with a numerical example. Corresponding arithmetic and geometric aggregates as well as results from the recent work of the authors on TFN aggregates have also been computed.