An Intuitionistic Fuzzy AHP Based on Synthesis of Eigenvectors and its Application


	Information Technology Journal
	Year: 2011 \| Volume: 10 \| Issue: 10 \| Page No.: 1850-1866 DOI: 10.3923/itj.2011.1850.1866

An Intuitionistic Fuzzy AHP Based on Synthesis of Eigenvectors and its Application

Hai Wang, Gang Qian and Xiangqian Feng

Abstract: With regard to multi Criteria Decision Making (MCDM) problems, performances of the Analytical Hierarchy Process (AHP) are prominent. Fuzzy AHP, an extension of AHP, serves as a grateful approach due to its outstanding advantage when dealing with uncertainties. Based on advantages of Intuitionistic Fuzzy Sets (IFSs) in expressing information of preferences, this study presents an intuitionistic fuzzy AHP (IF-AHP) approach. The proposed IF-AHP synthesizes eigenvectors of Intuitionistic Fuzzy Comparison Matrix (IFCM) in which all the information for decision are represented by Intuitionistic Fuzzy Values (IFVs). The IF-AHP approach enables to handle MCDM problems without loss of information or defuzzification and represent arbitrary hesitation in interval [0, 1]. Firstly, Intuitionistic Fuzzy (IF) matrix and IFCM associated with its consistency and satisfactory consistency are defined after some relative basal knowledge are introduced. Secondly, the eigenvector and eigenvalue of IFCM is defined and a linear program model is presented to obtain it as the priority of relative criteria. Furthermore, methods for comparisons of IFVs are proposed in order to rank alternatives utilizing eigenvectors. And then, a integrate procedure of IF-AHP involving comparison and rating is presented and illustrated by two applied examples cited from literatures. An involved decision support system can be setup according to the procedure. Comparing with some existing methods, the proposed approach gives both rational global priorities and robust final decision.

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How to cite this article:

Hai Wang, Gang Qian and Xiangqian Feng, 2011. An Intuitionistic Fuzzy AHP Based on Synthesis of Eigenvectors and its Application. Information Technology Journal, 10: 1850-1866.

DOI: 10.3923/itj.2011.1850.1866

URL: https://scialert.net/abstract/?doi=itj.2011.1850.1866

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