Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral

TL;DR: This paper proposes the Choquet integral of measurable functions on the credibility space, bridging Choquet integral and credibility theory, and investigates its properties, including monotonicity and translatability, for nonnegative and symmetric functions.

TL;DR: The classical method named superiority and inferiority ranking (i.e. SIR) method is extended to solve the MAGDM problems in an IGL environment and the Gaussian criterion is employed to describe the DM’s preference structure.

TL;DR: Four broad approaches to dealing with external uncertainties are discussed, primarily in the context of pairwise comparisons of alternatives; stochastic dominance concepts; the use of surrogate risk measures as additional decision criteria; and the integration of MCDA and scenario planning.

TL;DR: This book develops an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions.

TL;DR: In this article, a confused decision maker, who wishes to make a reasonable and responsible choice among alternatives, can systematically probe his true feelings in order to make those critically important, vexing trade-offs between incommensurable objectives.

TL;DR: In this paper, an examination of elementary properties of a value for the essential case is presented, which is deduced from a set of three axioms, having simple intuitive interpretations.

Abstract: Many of the complex problems faced by decision makers involve multiple conflicting objectives. This book describes how a confused decision maker, who wishes to make a reasonable and responsible choice among alternatives, can systematically probe his true feelings in order to make those critically important, vexing trade-offs between incommensurable objectives. The theory is illustrated by many real concrete examples taken from a host of disciplinary settings. The standard approach in decision theory or decision analysis specifies a simplified single objective like monetary return to maximise. By generalising from the single objective case to the multiple objective case, this book considerably widens the range of applicability of decision analysis.