Computational techniques for a simple theory of conditional preferences

Abstract

A simple logic of conditional preferences is defined, with a language that allows the compact representation of certain kinds of conditional preference statements, a semantics and a proof theory. CP-nets and TCP-nets can be mapped into this logic, and the semantics and proof theory generalise those of CP-nets and TCP-nets. The system can also express preferences of a lexicographic kind. The paper derives various sufficient conditions for a set of conditional preferences to be consistent, along with algorithmic techniques for checking such conditions and hence confirming consistency. These techniques can also be used for totally ordering outcomes in a way that is consistent with the set of preferences, and they are further developed to give an approach to the problem of constrained optimisation for conditional preferences

Pruning Rules for Constrained Optimisation for Conditional Preferences

“…In the constrained optimisation algorithms in [5,14,15] a search tree is used to find solutions of a CSP, where the search tree is chosen to be compatible with the cp-theory Γ , i.e., so that its associated total ordering on outcomes extends relations Γ and Γ (defined above in Sections 2.1 and 2.2, respectively). Methods for finding such search trees have been developed in [15], Sections 5 and 6.…”

“…The algorithm in [5], as well as related algorithms in [14,15], involve using appropriate variable and value orderings so that solutions are generated in an order compatible with the conditional preference statements. At each leaf node we check to see if the corresponding solution of the CSP is dominated by any of the optimal solutions found so far; if not, then we add this solution to the set of optimal solutions.…”

“…Conditional preference languages, such as CP-nets and more general formalisms [4,9,6,15,2], can give a natural way for the user of a decision support system to express their preferences over multivariate options. A basic problem is: given a set of outcomes, determine which are the undominated ones, i.e., which are not considered worse than another outcome.…”

Configuration of service oriented architectures with semantic technologies based on non-functional requirements

“…Лексикографски поредак је специјалан врста сортирања, која се често среће у литератури у различитим контекстима и значењима [113]. Она представља генерализацију алфабетског поретка међу речима над датим алфабетом, а може се интерпретирати као сортирање на основу односа вредности променљивих истог нивоа, без обзира на вредности променљивих нижег нивоа [113].…”

“…Она представља генерализацију алфабетског поретка међу речима над датим алфабетом, а може се интерпретирати као сортирање на основу односа вредности променљивих истог нивоа, без обзира на вредности променљивих нижег нивоа [113]. Оваква врста захтева има широку могућност примене у реалним проблемима и свакодневно се среће у животу.…”