Robustness of MULTIMOORA: A Method for Multi-Objective Optimization

Multi-Objective Optimization takes care of different objectives with the objectives keeping their own units. The internal mechanical solution of a Ratio System, producing dimensionless numbers, is preferred. The ratio system creates the opportunity to use a second approach: a Reference Point Theory, which uses the ratios of the ratio system. This overall theory is called MOORA (Multi-Objective Optimization by Ratio Analysis). The results are still more convincing if a Full Multiplicative Form is added forming MULTIMOORA. The control by three different approaches forms a guaranty for a solution being as non-subjective as possible. MULTIMOORA, tested after robustness, showed positive results.

[1]  W. Brauers,et al.  Robustness in regional development studies. The case of Lithuania , 2009 .

[2]  Yulei Luo,et al.  Mathematical Economics , 2019, Springer Texts in Business and Economics.

[3]  L. A. Goodman,et al.  Social Choice and Individual Values , 1951 .

[4]  Shankar Chakraborty,et al.  Applications of the MOORA method for decision making in manufacturing environment , 2011 .

[5]  Ching-Lai Hwang,et al.  Multiple Attribute Decision Making: Methods and Applications - A State-of-the-Art Survey , 1981, Lecture Notes in Economics and Mathematical Systems.

[6]  Edmundas Kazimieras Zavadskas,et al.  Multimoora Optimization Used to Decide on a Bank Loan to Buy Property , 2011 .

[7]  Willem K. Brauers Multi‐objective optimization for facilities management , 2004 .

[8]  Bernard Roy,et al.  Classement et choix en présence de points de vue multiples , 1968 .

[9]  Willem K. Brauers Multiobjective optimization (moo) in privatization , 2004 .

[10]  J. Koerts,et al.  Some Statistical Implications of the Log Transformation of Multiplicative Models , 1972 .

[11]  Stephen,et al.  THE HISTORY OF ROBUST ESTIMATION , 1385-1920 , 2022 .

[12]  Patrick Sevestre,et al.  The Econometrics of Panel Data , 1993 .

[13]  A. C. Pigou Economics of welfare , 1920 .

[14]  William A Quade,et al.  Dimensional analysis for economists , 1968 .

[15]  William A Quade,et al.  Dimensional analysis for economists , 1967 .

[16]  Russell L. Ackoff,et al.  An Approximate Measure of Value , 1954, Oper. Res..

[17]  Alain Schärlig,et al.  Pratiquer Electre et Prométhée : un complément à Décider sur plusieurs critères , 1996 .

[18]  H. Minkowski,et al.  Geometrie der Zahlen , 1896 .

[19]  E. Zavadskas,et al.  Project management by multimoora as an instrument for transition economies , 2010 .

[20]  W. Behrens,et al.  Manual for the preparation of industrial feasibility studies , 1991 .

[21]  M. Kendall Elementary Statistics , 1945, Nature.

[22]  Hermann Heinrich Gossen Gossen, Hermann Heinrich: Entwickelung der Gesetze des menschlichen Verkehrs, und der daraus fließenden Regeln für menschliches Handeln , 2019, Die 100 wichtigsten Werke der Ökonomie.

[23]  Ching-Lai Hwang,et al.  Fuzzy Multiple Attribute Decision Making - Methods and Applications , 1992, Lecture Notes in Economics and Mathematical Systems.

[24]  David M. Kreps,et al.  Game Theory and Economic Modelling , 1992 .

[25]  Willem Karel M. Brauers,et al.  Multi-objective decision making by reference point theory for a wellbeing economy , 2008, Oper. Res..

[26]  M. Bohanec,et al.  The Analytic Hierarchy Process , 2004 .

[27]  Alain Schaerlig,et al.  Décider sur plusieurs critères , 1985 .

[28]  Jean Pierre Brans,et al.  HOW TO SELECT AND HOW TO RANK PROJECTS: THE PROMETHEE METHOD , 1986 .

[29]  C. Spearman CORRELATION CALCULATED FROM FAULTY DATA , 1910 .

[30]  Nicolaus Tideman,et al.  Independence of irrelevant alternatives in the theory of voting , 1991 .

[31]  Edmundas Kazimieras Zavadskas,et al.  The MOORA method and its application to privatization in a transition economy , 2006 .

[32]  Philippe Vincke,et al.  Robust solutions and methods in decision‐aid , 1999 .

[33]  Schrutka Geometrie der Zahlen , 1911 .

[34]  Nicolas de Condorcet Essai Sur L'Application de L'Analyse a la Probabilite Des Decisions Rendues a la Pluralite Des Voix , 2009 .

[35]  C. Spearman ‘FOOTRULE’ FOR MEASURING CORRELATION , 1906 .

[36]  R. L. Keeney,et al.  Decisions with Multiple Objectives: Preferences and Value Trade-Offs , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[37]  Edmundas Kazimieras Zavadskas,et al.  _Is robustness really robust? Robustness from the point of view of statistics and econometrics with an application for multi-objective optimization , 2012 .

[38]  Michael D. Intriligator,et al.  Econometric Models, Techniques, and Applications. , 1979 .

[39]  H. Raiffa,et al.  Decisions with Multiple Objectives , 1993 .

[40]  Kenneth J. Arrow,et al.  General Economic Equilibrium: Purpose, Analytic Techniques, Collective Choice , 1972 .

[41]  R. Forthofer,et al.  Rank Correlation Methods , 1981 .

[42]  Willem K. Brauers,et al.  What is meant by normalisation in decision making , 2007 .

[43]  F. B. Vernadat,et al.  Decisions with Multiple Objectives: Preferences and Value Tradeoffs , 1994 .

[44]  Robert L. Wolpert,et al.  Statistical Inference , 2019, Encyclopedia of Social Network Analysis and Mining.

[45]  G. W. Sears,et al.  Executive Decisions and Operations Research , 1962 .

[46]  T. Baležentis,et al.  Multimoora for the EU member states updated with fuzzy number theory , 2011 .

[47]  P. Huber Théorie de l'inférence statistique robuste , 1969 .

[48]  C. Spearman The proof and measurement of association between two things. , 2015, International journal of epidemiology.

[49]  R. Faure,et al.  Introduction to operations research , 1968 .

[50]  M. Kendall,et al.  Rank Correlation Methods , 1949 .

[51]  L. Bauwens,et al.  Econometrics , 2005 .

[52]  Ralph L. Keeney,et al.  A Decision Analysis with Multiple Objectives: the Mexico City Airport , 1973 .

[53]  Patrick Sevestre,et al.  The Econometrics of panel data : handbook of theory and applications , 1994 .

[54]  Willem K. Brauers,et al.  Optimization Methods for a Stakeholder Society: A Revolution in Economic Thinking by Multi-objective Optimization , 2003 .

[55]  W. J. Studden,et al.  Tchebycheff Systems: With Applications in Analysis and Statistics. , 1967 .

[56]  Bertrand Mareschal,et al.  Prométhée: a new family of outranking methods in multicriteria analysis , 1984 .

[57]  Gwo-Hshiung Tzeng,et al.  Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS , 2004, Eur. J. Oper. Res..

[58]  Willem K. Brauers,et al.  The multiplicative representation for multiple objectives optimization with an application for arms procurement , 2002 .