A Ranking Procedure by Incomplete Pairwise Comparisons Using Information Entropy and Dempster-Shafer Evidence Theory

Decision-making, as a way to discover the preference of ranking, has been used in various fields. However, owing to the uncertainty in group decision-making, how to rank alternatives by incomplete pairwise comparisons has become an open issue. In this paper, an improved method is proposed for ranking of alternatives by incomplete pairwise comparisons using Dempster-Shafer evidence theory and information entropy. Firstly, taking the probability assignment of the chosen preference into consideration, the comparison of alternatives to each group is addressed. Experiments verified that the information entropy of the data itself can determine the different weight of each group's choices objectively. Numerical examples in group decision-making environments are used to test the effectiveness of the proposed method. Moreover, the divergence of ranking mechanism is analyzed briefly in conclusion section.

[1]  George J. Klir,et al.  Uncertainty Modeling and Analysis in Engineering and the Sciences (Hardcover) , 2006 .

[2]  Yejun Xu,et al.  Logarithmic least squares method to priority for group decision making with incomplete fuzzy preference relations , 2013 .

[3]  P. Walley.  Inferences from Multinomial Data: Learning About a Bag of Marbles , 1996 .

[4]  Z. S. Xu,et al.  Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation , 2004, Int. J. Approx. Reason..

[5]  Okyay Kaynak,et al.  Computational Intelligence: Soft Computing and Fuzzy-Neuro Integration with Applications , 1998, NATO ASI Series.

[6]  Lev V. Utkin.  Extensions of belief functions and possibility distributions by using the imprecise Dirichlet model , 2005, Fuzzy Sets Syst..

[7]  Ronald R. Yager,et al.  On the fusion of non-independent belief structures , 2009, Int. J. Gen. Syst..

[8]  Leo Egghe,et al.  Uncertainty and information: Foundations of generalized information theory , 2007, J. Assoc. Inf. Sci. Technol..

[9]  L. Jones.  Measurement of Values , 1959, Nature.

[10]  Qing Chen,et al.  Estimating Data for Multicriteria Decision Making Problems: Optimization Techniques , 2009, Encyclopedia of Optimization.

[11]  Qi Liu,et al.  A TOPSIS-BASED CENTROID–INDEX RANKING METHOD OF FUZZY NUMBERS AND ITS APPLICATION IN DECISION-MAKING , 2005, Cybern. Syst..

[12]  S. Shiraishi,et al.  PROPERTIES OF A POSITIVE RECIPROCAL MATRIX AND THEIR APPLICATION TO AHP , 1998 .

[13]  Cengiz Kahraman,et al.  Developing a group decision support system based on fuzzy information axiom , 2010, Knowl. Based Syst..

[14]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[15]  Lev V. Utkin,et al.  A new ranking procedure by incomplete pairwise comparisons using preference subsets , 2009, Intell. Data Anal..

[16]  Yong Deng,et al.  A new optimal consensus method with minimum cost in fuzzy group decision , 2012, Knowl. Based Syst..

[17]  Sándor Bozóki,et al.  An inconsistency control system based on incomplete pairwise comparison matrices , 2011 .

[18]  P. Harker.  Incomplete pairwise comparisons in the analytic hierarchy process , 1987 .

[19]  Lev V. Utkin,et al.  Probabilities of judgments provided by unknown experts by using the imprecise Dirichlet model , 2004 .

[20]  H. A. David,et al.  The method of paired comparisons , 1966 .

[21]  R. Duncan Luce,et al.  Individual Choice Behavior: A Theoretical Analysis , 1979 .

[22]  L. Thurstone.  A law of comparative judgment. , 1994 .

[23]  Panos M. Pardalos,et al.  Encyclopedia of Optimization , 2006 .

[24]  Michael Pittarelli.  Uncertainty and Information: Foundations of Generalized Information Theory, George J. Klir. Wiley, New York (2005), 499 pages + xv, $94.95, ISBN: 0471748676 , 2007 .

[25]  Thomas L. Saaty,et al.  The possibility of group choice: pairwise comparisons and merging functions , 2011, Social Choice and Welfare.

[26]  R. A. Bradley,et al.  RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS , 1952 .

[27]  Deng Yong,et al.  A TOPSIS-BASED CENTROID–INDEX RANKING METHOD OF FUZZY NUMBERS AND ITS APPLICATION IN DECISION-MAKING , 2005 .

[28]  R. Luce,et al.  Individual Choice Behavior: A Theoretical Analysis. , 1960 .

[29]  P. Harker.  Alternative modes of questioning in the analytic hierarchy process , 1987 .

[30]  Yong Deng,et al.  A new fuzzy dempster MCDM method and its application in supplier selection , 2011, Expert Syst. Appl..

[31]  Francisco Herrera,et al.  A web based consensus support system for group decision making problems and incomplete preferences , 2010, Inf. Sci..

[32]  Ying Wu,et al.  A new linguistic MCDM method based on multiple-criterion data fusion , 2011, Expert Syst. Appl..

[33]  A. M. M. Sharif Ullah,et al.  Algorithms for fuzzy multi expert multi criteria decision making (ME-MCDM) , 2011, Knowl. Based Syst..

[34]  Robert D. Nowak,et al.  Active Ranking using Pairwise Comparisons , 2011, NIPS.

[35]  Eyke Hüllermeier,et al.  Ranking by pairwise comparison a note on risk minimization , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[36]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[37]  Eyke Hüllermeier,et al.  Comparison of Ranking Procedures in Pairwise Preference Learning , 2004 .

[38]  KahramanCengiz,et al.  Developing a group decision support system based on fuzzy information axiom , 2010 .

[39]  Zeshui Xu,et al.  A Procedure for Decision Making Based on Incomplete Fuzzy Preference Relation , 2005, Fuzzy Optim. Decis. Mak..

[40]  R. A. Bradley,et al.  RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS THE METHOD OF PAIRED COMPARISONS , 1952 .

[41]  Yejun Xu,et al.  Eigenvector method, consistency test and inconsistency repairing for an incomplete fuzzy preference relation , 2013 .

[42]  Ronald R. Yager,et al.  Entropy and Specificity in a Mathematical Theory of Evidence , 2008, Classic Works of the Dempster-Shafer Theory of Belief Functions.