Introduction to the Analytic Hierarchy Process

Introduction and fundamentals.- Priority vector and consistency.- Missing comparisons and group decisions.- Extensions.- Conclusions.

[1]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[2]  Thomas L. Saaty.  Mathematical Methods Of Operational Research , 1959 .

[3]  Steven Vajda,et al.  Games and Decisions. By R. Duncan Luce and Howard Raiffa. Pp. xi, 509. 70s. 1957. (J Wiley & Sons) , 1959, The Mathematical Gazette.

[4]  John B. Fraleigh.  A first course in abstract algebra , 1967 .

[5]  Peter C. Fishburn,et al.  Utility theory for decision making , 1970 .

[6]  Lotfi A. Zadeh,et al.  Similarity relations and fuzzy orderings , 1971, Inf. Sci..

[7]  M. Shimura.  Fuzzy sets concept in rank-ordering objects , 1973 .

[8]  Ralph L. Keeney,et al.  Decisions with multiple objectives: preferences and value tradeoffs , 1976 .

[9]  T. L. Saaty.  A Scaling Method for Priorities in Hierarchical Structures , 1977 .

[10]  R. Yager.  An eigenvalue method of obtaining subjective probabilities , 1979 .

[11]  Thomas L. Saaty,et al.  Hierarchical analysis of behavior in competition: Prediction in chess , 1980 .

[12]  Thomas L. Saaty,et al.  Multicriteria Decision Making: The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation , 1990 .

[13]  Thomas L. Saaty,et al.  The Logic of Priorities: Applications in Business Energy, Health, and Transportation , 1981 .

[14]  H. Carter.  Fuzzy Sets and Systems — Theory and Applications , 1982 .

[15]  Valerie Belton,et al.  On a short-coming of Saaty's method of analytic hierarchies , 1983 .

[16]  W. Pedrycz,et al.  A fuzzy extension of Saaty's priority theory , 1983 .

[17]  T. Saaty,et al.  Procedures for Synthesizing Ratio Judgements , 1983 .

[18]  Luis G. Vargas,et al.  Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios , 1984 .

[19]  T. Tanino.  Fuzzy preference orderings in group decision making , 1984 .

[20]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[21]  V. Belton,et al.  The legitimacy of rank reversal—A comment , 1985 .

[22]  Thomas L. Saaty,et al.  Modeling behavior in competition: The analytic hierarchy process , 1985 .

[23]  G. Crawford,et al.  A note on the analysis of subjective judgment matrices , 1985 .

[24]  Fatemeh Zahedi,et al.  The Analytic Hierarchy Process—A Survey of the Method and its Applications , 1986 .

[25]  T. Saaty.  Axiomatic foundation of the analytic hierarchy process , 1986 .

[26]  Thomas L. Saaty,et al.  Absolute and relative measurement with the AHP. The most livable cities in the United States , 1986 .

[27]  J. Fichtner.  On deriving priority vectors from matrices of pairwise comparisons , 1986 .

[28]  J. Aczél,et al.  On synthesis of judgements , 1986 .

[29]  Luis G. Vargas,et al.  Uncertainty and rank order in the analytic hierarchy process , 1987 .

[30]  P. Harker.  Derivatives of the Perron root of a positive reciprocal matrix: With application to the analytic hierarchy process , 1987 .

[31]  J. Barzilai,et al.  Consistent weights for judgements matrices of the relative importance of alternatives , 1987 .

[32]  G. Crawford.  The geometric mean procedure for estimating the scale of a judgement matrix , 1987 .

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

[34]  K. Peniwati,et al.  Ranking countries according to economic, social and political indicators☆ , 1987 .

[35]  W. Cook,et al.  Deriving weights from pairwise comparison ratio matrices: An axiomatic approach , 1988 .

[36]  Thomas L. Saaty.  What is the analytic hierarchy process , 1988 .

[37]  Ami Arbel,et al.  Approximate articulation of preference and priority derivation , 1989 .

[38]  Qiwen Wang,et al.  An Alternate Measure of Consistency , 1989 .

[39]  Bruce L. Golden,et al.  Applications of the Analytic Hierarchy Process: A Categorized, Annotated Bibliography , 1989 .

