• FUZZY ANALYTIC HIERARCHICAL PROCESS TO DETERMINE THE RELATIVE WEIGHTS IN MULTI-LEVEL PROGRAMMING PROBLEMS

Abstract

Multi-Level Programming (MLP) has been employed to organize and facilitate the procedure of analyzing great number of decision making situations. Analytic Hierarchy Process (AHP) is a powerful approach of hierarchical structure analysis and used here for weight the significance or importance of objective functions. However due to some intrinsic uncertainty and vagueness existing  in the significance attributed to judgment of Decision Makers (DMs) requirements, the crisp pairwise comparisons in the conventional AHP seems to be insufficient. In this article, the main objective is to calculate and determine the relative weights the DMs objective functions by using a Fuzzy-AHP (FAHP) approach with different methods; eigen vector and geometric mean. Triangular and trapezoidal fuzzy numbers were introduced to improve the scaling scheme of Saaty’s method. The approach allows DMs to provide their preferences that are upper and lower bounds of the variables they control. The hierarchical system then was converted into Scalar Optimization Problem (SOP) such that objective functions can be combined into a single one. A numerical illustrative example was presented.