An Approach for Modelling Preferences of Multiple Decision Makers (original) (raw)

A generic framework to include belief functions in preference handling and multi-criteria decision

International Journal of Approximate Reasoning, 2018

Modelling the preferences of a decision maker about alternatives having multiple criteria usually starts by collecting preference information (comparisons of alternatives, importance of criteria,. . .), which are then used to fit a preference model issued from some set of hypothesis (weighted average, CP-net, lexicographic orderings,. . .). In practice, this process may often lead to inconsistencies that may be due to inaccurate information provided by the decision maker, who can be unsure about the provided information, or to a poor choice of hypothesis set, which can be too restrictive or not well adapted to the decision process. In this paper, we propose to use belief functions as a way to quantify and resolve such inconsistencies, notably by allowing the decision maker to express her/his certainty about the provided preferential information. Our framework is generic, in the sense that it does not assume a given set of hypothesis a priori, and is consistent with precise methods, in the sense that in the absence of uncertainty and inconsistencies in the information, precise models are ultimately retrieved.

The Dempster–Shafer theory of evidence: an alternative approach to multicriteria decision modelling

Omega-international Journal of Management Science, 2000

The objective of this paper is to describe the potential oered by the Dempster±Shafer theory (DST) of evidence as a promising improvement on``traditional'' approaches to decision analysis. Dempster±Shafer techniques originated in the work of Dempster on the use of probabilities with upper and lower bounds. They have subsequently been popularised in the literature on Arti®cial Intelligence (AI) and Expert Systems, with particular emphasis placed on combining evidence from dierent sources. In the paper we introduce the basic concepts of the DST of evidence, brie¯y mentioning its origins and comparisons with the more traditional Bayesian theory. Following this we discuss recent developments of this theory including analytical and application areas of interest. Finally we discuss developments via the use of an example incorporating DST with the Analytic Hierarchy Process (AHP). #

Modelling dependent uncertainties in Stochastic Multicriteria Acceptability Analysis

2002

We consider multicriteria decision-making (MCDM) problems with multiple decision makers. In such problems, the uncertainty or inaccuracy of the criteria measurements can be represented as probability distributions. In many real-life problems the uncertainties may be dependent. However, it is often difficult to quantify these dependencies. Also most of the existing MCDM methods are unable to handle such dependency information. In

Multi-Criteria Decision Making Method with Belief Preference Relations

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2014

In modeling Multi-Criteria Decision Making (MCDM) problem, we usually assume that the decision maker is able to elicitate his preferences with precision and without difficulty. However, in many situations, the expert is unable to provide his assessment with certainty or he is unwilling to quantify his preferences. To deal with such situations, a new MCDM model under uncertainty is introduced. In fact, we focus here on the problem of modeling expert opinions despite the presence of incompleteness and uncertainty in their preference assessments. Besides, our proposed solution suggests to model these preferences qualitatively rather than exact numbers. Therefore, we propose to incorporate belief preference relations into a MCDM method. The expert assessments are then formulated as a belief function problem since this theory is considered as a useful tool to model expert judgments.

Implementing stochastic multicriteria acceptability analysis

European Journal of Operational Research, 2007

Stochastic multicriteria acceptability analysis (SMAA) is a family of methods for aiding multicriteria group decision making in problems with inaccurate, uncertain, or missing information. These methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one, or that would give a certain rank for a specific alternative. The main results of the analysis are rank acceptability indices, central weight vectors and confidence factors for different alternatives. The rank acceptability indices describe the variety of different preferences resulting in a certain rank for an alternative, the central weight vectors represent the typical preferences favouring each alternative, and the confidence factors measure whether the criteria measurements are sufficiently accurate for making an informed decision.

COMPUTATIONAL METHODS FOR STOCHASTIC MULTICRITERIA ACCEPTABILITY ANALYSIS

2004

Stochastic multicriteria acceptability analysis (SMAA) is a family of methods for aiding multicriteria group decision making in problems with inaccurate, uncertain, or missing information. These methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one, or that would give a certain rank for a specic alternative. The main

Ordinal criteria in stochastic multicriteria acceptability analysis (SMAA)

European Journal of Operational Research, 2003

We suggest a method for providing descriptive information about the acceptability of decision alternatives in discrete co-operative group decision-making problems. The new SMAA-O method is a variant of the stochastic multicriteria acceptability analysis (SMAA). SMAA-O is designed for problems where criteria information for some or all criteria is ordinal; that is, experts (or decision-makers) have ranked the alternatives according to each (ordinal) criterion. Considerable savings can be obtained if rank information for some or all the criteria is sufficient for making decisions without significant loss of quality. The approach is particularly useful for group decision making when the group can agree on the use of an additive decision model but only partial preference information, or none at all, is available.

Dempster–Shafer belief structures for decision making under uncertainty

Knowledge-Based Systems, 2015

We discuss the need for tools for representing various types of uncertain information in decision-making. We introduce the Dempster-Shafer belief structure and discuss how it provides a formal mathematical framework for representing various types of uncertain information. We provide some fundamental ideas and mechanisms related to these structures. We then investigate their role in the important task of decision-making under uncertainty.

Evidential Group Decision Making Model with Belief-Based Preferences

2018

In a large number of problems such as product configuration, automated recommendation and combinatorial auctions, decisions stem from agents subjective preferences and requirements in the presence of uncertainty. In this paper, we introduce a framework based on the belief function theory to deal with problems in group decision settings where the preferences of the agents may be uncertain, imprecise, incomplete, conflicting and possibly distorted. A case study is conducted on product recommendation to illustrate the applicability and validity of the proposed framework.