Using Different Qualitative Scales in a Multi-Criteria Decision-Making Procedure

Many decision problems manage linguistic information assessed through several ordered qualitative scales. In these contexts, the main problem arising is how to aggregate this qualitative information. In this paper, we present a multi-criteria decision-making procedure that ranks a set of alternatives assessed by means of a specific ordered qualitative scale for each criterion. These ordered qualitative scales can be non-uniform and be formed by a different number of linguistic terms. The proposed procedure follows an ordinal approach by means of the notion of ordinal proximity measure that assigns an ordinal degree of proximity to each pair of linguistic terms of the qualitative scales. To manage the ordinal degree of proximity from different ordered qualitative scales, we provide a homogenization process. We also introduce a stochastic approach to assess the robustness of the conclusions.

[1]  Francisco Herrera,et al.  Managing non-homogeneous information in group decision making , 2005, Eur. J. Oper. Res..

[2]  Bernard Roy,et al.  Determining the weights of criteria in the ELECTRE type methods with a revised Simos' procedure , 2002, Eur. J. Oper. Res..

[3]  Fiorenzo Franceschini,et al.  Ordered Samples Control Charts for Ordinal Variables , 2005 .

[4]  S S Stevens,et al.  On the Theory of Scales of Measurement. , 1946, Science.

[5]  José Luis García-Lapresta,et al.  Metrizable ordinal proximity measures and their aggregation , 2018, Inf. Sci..

[6]  José Luis García-Lapresta,et al.  Ordinal proximity measures in the context of unbalanced qualitative scales and some applications to consensus and clustering , 2015, Appl. Soft Comput..

[7]  Gary L. Wells,et al.  Measuring Psychological Uncertainty : Verbal Versus Numeric Methods , 2004 .

[8]  José Luis García-Lapresta,et al.  Aggregating opinions in non-uniform ordered qualitative scales , 2017, Appl. Soft Comput..

[9]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[10]  Thomas S. Wallsten,et al.  Base rate effects on the interpretations of probability and frequency expressions , 1986 .

[11]  J. Brans,et al.  A Preference Ranking Organisation Method: (The PROMETHEE Method for Multiple Criteria Decision-Making) , 2008 .

[12]  J C Grip,et al.  Ordinal scales and foundations of misinference. , 1989, Archives of physical medicine and rehabilitation.

[13]  Lotfi A. Zadeh.  Key Roles of Information Granulation and Fuzzy Logic in Human Reasoning, Concept Formulation and Computing with Words , 1996, Proceedings of IEEE 5th International Fuzzy Systems.

[14]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning - II , 1975, Inf. Sci..

[15]  G. Mavrotas,et al.  Determining objective weights in multiple criteria problems: The critic method , 1995, Comput. Oper. Res..

[16]  Alf Zimmer,et al.  Verbal Vs. Numerical Processing of Subjective Probabilities , 1983 .

[17]  Wen-Pai Wang,et al.  A fuzzy linguistic computing approach to supplier evaluation , 2010 .

[18]  Ron Anjard,et al.  Advanced Quality Function Deployment , 2003 .

[19]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[20]  J. Figueira,et al.  A survey on stochastic multicriteria acceptability analysis methods , 2008 .

[21]  Oleg I. Larichev,et al.  Ranking multicriteria alternatives: The method ZAPROS III , 2001, Eur. J. Oper. Res..

[22]  Jun Liu,et al.  A Linguistic-Valued Weighted Aggregation Operator to Multiple Attribute Group Decision Making with Quantitative and Qualitative Information , 2008, Int. J. Comput. Intell. Syst..

[23]  Francisco Herrera,et al.  Combining Numerical and Linguistic Information in Group Decision Making , 1998, Inf. Sci..

[24]  Jean-Luc Marichal,et al.  Determination of weights of interacting criteria from a reference set , 2000, Eur. J. Oper. Res..

