New Aggregation Operator for Trapezoidal Fuzzy Numbers based on the Geometric Means of the Left and Right Apex Angles

In previous work, authors have proposed two new aggregation operators for a class of LR fuzzy numbers known as triangular fuzzy numbers (TFNs) in which the Land Rapex angles of the piecewise continuous linear membership function of the composite or resultant or aggregate TFN are the arithmetic means [1] and the geometric means [2] of the Land Rapex angles of the individual TFNs. In another paper [3] the concept of an aggregation operator for triangular fuzzy numbers based on the arithmetic means of the corresponding Land Rapex angles has been extended for a class of Interval Fuzzy Numbers known as Trapezoidal Fuzzy Numbers (TrFNs) with the left and right side angles treated independently. This paper extends the concept further for TrFNs and an aggregate based on the geometric means of the left and right side apex angles of the individual TrFNs is proposed. The left and right side apex angles have been treated independently. Computation of the aggregate is demonstrated with a numerical example. Corresponding arithmetic and geometric aggregates of the TrFNs and the aggregate of [3] have also been computed.