OWA aggregation over a continuous interval argument with applications to decision making

We briefly describe the ordered weighted average (OWA) operator. We discuss its role in decision making under uncertainty. We provide an extension of the OWA operator to the case in which our argument is a continuous valued interval rather than a finite set of values. We look at some examples of this type of aggregation. We show how it can be used in some tasks that arise in decision making. We consider the extension of the continuous interval argument OWA operator to the more general case in which the argument values have importance weights. We use this to introduce the idea of an attitudinal-based expected value associated with a continuous random variable.

[1]  David Gale,et al.  Review: R. Duncan Luce and Howard Raiffa, Games and decisions: Introduction and critical survey , 1958 .

[2]  H. Raiffa,et al.  GAMES AND DECISIONS; INTRODUCTION AND CRITICAL SURVEY. , 1958 .

[3]  Kenneth J. Arrow,et al.  Studies in Resource Allocation Processes: Appendix: An optimality criterion for decision-making under ignorance , 1977 .

[4]  Ronald R. Yager,et al.  A procedure for ordering fuzzy subsets of the unit interval , 1981, Inf. Sci..

[5]  G. Bortolan,et al.  A review of some methods for ranking fuzzy subsets , 1985 .

[6]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decisionmaking , 1988, IEEE Trans. Syst. Man Cybern..

[7]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decision-making , 1988 .

[8]  Ronald R. Yager,et al.  Applications and Extensions of OWA Aggregations , 1992, Int. J. Man Mach. Stud..

[9]  D. Dubois,et al.  FUZZY NUMBERS: AN OVERVIEW , 1993 .

[10]  R. Yager.  Families of OWA operators , 1993 .

[11]  R. Yager.  Quantifier guided aggregation using OWA operators , 1996, Int. J. Intell. Syst..

[12]  Lotfi A. Zadeh,et al.  Fuzzy logic = computing with words , 1996, IEEE Trans. Fuzzy Syst..

[13]  J. Kacprzyk,et al.  The Ordered Weighted Averaging Operators: Theory and Applications , 1997 .

[14]  Janusz Kacprzyk,et al.  The Ordered Weighted Averaging Operators , 1997 .

[15]  Ronald R. Yager,et al.  On the inclusion of importances in OWA aggregations , 1997 .

[16]  Silvia Muzzioli,et al.  Note on ranking fuzzy triangular numbers , 1998, Int. J. Intell. Syst..

[17]  Janusz Kacprzyk,et al.  Computing with Words in Information/Intelligent Systems 1 , 1999 .

[18]  T. Calvo,et al.  Generation of weighting triangles associated with aggregation functions , 2000 .

[19]  T. Bedford,et al.  Probabilistic Risk Analysis: Foundations and Methods , 2001 .

[20]  V. Torra,et al.  Continuous WOWA operators with application to defuzzification , 2002 .

[21]  Lotfi A. Zadeh.  Toward a perception-based theory of probabilistic reasoning with imprecise probabilities , 2003 .

[22]  Lotfi A. Zadeh.  Precisiated natural language (PNL) - toward an enlargement of the role of natural languages in scientific theories , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).

[23]  Roger Sauter,et al.  Introduction to Probability and Statistics for Engineers and Scientists , 2005, Technometrics.

[24]  Lotfi A. Zadeh,et al.  From Computing with Numbers to Computing with Words - from Manipulation of Measurements to Manipulation of Perceptions , 2005, Logic, Thought and Action.