Abstract
This paper presents a method using multiobjective particle swarm optimization (PSO) approach to improve the consistency matrix in analytic hierarchy process (AHP), called PSOMOF. The purpose of this method is to optimize two objectives which conflict each other, while improving the consistency matrix. They are minimizing consistent ratio (CR) and deviation matrix. This study focuses on fuzzy preference matrix as one model comparison matrix in AHP. Some inconsistent matrices are repaired successfully to be consistent by this method. This proposed method offers some alternative consistent matrices as solutions.
Highlights
One important issue in comparison matrix of analytic hierarchy process (AHP) is the consistency
Element comparison matrix is stated as aij, which defines the preference of alternative i over j, where 0 < aij < 1 and aij + aji = 1
The inconsistent matrix can be taken from the real life application which needs the decision maker opinions of comparing several criteria to get some alternatives
Summary
One important issue in comparison matrix of AHP is the consistency. In multicriteria decision making (MCDM), decision makers (DMs) reveal their opinion to choose some decision alternatives by a comparison matrix [1]. The comparison matrix which is identified as inconsistent cannot be used as a judgment. There are two models of a comparison matrix, multiplicative preference relations [1] and fuzzy preference relations [2, 3]. The element comparison matrix of multiplicative preference relation is stated as aij which defines the dominance of alternative i over j, where 1 < aij < 9 and aij = 1/aji. Element comparison matrix is stated as aij, which defines the preference of alternative i over j, where 0 < aij < 1 and aij + aji = 1.
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