Fuzzy multiple objective programming and compromise programming with Pareto optimum
Fuzzy Sets and Systems
Deriving priorities from fuzzy pairwise comparison judgements
Fuzzy Sets and Systems - Optimisation and decision
Fuzzy group decision-making for facility location selection
Information Sciences—Informatics and Computer Science: An International Journal
Linear programming models for estimating weights in the analytic hierarchy process
Computers and Operations Research
A hybrid multi-criteria decision-making model for firms competence evaluation
Expert Systems with Applications: An International Journal
Fuzzy analytic hierarchy process: A logarithmic fuzzy preference programming methodology
International Journal of Approximate Reasoning
A hybrid ANP evaluation model for electronic service quality
Applied Soft Computing
Fuzzy analytic network process and its application to the development of decision support systems
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Consistent weights for judgements matrices of the relative importance of alternatives
Operations Research Letters
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This paper proposes a two-stage fuzzy logarithmic preference programming with multi-criteria decision-making, in order to derive the priorities of comparison matrices in the analytic hierarchy pprocess (AHP) and the analytic network process (ANP). The Fuzzy Preference Programming (FPP) proposed by Mikhailov and Singh [L. Mikhailov, M.G. Singh, Fuzzy assessment of priorities with application to competitive bidding, Journal of Decision Systems 8 (1999) 11-28] is suitable for deriving weights in interval or fuzzy comparison matrices, especially those displaying inconsistencies. However, the weakness of the FPP is that it obtains priorities of comparison matrices by additive constraints, and generates different priorities by processing upper and lower triangular judgments. In addition, the FPP solves the comparison matrix individually. By using multiplicative constraints, the method proposed in this paper can generate the same priorities from upper and lower triangular judgments with crisp, interval or fuzzy values. Our proposed method can solve all of the matrices simultaneously by multiple objective programming. Finally, five examples are demonstrated to show the proposed method in more detail.