Decision making with imprecise probabilities and utilities by means of statistical preference and stochastic dominance

A problem of decision making under uncertainty in which the choice must be made between two sets of alternatives instead of two single ones is considered. A number of choice rules are proposed and their main properties are investigated, focusing particularly on the generalizations of stochastic dominance and statistical preference. The particular cases where imprecision is present in the utilities or in the beliefs associated to two alternatives are considered.

[1]  Didier Dubois,et al.  An Imprecise Probability Approach to Joint Extensions of Stochastic and Interval Orderings , 2012, IPMU.

[2]  Milosz Kadzinski,et al.  Selection of a representative value function in robust multiple criteria ranking and choice , 2012, Eur. J. Oper. Res..

[3]  R. Kruse,et al.  Statistics with vague data , 1987 .

[4]  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.

[5]  J. Bezdek,et al.  A fuzzy relation space for group decision theory , 1978 .

[6]  Alexis Tsoukiàs,et al.  Preference Modelling , 2004, Preferences.

[7]  G. Choquet.  Theory of capacities , 1954 .

[8]  Didier Dubois,et al.  Qualitative decision theory with preference relations and comparative uncertainty: An axiomatic approach , 2003, Artif. Intell..

[9]  B. De Baets,et al.  On the Cycle-Transitivity of the Dice Model , 2003 .

[10]  Marco Zaffalon,et al.  Conservative Inference Rule for Uncertain Reasoning under Incompleteness , 2009, J. Artif. Intell. Res..

[11]  Inés Couso,et al.  The Behavioral Meaning of the Median , 2010, SMPS.

[12]  R. Mesiar,et al.  Aggregation operators: new trends and applications , 2002 .

[13]  Marc Goovaerts,et al.  Effective actuarial methods , 1990 .

[14]  Matthias C. M. Troffaes.  Decision making under uncertainty using imprecise probabilities , 2007, Int. J. Approx. Reason..

[15]  P. Walley.  Statistical Reasoning with Imprecise Probabilities , 1990 .

[16]  Inés Couso,et al.  Upper Probabilities and Selectors of Random Sets , 2002 .

[17]  Isaac Levi,et al.  The Enterprise Of Knowledge , 1980 .

[18]  Salvatore Greco,et al.  Robust Ordinal Regression , 2014, Trends in Multiple Criteria Decision Analysis.

[19]  Marco Zaffalon,et al.  Reliable diagnoses of dementia by the naive credal classifier inferred from incomplete cognitive data , 2003, Artif. Intell. Medicine.

[20]  J. García-Lapresta,et al.  Majority decisions based on difference of votes , 2001 .

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

[22]  Robert Nau.  The Shape of Incomplete Preferences , 2003, ISIPTA.

[23]  J. K. Satia,et al.  Markovian Decision Processes with Uncertain Transition Probabilities , 1973, Oper. Res..

[24]  Hung T. Nguyen,et al.  An Introduction to Random Sets , 2006 .

[25]  R. Aumann.  UTILITY THEORY WITHOUT THE COMPLETENESS AXIOM , 1962 .

[26]  S. Greco,et al.  Extreme ranking analysis in robust ordinal regression , 2012 .

[27]  M. Schervish,et al.  A Representation of Partially Ordered Preferences , 1995 .

[28]  Inés Couso,et al.  Approximations of upper and lower probabilities by measurable selections , 2010, Inf. Sci..

[29]  Salvatore Greco,et al.  Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions , 2008, Eur. J. Oper. Res..

[30]  K. Joag-dev,et al.  Bivariate Dependence Properties of Order Statistics , 1996 .

[31]  Gaspar Mayor,et al.  Aggregation Operators , 2002 .

[32]  I. Gilboa,et al.  Maxmin Expected Utility with Non-Unique Prior , 1989 .

[33]  Scott Ferson,et al.  Constructing Probability Boxes and Dempster-Shafer Structures , 2003 .

[34]  Xin Zhang,et al.  Research on the multi-attribute decision-making under risk with interval probability based on prospect theory and the uncertain linguistic variables , 2011, Knowl. Based Syst..

[35]  Jitka Dupacová,et al.  Robustness of optimal portfolios under risk and stochastic dominance constraints , 2014, Eur. J. Oper. Res..

[36]  R. Mesiar,et al.  Aggregation operators: properties, classes and construction methods , 2002 .

[37]  F. Fred Choobineh,et al.  Stochastic dominance based comparison for system selection , 2012, Eur. J. Oper. Res..

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

[39]  A. Müller,et al.  Comparison Methods for Stochastic Models and Risks , 2002 .

[40]  Didier Dubois,et al.  Gradualness, uncertainty and bipolarity: Making sense of fuzzy sets , 2012, Fuzzy Sets Syst..

[41]  Susana Montes,et al.  Stochastic dominance with imprecise information , 2014, Comput. Stat. Data Anal..

[42]  D. Bunn.  Stochastic Dominance , 1979 .

[43]  Bernard De Baets,et al.  A Fuzzy Approach to Stochastic Dominance of Random Variables , 2003, IFSA.