[25]  D. Winterfeldt,et al.  Comparison of weighting judgments in multiattribute utility measurement , 1991 .

[26]  Zhi Xiao,et al.  The trapezoidal fuzzy soft set and its application in MCDM , 2012 .

[27]  F. Franceschini,et al.  Qualitative Ordinal Scales: The Concept of Ordinal Range , 2004 .

[28]  Matthias Ehrgott,et al.  Multiple criteria decision analysis: state of the art surveys , 2005 .

[29]  Francisco Herrera,et al.  Computing with words in decision making: foundations, trends and prospects , 2009, Fuzzy Optim. Decis. Mak..

[30]  José Luis García-Lapresta,et al.  An ordinal multi-criteria decision-making procedure under imprecise linguistic assessments , 2019, Eur. J. Oper. Res..

[31]  Tommi Tervonen,et al.  Implementing stochastic multicriteria acceptability analysis , 2007, Eur. J. Oper. Res..

[32]  Tamar Gadrich,et al.  Evaluating quality measured on a ternary ordinal scale , 2008, Qual. Reliab. Eng. Int..

[33]  Alf C. Zimmer,et al.  A Model for the Interpretation of Verbal Predictions , 1984, Int. J. Man Mach. Stud..

[34]  Karl Halvor Teigen,et al.  The language of uncertainty , 1988 .

[35]  P. Vincke,et al.  Note-A Preference Ranking Organisation Method: The PROMETHEE Method for Multiple Criteria Decision-Making , 1985 .

[36]  Francisco Herrera,et al.  A Fuzzy Linguistic Methodology to Deal With Unbalanced Linguistic Term Sets , 2008, IEEE Transactions on Fuzzy Systems.

[37]  Laurent Botti,et al.  Weight of criteria in hotel selection: An empirical illustration based on TripAdvisor criteria , 2016, European Journal of Tourism Research.

[38]  Luis Martínez-López,et al.  A multi-granular linguistic model for management decision-making in performance appraisal , 2009, Soft Comput..

[39]  J. Dombi,et al.  A method for determining the weights of criteria: the centralized weights , 1986 .

[40]  G. Huston.  The Hospital Anxiety and Depression Scale. , 1987, The Journal of rheumatology.

[41]  Tamar Gadrich,et al.  Assessing variation: a unifying approach for all scales of measurement , 2015 .

[42]  Peide Liu,et al.  A multi-attribute group decision-making method based on weighted geometric aggregation operators of interval-valued trapezoidal fuzzy numbers , 2012 .

[43]  Francisco Herrera,et al.  A fusion approach for managing multi-granularity linguistic term sets in decision making , 2000, Fuzzy Sets Syst..

[44]  D. Bouyssou.  Ranking methods based on valued preference relations: A characterization of the net flow method , 1992 .

[45]  Kaisa Miettinen,et al.  Ordinal criteria in stochastic multicriteria acceptability analysis (SMAA) , 2003, Eur. J. Oper. Res..

[46]  Ruth Beyth-Marom,et al.  How probable is probable? A numerical translation of verbal probability expressions , 1982 .

[47]  Gary L. Wells,et al.  Measuring psychological uncertainty: Verbal versus numeric methods , 1996 .

[48]  Francisco Herrera,et al.  A 2-tuple fuzzy linguistic representation model for computing with words , 2000, IEEE Trans. Fuzzy Syst..

[49]  José Luis García-Lapresta,et al.  Reciprocal and Linguistic Preferences , 2013, On Fuzziness.

[50]  Luis C. Dias,et al.  On generating utility functions in Stochastic Multicriteria Acceptability Analysis , 2019, Eur. J. Oper. Res..

[51]  Michael G. Lacy,et al.  Statistics of Ordinal Variation , 2000 .

[52]  Chiang Kao,et al.  Weight determination for consistently ranking alternatives in multiple criteria decision analysis , 2010 .