Analysis of Aggregation Operators
Harsh Vardhan ShrivastavaOral Defence Date:
Friday, June 1, 2012 - 11:00Location:
Professors Jozo Dujmovic and James Wong
The goal of this project is to analyze and compare various implementations of soft computing aggregation operators. These operators are based on means. The basic operator is a generalized conjunction/disjunction that is characterized by its andness/orness and weights. The project includes accurate numerical computation of main types of andness/orness (local, global, functional), visualization of aggregation operators, and numerical approximation of their behavior. The results of this project help to better understand the properties of various aggregation operators and to choose the best among them. In this project we have studied following means in detail: Power, Exponential, Logarithmic, Counter Harmonic, Bonferroni, Centroidal, Gini, Heronian, Identric, Interpolated Weighted Power Means (IWPM), Lehmer and Stolarsky means. For all the mentioned preference logic aggregators computation of andness and orness is completed using both analytic and numeric outputs of Mathematica. The graphs and plots for each mean help us in understanding all fundamental properties of each aggregation operator. The main result of the project is a comparison of various implementations and selection of the most appropriate aggregators.