A multi-criteria group decision-making method with fuzzy preference relations based on filtration-and-weighting-based triangular bounded consistency

In multi-criteria group decision-making (MCGDM) problems with incomplete fuzzy preference relations (FPRs), the consistency based on bounded rationality is preferred to depend on the historical preferences of decision makers to generate complete FPR matrices. There are two factors in influencing the effect of historical preferences on complete FPR matrices and further decision makers’ satisfaction of group solutions. One is the effectiveness of historical preferences and the other is their relative weights. On this basis, this paper proposes a new MCGDM method with FPRs based on the filtration-and-weighting-based triangular bounded consistency (FWBTBC), where historical FPRs between three adjacent pairs of alternatives are characterized by triangles and these two factors are considered comprehensively. A triangle filtration process is designed based on the Grubbs criterion to filter the abnormal triangles in the collected ones. A weight determination process is developed, where a distance measure between remaining triangles is constructed to calculate their weights. Based on the combination of the two processes, the FWBTBC of FPRs is created and then the proposed method is presented. The validity of the proposed method is demonstrated by its application in analyzing a drainage tube supplier selection problem for a tertiary hospital located in Hefei, Anhui, China.</p

Regression model for estimation of attribute reliability

In this paper, a regression model is developed to estimate attribute reliability in the evidential reasoning (ER) context. By analysing the difference between attribute weight and attribute reliability, a general qualitative definition of attribute reliability is provided. The reliability of an attribute is quantitatively measured in consistence with the qualitative definition in the context of the ER approach. A regression model is then constructed to generate attribute reliabilities by minimising the maximum differences between the real value of attribute reliability and its estimation. Within the post-optimal solution space of attribute reliabilities, an optimisation model is constructed to determine the expected utilities of each alternative in order to generate solutions to multiple attribute decision analysis problems. A sale place selection problem in Qingyang County of Chizhou in Anhui province of China is analysed using the proposed regression model to demonstrate its detailed implementation process, validity and applicability.</p

Aggregated IDPRs between neighboring candidates in the manager selection problem.

<p>Aggregated IDPRs between neighboring candidates in the manager selection problem.</p

Score intervals of the IDPRs between any two candidates in the manager selection problem.

Score intervals of the IDPRs between any two candidates in the manager selection problem.</p

The six sets of functions for the least square method and their relevant optimization results.

<p>The six sets of functions for the least square method and their relevant optimization results.</p

Supplementary material of “Interval-valued distributed preference relation and its application to group decision making”.

Appendix A. (Figure A) The function G′ with respect to x. (Figure B) The function K′ with respect to y. Appendix B. (Table A) Explanation of the ten criteria in the manager selection problem. (Table B) Relative weights of the four decision makers on the ten criteria in the manager selection problem. (Table C) IDPRs between the neighboring candidates and the IDPRs between specific pair of candidates used to construct additive consistency in the manager selection problem. (Table D) Group IDPRs between the neighboring candidates and the group IDPRs between specific pair of candidates used to construct additive consistency in the manager selection problem. (Table E) Values of the parameter a for decision makers and the group with the variation in s(Hn). (Figure C) Movement of the parameter a for decision makers and the group with the variation in s(Hn). (Table F) Values of the parameter b for decision makers and the group with the variation in s(Hn). (Figure D) Movement of the parameter b for decision makers and the group with the variation in s(Hn). (DOC)</p

Possibility matrix of the five candidates in the manager selection problem.

<p>Possibility matrix of the five candidates in the manager selection problem.</p

The comparison of the combinations of <i>a</i>_<i>j</i> generated by using the four sets of functions for the manager selection problem.

<p>The comparison of the combinations of <i>a</i>_<i>j</i> generated by using the four sets of functions for the manager selection problem.</p

Process of generating a solution to the MCGDM problem with IDPRs.

<p>Process of generating a solution to the MCGDM problem with IDPRs.</p

Score intervals of the group IDPRs between neighboring candidates in the manager selection problem.

<p>Score intervals of the group IDPRs between neighboring candidates in the manager selection problem.</p