A new preference scale of intuitionistic fuzzy analytic hierarchy process in multi-criteria decision making problems

Article type: Research Article

Authors: Abdullah, Lazim | Najib, Liana

Affiliations: Department of Mathematics, Faculty of Science & Technology, University Malaysia Terengganu, Terengganu, Malaysia

Note: [] Corresponding author. Lazim Abdullah, Department of Mathematics, Faculty of Science & Technology, University Malaysia Terengganu, 21030 Kuala Terengganu, Terengganu, Malaysia. Tel.: +60 9 6683452; Fax: +60 9 6694660; E-mail: lazim_m@umt.edu.my

Abstract: Analytic Hierarchy Process (AHP) is a tool of decision making technique which complies with complex decision making in any kind of situations. AHP deals with structuring the hierarchical layer to perform the preference judgement of each criterion and alternatives in multi-criteria decision making (MCDM) problems. The sequence of AHP structure unfortunately lack of certainty as the evaluation consists of vagueness. Thus, the theory of intuitionistic fuzzy sets (IFS) is integrated with AHP method to deal with these uncertainty and vagueness of the AHP preference judgement. The aim of this paper is to propose a new intuitionistic fuzzy analytic hierarchy process (IF-AHP) method characterised by new preference scale of pair-wise comparison matrix measurement. The new preference scale considers the degree of hesitation of IFS in expressing the conversion of consistency to a triangular intuitionistic fuzzy numbers (TIFNs). The values of hesitation degree are averaged to test consistency of matrix judgment. The intuitionistic fuzzy weighted averaging (IFWA) is utilized to aggregate the matrix assessment of the decision makers (DMs) into a group opinion. Modified intuitionistic fuzzy entropy is used to obtain the entropy weights of each criterion and alternatives. Three MCDM problems were used to illustrate the proposed method. It is found the ranking of MCDM problems using the proposed method were slightly inconsistent with the original ranking.

Keywords: Analytic hierarchy process, hesitation degree, intuitionistic fuzzy sets, consistency ratio, preference scale

DOI: 10.3233/IFS-130796

Journal: Journal of Intelligent & Fuzzy Systems, vol. 26, no. 2, pp. 1039-1049, 2014