New Graphical Model for Computing Optimistic Decisions in Possibility Theory Framework

This paper first proposes a new graphical model for decision making under uncertainty based on min-based possibilistic networks. A decision problem under uncertainty is described by means of two distinct min-based possibilistic networks: the first one expresses agent's knowledge while the second one encodes agent's preferences representing a qualitative utility. We then propose an efficient algorithm for computing optimistic optimal decisions using our new model for representing possibilistic decision making under uncertainty. We show that the computation of optimal decisions comes down to compute a normalization degree of the junction tree associated with the graph resulting from the fusion of agent's beliefs and preferences. This paper also proposes an alternative way for computing optimal optimistic decisions. The idea is to transform the two possibilistic networks into two equivalent possibilistic logic knowledge bases, one representing agent's knowledge and the other represents agent's preferences. We show that computing an optimal optimistic decision comes down to compute the inconsistency degree of the union of the two possibilistic bases augmented with a given decision

The PITA System: Tabling and Answer Subsumption for Reasoning under Uncertainty

Many real world domains require the representation of a measure of uncertainty. The most common such representation is probability, and the combination of probability with logic programs has given rise to the field of Probabilistic Logic Programming (PLP), leading to languages such as the Independent Choice Logic, Logic Programs with Annotated Disjunctions (LPADs), Problog, PRISM and others. These languages share a similar distribution semantics, and methods have been devised to translate programs between these languages. The complexity of computing the probability of queries to these general PLP programs is very high due to the need to combine the probabilities of explanations that may not be exclusive. As one alternative, the PRISM system reduces the complexity of query answering by restricting the form of programs it can evaluate. As an entirely different alternative, Possibilistic Logic Programs adopt a simpler metric of uncertainty than probability. Each of these approaches -- general PLP, restricted PLP, and Possibilistic Logic Programming -- can be useful in different domains depending on the form of uncertainty to be represented, on the form of programs needed to model problems, and on the scale of the problems to be solved. In this paper, we show how the PITA system, which originally supported the general PLP language of LPADs, can also efficiently support restricted PLP and Possibilistic Logic Programs. PITA relies on tabling with answer subsumption and consists of a transformation along with an API for library functions that interface with answer subsumption

Weighted logics for artificial intelligence : an introductory discussion

International audienceBefore presenting the contents of the special issue, we propose a structured introductory overview of a landscape of the weighted logics (in a general sense) that can be found in the Artificial Intelligence literature, highlighting their fundamental differences and their application areas

Possibilistic decision theory: from theoretical foundations to influence diagrams methodology

Le domaine de prise de décision est un domaine multidisciplinaire en relation avec plusieurs disciplines telles que l'économie, la recherche opérationnelle, etc. La théorie de l'utilité espérée a été proposée pour modéliser et résoudre les problèmes de décision. Ces théories ont été mises en cause par plusieurs paradoxes (Allais, Ellsberg) qui ont montré les limites de son applicabilité. Par ailleurs, le cadre probabiliste utilisé dans ces théories s'avère non approprié dans certaines situations particulières (ignorance totale, incertitude qualitative). Pour pallier ces limites, plusieurs travaux ont été élaborés concernant l'utilisation des intégrales de Choquet et de Sugeno comme critères de décision d'une part et l'utilisation d'une théorie d'incertitude autre que la théorie des probabilités pour la modélisation de l'incertitude d'une autre part. Notre idée principale est de profiter de ces deux directions de recherche afin de développer, dans le cadre de la décision séquentielle, des modèles de décision qui se basent sur les intégrales de Choquet comme critères de décision et sur la théorie des possibilités pour la représentation de l'incertitude. Notre objectif est de développer des modèles graphiques décisionnels, qui représentent des modèles compacts et simples pour la prise de décision dans un contexte possibiliste. Nous nous intéressons en particulier aux arbres de décision et aux diagrammes d'influence possibilistes et à leurs algorithmes d'évaluation.The field of decision making is a multidisciplinary field in relation with several disciplines such as economics, operations research, etc. Theory of expected utility has been proposed to model and solve decision problems. These theories have been questioned by several paradoxes (Allais, Ellsberg) who have shown the limits of its applicability. Moreover, the probabilistic framework used in these theories is not appropriate in particular situations (total ignorance, qualitative uncertainty). To overcome these limitations, several studies have been developed basing on the use of Choquet and Sugeno integrals as decision criteria and a non classical theory to model uncertainty. Our main idea is to use these two lines of research to develop, within the framework of sequential decision making, decision models based on Choquet integrals as decision criteria and possibility theory to represent uncertainty. Our goal is to develop graphical decision models that represent compact models for decision making when uncertainty is represented using possibility theory. We are particularly interested by possibilistic decision trees and influence diagrams and their evaluation algorithms

A Web Based Optimization System Using Goal Programming for Supply Chain Network

Considering high competitive nature of todays industries,being on plan is very vital for supply chain network of an organization. Allthe flows of materials from initial suppliers to final customers need to besmooth. Hence, distribution network design is an important strategic decisionproblem for the supply chain managers. The aim of this research is to propose a web-based Decision Support System (DSS) foroptimizing fuzzy distribution network in the context of supply-chain management. A fuzzy goal-programming model has been designedfor the proposed DSS to consider the uncertain and imprecise data. Thisresearch focuses on four conflict fuzzy goals of (i). all demands must be covered by distribution center, (ii).investment goals for opening new sites considering fix costs, (iii). Investmentgoals for opening new distribution centers considering fix costs, (iv). Supplycosts goals, to meet the optimized results. Hence with those attributes ofmembership function of goals, the decision makers can apply this model toobtain the investment policy and the achieved level of each individual goal

Possibilistic sequential decision making

International audienceWhen the information about uncertainty cannot be quantified in a simple, probabilistic way, the topic of possibilistic decision theory is often a natural one to consider. The development of possibilistic decision theory has lead to the proposition a series of possibilistic criteria, namely: optimistic and pessimistic possibilistic qualitative criteria [7], possibilistic likely dominance [2] and [9], binary possibilistic utility [11] and possibilistic Choquet integrals [24]. This paper focuses on sequential decision making in possibilistic decision trees. It proposes a theoretical study on the complexity of the problem of finding an optimal strategy depending on the monotonicity property of the optimization criteria – when the criterion is transitive, this property indeed allows a polytime solving of the problem by Dynamic Programming. We show that most possibilistic decision criteria, but possibilistic Choquet integrals, satisfy monotonicity and that the corresponding optimization problems can be solved in polynomial time by Dynamic Programming. Concerning the possibilistic likely dominance criteria which is quasi-transitive but not fully transitive, we propose an extended version of Dynamic Programming which remains polynomial in the size of the decision tree. We also show that for the particular case of possibilistic Choquet integrals, the problem of finding an optimal strategy is NP-hard. It can be solved by a Branch and Bound algorithm. Experiments show that even not necessarily optimal, the strategies built by Dynamic Programming are generally very good