[40]  J. Dyer.  Remarks on the analytic hierarchy process , 1990 .

[41]  T. Saaty.  Eigenvector and logarithmic least squares , 1990 .

[42]  Luis G. Vargas.  An overview of the analytic hierarchy process and its applications , 1990 .

[43]  Ernest H. Forman,et al.  Group decision support with the Analytic Hierarchy Process , 1992, Decis. Support Syst..

[44]  T. Saaty.  What is relative measurement? The ratio scale phantom , 1993 .

[45]  W. W. Koczkodaj.  A new definition of consistency of pairwise comparisons , 1993 .

[46]  Amartya Sen,et al.  Human development Index: Methodology and Measurement , 1994 .

[47]  W. Pedrycz.  Why triangular membership functions , 1994 .

[48]  J. Barzilai,et al.  Ahp Rank Reversal, Normalization and Aggregation Rules , 1994 .

[49]  Waldemar W. Koczkodaj,et al.  Generalization of a New Definition of Consistency for Pairwise Comparisons , 1994, Inf. Process. Lett..

[50]  G. Fliedner,et al.  Comparison of the REMBRANDT system with analytic hierarchy process , 1995 .

[51]  C. Carlsson,et al.  AHP in Political Group Decisions: A Study in the Art of Possibilities , 1995 .

[52]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[53]  R. Hämäläinen,et al.  Preference programming through approximate ratio comparisons , 1995 .

[54]  R. Hämäläinen,et al.  An Experiment on the Numerical Modelling of Verbal Ratio Statements , 1997 .

[55]  J. Crisp,et al.  The Delphi method? , 1997, Nursing research.

[56]  Luis G. Vargas.  Comments on Barzilai and Lootsma: Why the Multiplicative AHP Is Invalid: A Practical Counterexample , 1997 .

[57]  J. Barzilai.  Deriving weights from pairwise comparison matrices , 1997 .

[58]  S. H. Zanakis,et al.  A Monte Carlo investigation of incomplete pairwise comparison matrices in AHP , 1997 .

[59]  R. Hämäläinen,et al.  On the measurement of preferences in the analytic hierarchy process , 1997 .

[60]  J. Barzilai.  Consistency Measures for Pairwise Comparison Matrices , 1998 .

[61]  T. Saaty,et al.  Ranking by Eigenvector Versus Other Methods in the Analytic Hierarchy Process , 1998 .

[62]  E. Forman,et al.  Aggregating individual judgments and priorities with the analytic hierarchy process , 1998, Eur. J. Oper. Res..

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

[64]  Peter C. Fishburn,et al.  Preference Structures and Their Numerical Representations , 1999, Theor. Comput. Sci..

[65]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[66]  N. Nakajima,et al.  ASSESSMENT FOR AN INCOMPLETE COMPARISON MATRIX AND IMPROVEMENT OF AN INCONSISTENT COMPARISON : COMPUTATIONAL EXPERIMENTS , 1999 .

[67]  F. Lootsma.  Multi-Criteria Decision Analysis via Ratio and Difference Judgement , 1999 .

[68]  J. Buckley,et al.  Fuzzy hierarchical analysis , 1999, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

[69]  Etienne E. Kerre,et al.  Reasonable properties for the ordering of fuzzy quantities (II) , 2001, Fuzzy Sets Syst..

[70]  Dae-Ho Byun,et al.  The AHP approach for selecting an automobile purchase model , 2001, Inf. Manag..

[71]  Livia D'Apuzzo,et al.  Weak Consistency and Quasi-Linear Means Imply the Actual Ranking , 2002, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[72]  S. Shiraishi,et al.  ON A MAXIMIZATION PROBLEM ARISING FROM A POSITIVE RECIPROCAL MATRIX IN AHP , 2002 .

[73]  G. Klir.  Uncertainty In Economics: The Heritage Of G.L.S. Shackle , 2002 .

[74]  T. Saaty,et al.  Why the magic number seven plus or minus two , 2003 .

[75]  José María Moreno-Jiménez,et al.  The geometric consistency index: Approximated thresholds , 2003, Eur. J. Oper. Res..

