Possibilistic preference networks

Abstract

This paper studies the use of product-based possibilistic networks for representing preferences in multidimensional decision problems. This approach uses symbolic possibility weights and defines a partial preference order among solutions to a set of conditional preference statements on the domains of discrete decision variables. In the case of Boolean decision variables, this partial ordering is shown to be consistent with the preference ordering induced by the ceteris paribus assumption adopted in CP-nets. Namely, by completng the possibilistic net ordering with suitable constraints between products of symbolic weights, all CP-net preferences can be recovered. Computing procedures for comparing solutions are provided. The flexibility and representational power of the approach is stressed.R Dedication : This paper is dedicated to Janusz Kacprzyk on the occasion of his jubilee. The second and the fourth author, who have a long and fruitful research companionship with him, are glad to offer him this new piece of work.

Handling qualitative conditional preferencequeries in SPARQL: Possibilistic logic approach

“…Recently, possibilistic logic become a known framework in preferences representation since it proposes a language that incorporates the priority levels in a natural way. Otherwise, in possibilistic logic, a variety of preference representation options are available [17,[22][23][24]. Preferences, in particular, can be represented as ranked constraints, which is a possibilistic formulas, or in conditional situation as statements of the form "if c is true then having p is preferred to having ¬p".…”

Possibility Theory and Possibilistic Logic: Tools for Reasoning Under and About Incomplete Information

“…Beyond PL, interpretations (corresponding to different alternatives) can be compared in terms of vectors acknowledging the satisfaction or the violation of the formulas associated with the different goals, using suitable order relations. Thus, partial orderings of interpretations can be obtained [13]. -Modeling desires: In contrast with static beliefs, (positive) desires are such that endorsing a ∨ b as a desire means to desire a and to desire b.…”

Representations of Uncertainty in Artificial Intelligence: Probability and Possibility

“…For an introduction to possibilistic networks and their algorithms, the reader is referred to Chapter 8 in Volume 2. Possibilistic networks are also useful for preference modeling [Ben Amor et al, 2017] (see also Chapter 7 in this volume).…”