"The connection between distortion risk measures and ordered weighted averaging operators"

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and nite random variables is presented. This connection oers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.Fuzzy systems; Degree of orness; Risk quantification; Discrete random variable JEL classification:C02,C60

The Choquet integral for the aggregation of interval scales in multicriteria decision making

This paper addresses the question of which models fit with information concerning the preferences of the decision maker over each attribute, and his preferences about aggregation of criteria (interacting criteria). We show that the conditions induced by these information plus some intuitive conditions lead to a unique possible aggregation operator: the Choquet integral.

Fuzzy measures and integrals in MCDA

This chapter aims at a unified presentation of various methods of MCDA based onfuzzy measures (capacity) and fuzzy integrals, essentially the Choquet andSugeno integral. A first section sets the position of the problem ofmulticriteria decision making, and describes the various possible scales ofmeasurement (difference, ratio, and ordinal). Then a whole section is devotedto each case in detail: after introducing necessary concepts, the methodologyis described, and the problem of the practical identification of fuzzy measuresis given. The important concept of interaction between criteria, central inthis chapter, is explained in details. It is shown how it leads to k-additivefuzzy measures. The case of bipolar scales leads to thegeneral model based on bi-capacities, encompassing usual models based oncapacities. A general definition of interaction for bipolar scales isintroduced. The case of ordinal scales leads to the use of Sugeno integral, andits symmetrized version when one considers symmetric ordinal scales. Apractical methodology for the identification of fuzzy measures in this contextis given. Lastly, we give a short description of some practical applications.Choquet integral; fuzzy measure; interaction; bi-capacities

Ordering based decision making: a survey

Decision making is the crucial step in many real applications such as organization management, financial planning, products evaluation and recommendation. Rational decision making is to select an alternative from a set of different ones which has the best utility (i.e., maximally satisfies given criteria, objectives, or preferences). In many cases, decision making is to order alternatives and select one or a few among the top of the ranking. Orderings provide a natural and effective way for representing indeterminate situations which are pervasive in commonsense reasoning. Ordering based decision making is then to find the suitable method for evaluating candidates or ranking alternatives based on provided ordinal information and criteria, and this in many cases is to rank alternatives based on qualitative ordering information. In this paper, we discuss the importance and research aspects of ordering based decision making, and review the existing ordering based decision making theories and methods along with some future research directions

REVIEW OF MODELING PREFERENCES FOR DECISION MODELS

A group decision problem is set in environments where there is a common issue to solve, a set of possible options to choose, and a set of individuals who are experts and express their opinions about the set of possible alternatives with the intention to reach a collective decision as the unique solution of the problem in question. The modeling of the preferences of the decision-maker is an essential stage in the construction of models used in the theory of decision, operations research, economics, etc. On decision problems experts use models of representation of preferences that are close to their disciplines or fields of work. The structures of information most commonly used for the representation of the preferences of experts are vectors of utility, orders of preference and preference relations. In decision problems, the expression of preferences domain is the domain of information used by the experts to express their preferences, the main are numerical, linguistic, and intervalar stressing the multi-granular linguistic. This paper is a review of these concepts. Its purpose is to provide a guide of bibliographic references for these concepts, which are briefly discussed in this document

A Linguistic Multi-Criteria Decision Making Model Applied to the Integration of Education Questionnaires

We present a model made up of linguistic multi-criteria decision making processes to integrate the answers to heterogeneous questionnaires, based on a five-point Likert scale, into a unique form rooted in the widespread course experience questionnaire. The main advantage of having the resulting integrated questionnaire is that it can be incorporated into other course experience questionnaire surveys to make benchmarking among organizations. This model has been applied to integrate heterogeneous educational questionnaires at the University of Granada.European Union (EU) TIN2010-17876Andalusian Excellence Projects TIC-05299 TIC-599

Modelling Heterogeneity among Experts in Multi-criteria Group Decision Making Problems

Heterogeneity in group decision making problems has been recently studied in the literature. Some instances of these studies include the use of heterogeneous preference representation structures, heterogeneous preference representation domains and heterogeneous importance degrees. On this last heterogeneity level, the importance degrees are associated to the experts regardless of what is being assessed by them, and these degrees are fixed through the problem. However, there are some situations in which the experts’ importance degrees do not depend only on the expert. Sometimes we can find sets of heterogeneously specialized experts, that is, experts whose knowledge level is higher on some alternatives and criteria than it is on any others. Consequently, their importance degree should be established in accordance with what is being assessed. Thus, there is still a gap on heterogeneous group decision making frameworks to be studied. We propose a new fuzzy linguistic multi-criteria group decision making model which considers different importance degrees for each expert depending not only on the alternatives but also on the criterion which is taken into account to evaluate them.FUZZYLINGProject TIN200761079FUZZYLING-II Project TIN201017876PETRI Project PET20070460Andalusian Excellence Project TIC-05299project of Ministry of Public Works 90/0