[76]  R. Jiang,et al.  Scale transitivity in the AHP , 2003, J. Oper. Res. Soc..

[77]  M. T. Lamata,et al.  A new measure of consistency for positive reciprocal matrices , 2003 .

[78]  Saul I. Gass,et al.  On teaching the analytic hierarchy process , 2003, Comput. Oper. Res..

[79]  Saul I. Gass,et al.  Exercises for Teaching the Analytic Hierarchy Process , 2004 .

[80]  Eng Ung Choo,et al.  A common framework for deriving preference values from pairwise comparison matrices , 2004, Comput. Oper. Res..

[81]  Saul I. Gass,et al.  Singular value decomposition in AHP , 2004, Eur. J. Oper. Res..

[82]  Francisco Herrera,et al.  Some issues on consistency of fuzzy preference relations , 2004, Eur. J. Oper. Res..

[83]  Raimo P. Hämäläinen,et al.  Decisionarium ‐ aiding decisions, negotiating and collecting opinions on the web , 2005 .

[84]  Simon French,et al.  Comparison study of multi-attribute decision analytic software , 2005 .

[85]  Saul I. Gass,et al.  Model World: The Great Debate - MAUT Versus AHP , 2005, Interfaces.

[86]  María Teresa Lamata,et al.  Consistency in the Analytic Hierarchy Process: a New Approach , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[87]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[88]  Alex M. Andrew,et al.  Uncertainty and Information: Foundations of Generalized Information Theory , 2006 .

[89]  Eduardo Conde,et al.  Inferring Efficient Weights from Pairwise Comparison Matrices , 2006, Math. Methods Oper. Res..

[90]  Alessio Ishizaka,et al.  How to derive priorities in AHP: a comparative study , 2006, Central Eur. J. Oper. Res..

[91]  Livia D'Apuzzo,et al.  Transitive Matrices, Strict Preference Order and Ordinal Evaluation Operators , 2006, Soft Comput..

[92]  Bernard De Baets,et al.  Cyclic Evaluation of Transitivity of Reciprocal Relations , 2006, Soc. Choice Welf..

[93]  William E. Stein,et al.  The harmonic consistency index for the analytic hierarchy process , 2007, Eur. J. Oper. Res..

[94]  Chang-Chun Lin,et al.  A revised framework for deriving preference values from pairwise comparison matrices , 2007, Eur. J. Oper. Res..

[95]  Luis G. Vargas,et al.  Interval judgments and Euclidean centers , 2007, Math. Comput. Model..

[96]  Zeshui Xu,et al.  A survey of preference relations , 2007, Int. J. Gen. Syst..

[97]  Thomas L. Saaty,et al.  On the invalidity of fuzzifying numerical judgments in the Analytic Hierarchy Process , 2007, Math. Comput. Model..

[98]  Michele Fedrizzi,et al.  Reconstruction Methods for Incomplete Fuzzy Preference Relations: A Numerical Comparison , 2007, WILF.

[99]  Carlos A. Bana e Costa,et al.  A critical analysis of the eigenvalue method used to derive priorities in AHP , 2008, Eur. J. Oper. Res..

[100]  T. Saaty.  Relative measurement and its generalization in decision making why pairwise comparisons are central in mathematics for the measurement of intangible factors the analytic hierarchy/network process , 2008 .

[101]  Zhongsheng Hua,et al.  On the extent analysis method for fuzzy AHP and its applications , 2008, Eur. J. Oper. Res..

[102]  Kalyanmoy Deb,et al.  Multiple Criteria Decision Making, Multiattribute Utility Theory: Recent Accomplishments and What Lies Ahead , 2008, Manag. Sci..

[103]  Sándor Bozóki,et al.  Solution of the least squares method problem of pairwise comparison matrices , 2008, Central Eur. J. Oper. Res..

[104]  Alessio Ishizaka,et al.  Analytic Hierarchy Process and Expert Choice: Benefits and limitations , 2009, OR Insight.

