This paper deals with the calculation of a vector of reliable weights of decision alternatives on the basis of interval pairwise comparison judgments of experts. These weights are used to construct the ranking of deci...This paper deals with the calculation of a vector of reliable weights of decision alternatives on the basis of interval pairwise comparison judgments of experts. These weights are used to construct the ranking of decision alternatives and to solve selection problems, problems of ratings construction, resources allocation problems, scenarios evaluation problems, and other decision making problems. A comparative analysis of several popular models, which calculate interval weights on the basis of interval pairwise comparison matrices (IPCMs), was performed. The features of these models when they are applied to IPCMs with different inconsistency levels were identified. An algorithm is proposed which contains the stages for analyzing and increasing the IPCM inconsistency, calculating normalized interval weights, and calculating the ranking of decision alternatives on the basis of the resulting interval weights. It was found that the property of weak order preservation usually allowed identifying order-related intransitive expert pairwise comparison judgments. The correction of these elements leads to the removal of contradictions in resulting weights and increases the accuracy and reliability of results.展开更多
This article introduces a consistency index for measuring the consistency level of an interval fuzzy preference relation（IFPR）.An approach is then proposed to construct an additive consistent IFPR from a given incon...This article introduces a consistency index for measuring the consistency level of an interval fuzzy preference relation（IFPR）.An approach is then proposed to construct an additive consistent IFPR from a given inconsistent IFPR.By using a weighted averaging method combining the original IFPR and the constructed consistent IFPR,a formula is put forward to repair an inconsistent IFPR to generate an IFPR with acceptable consistency.An iterative algorithm is subsequently developed to rectify an inconsistent IFPR and derive one with acceptable consistency and weak transitivity.The proposed approaches can not only improve consistency of IFPRs but also preserve the initial interval uncertainty information as much as possible.Numerical examples are presented to illustrate how to apply the proposed approaches.展开更多
文摘This paper deals with the calculation of a vector of reliable weights of decision alternatives on the basis of interval pairwise comparison judgments of experts. These weights are used to construct the ranking of decision alternatives and to solve selection problems, problems of ratings construction, resources allocation problems, scenarios evaluation problems, and other decision making problems. A comparative analysis of several popular models, which calculate interval weights on the basis of interval pairwise comparison matrices (IPCMs), was performed. The features of these models when they are applied to IPCMs with different inconsistency levels were identified. An algorithm is proposed which contains the stages for analyzing and increasing the IPCM inconsistency, calculating normalized interval weights, and calculating the ranking of decision alternatives on the basis of the resulting interval weights. It was found that the property of weak order preservation usually allowed identifying order-related intransitive expert pairwise comparison judgments. The correction of these elements leads to the removal of contradictions in resulting weights and increases the accuracy and reliability of results.
基金partially supported by National Natural Sciences Foundation of China (71271188,71272129,71301061,71471059)Ministry of Education Humanities and Social Sciences Youth Fund(13YJC630120)+2 种基金National Social Science Fund Project(12AZD111)Natural Sciences and Engineering Research Council of Canada(NSERC) under its Discovery Grant programthe Jiangsu ITO Strategy Research Base Grant
文摘This article introduces a consistency index for measuring the consistency level of an interval fuzzy preference relation（IFPR）.An approach is then proposed to construct an additive consistent IFPR from a given inconsistent IFPR.By using a weighted averaging method combining the original IFPR and the constructed consistent IFPR,a formula is put forward to repair an inconsistent IFPR to generate an IFPR with acceptable consistency.An iterative algorithm is subsequently developed to rectify an inconsistent IFPR and derive one with acceptable consistency and weak transitivity.The proposed approaches can not only improve consistency of IFPRs but also preserve the initial interval uncertainty information as much as possible.Numerical examples are presented to illustrate how to apply the proposed approaches.