[105]  Francisco Herrera,et al.  Cardinal Consistency of Reciprocal Preference Relations: A Characterization of Multiplicative Transitivity , 2009, IEEE Transactions on Fuzzy Systems.

[106]  L. D'Apuzzo,et al.  A general unified framework for pairwise comparison matrices in multicriterial methods , 2009 .

[107]  Raffaello Seri,et al.  The Analytic Hierarchy Process and the Theory of Measurement , 2010, Manag. Sci..

[108]  Mariya A. Sodenkamp,et al.  The Analytic Hierarchy and Analytic Network Measurement Processes: The Measurement of Intangibles Decision Making under Benefits, Opportunities, Costs and Risks , 2010 .

[109]  Michele Fedrizzi,et al.  On the priority vector associated with a reciprocal relation and a pairwise comparison matrix , 2010, Soft Comput..

[110]  Lajos Rónyai,et al.  On optimal completion of incomplete pairwise comparison matrices , 2010, Math. Comput. Model..

[111]  Jaroslav Ramík,et al.  Inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean , 2010, Fuzzy Sets Syst..

[112]  Bice Cavallo,et al.  Characterizations of consistent pairwise comparison matrices over abelian linearly ordered groups , 2010, Int. J. Intell. Syst..

[113]  Didier Dubois,et al.  The role of fuzzy sets in decision sciences: Old techniques and new directions , 2011, Fuzzy Sets Syst..

[114]  Alessio Ishizaka,et al.  Does AHP help us make a choice? An experimental evaluation , 2011, J. Oper. Res. Soc..

[115]  John Mingers,et al.  Soft OR comes of age—but not everywhere! , 2011 .

[116]  T. Saaty,et al.  Global awareness, future city design and decision making , 2012 .

[117]  Sándor Bozóki,et al.  Analysis of pairwise comparison matrices: an empirical research , 2013, Ann. Oper. Res..

[118]  József Mezei,et al.  How different are ranking methods for fuzzy numbers? A numerical study , 2013, Int. J. Approx. Reason..

[119]  Sajjad Zahir,et al.  A Comprehensive Literature Review of the Rank Reversal Phenomenon in the Analytic Hierarchy Process , 2013 .

[120]  Alessio Ishizaka,et al.  Multi-criteria Decision Analysis: Methods and Software , 2013 .

[121]  Michele Fedrizzi,et al.  Inconsistency indices for pairwise comparison matrices: a numerical study , 2013, Annals of Operations Research.

[122]  Michele Fedrizzi,et al.  Optimal sequencing in incomplete pairwise comparisons for large-dimensional problems , 2013, Int. J. Gen. Syst..

[123]  Luis G. Vargas,et al.  Decision Making with the Analytic Network Process: Economic, Political, Social and Technological Applications with Benefits, Opportunities, Costs and Risks , 2013 .

[124]  Steen Leleur,et al.  Scaling Transformation in the Rembrandt Technique: Examination of the Progression Factors , 2013, Int. J. Inf. Technol. Decis. Mak..

[125]  Shannon L. Harris,et al.  A Unified Framework for the Prioritization of Organ Transplant Patients: Analytic Hierarchy Process, Sensitivity and Multifactor Robustness Study , 2013 .

[126]  Thomas L. Saaty,et al.  Criteria for Evaluating Group Decision-Making Methods , 2013 .

[127]  Michele Fedrizzi,et al.  A note on the proportionality between some consistency indices in the AHP , 2012, Appl. Math. Comput..

[128]  Shahrokh Nikou,et al.  Evaluation of mobile services and substantial adoption factors with Analytic Hierarchy Process (AHP) , 2013 .

[129]  Raffaello Seri,et al.  Empirical Properties of Group Preference Aggregation Methods Employed in AHP: Theory and Evidence , 2013, Eur. J. Oper. Res..

[130]  S. Bozóki,et al.  Inefficient weights from pairwise comparison matrices with arbitrarily small inconsistency , 2014 .

[131]  Michael Vitale,et al.  The Wisdom of Crowds , 2015, Cell.

[132]  Michele Fedrizzi,et al.  Axiomatic properties of inconsistency indices for pairwise comparisons , 2013, J. Oper. Res. Soc..