Amel Ennaceur

Handling partial preferences in the belief AHP method: application to life cycle assessment

This paper proposes a novel multi-criteria decision making method under uncertainty that combines the Analytic Hierarchy Process (AHP) with the belief function theory. Our method, named belief AHP, allows the expert to express incomplete and imprecise information about groups of alternatives instead of single ones. On the other hand and in order to judge the importance of criteria, he can also present his opinions on groups of criteria. Then, the uncertainty will be taken into account in the final decision. Finally, another purpose of this paper is also to solve a real application problem which deals with the PVC life cycle assessment.

Multi-Criteria Decision Making Method with Belief Preference Relations

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.

Reasoning under Uncertainty in the AHP Method Using the Belief Function Theory

The Analytic Hierarchy Process (AHP) method was introduced to help the decision maker to express judgments on alternatives over a number of criteria. In this paper, our proposal extends the AHP method to an uncertain environment, where the uncertainty is represented through the Transferable Belief Model (TBM), one interpretation of the belief function theory. In fact, we suggest a novel framework that tackles the challenge of introducing uncertainty in both the criterion and the alternative levels, where the objective is to represent imperfection that may appear in the pair-wise comparisons and to model the relationship between these alternatives and criteria through conditional beliefs.

Modeling Qualitative Assessments under the Belief Function Framework

This paper investigates the problem of preference modeling under the belief function framework. In this work, we introduce a new model that is able to generate quantitative information from qualitative assessments. Therefore, we suggest to represent the decision maker preferences in different levels where the indifference, strict preference, weak preference and incompleteness relations are considered. Introducing the weak preference relation separates the preference area from the indifference one by inserting an intermediate zone.

Modeling expert preference using the qualitative belief function framework

This paper investigates the problem of preference modeling under multi-criteria decision making methods in which some assessments cannot be provided in the pair-wise comparison process. Therefore, we introduce a new method that will be able to elicitate preferences in an uncertain environment, where the expert may express incomplete and incomparable ones. Indeed, we suggest to transform these qualitative assessments into quantitative information based on belief function framework. Then, in order to illustrate our approach, we propose to compare our method to the existing approaches.

An Extension of the Analytic Hierarchy Process Method under the Belief Function Framework

In this paper, an extension of the belief Analytic Hierarchy Process (AHP) method is proposed, based on the belief function framework. It takes into account the fact that the pair-wise comparison between criteria and alternatives may be uncertain and imprecise. Therefore, it introduces a new way to cope with expert judgments. Thus to express his preferences, the decision maker is allowed to use a belief assessment instead of exact ratios. The proposed extension also models the relationship between the alternative and criterion levels through conditional beliefs. Numerical examples explain in detail and illustrate the proposed approach.

Belief AHP Method — AHP Method with the Belief Function Framework

In this paper, the analytic hierarchy process (AHP) method is extended to an uncertain environment where the uncertainty is represented by belief functions as interpreted in the transferable belief model (TBM). Our proposed approach, called belief AHP, is developed to help the decision maker to determine what the best alternatives are, considering multiple conflicting criteria where both alternatives and criteria may be soiled with imperfection. The Belief AHP method aims at comparing subsets of criteria and groups of alternatives in order to reduce the pair-wise comparisons number. Furthermore, to handle uncertainty that may appear in the comparison procedure, we use basic belief assignments (BBA) instead of exact ratios to elicitate expert preferences. Finally, to illustrate the feasibility of our approach and to judge its performances, we have applied our proposed method on a real application problem: we have considered the polyvinyl chloride (PVC) life cycle assessment especially the end of life phase.

Qualitative AHP models under the belief function framework

This paper investigates a multi-criteria decision making method in an uncertain environment, where the uncertainty is represented using the belief function framework. In this context, we suggest a novel methodology that tackles the challenge of introducing uncertainty in the expert evaluations. Therefore, the Analytic Hierarchy Process with qualitative belief function framework is adopted to get numeric representation of qualitative assessment. In this work, we will also focus on two AHP extensions under qualitative AHP. Besides, we intend to describe some comparisons on the standard AHP and the presented models to judge their accuracy. We use also a simulation approach to compare the results of the different models based on different matrices dimensions.

Multicriteria Decision Making Based on Qualitative Assessments and Relational Belief

This paper investigates a multi-criteria decision making met-hod in an uncertain environment, where the uncertainty is represented using the belief function framework. Indeed, we suggest a novel methodology that tackles the challenge of introducing uncertainty in both the criterion and the alternative levels. On the one hand and in order to judge the criteria weights, our proposed approach suggests to use preference relations to elicitate the decision maker assessments. Therefore, the Analytic Hierarchy Process with qualitative belief function framework is adopted to get adequate numeric representation. On the other hand, our model assumes that the evaluation of each alternative with respect to each criterion may be imperfect and it can be represented by a basic belief assignment. That is why, a new aggregation procedure that is able to rank alternatives is introduced.

Qualitative AHP Method Based on Multiple Criteria Levels Under Group of Experts

In this paper, we consider a multi-criteria group decision making problem. We propose a novel version of the Analytic Hierarchy Process under the belief function theory. The presented approach uses groups of experts to express their assessments regarding the evaluation criteria and the evaluation alternatives. It considers also more complex multi-criteria decision problems that have multiple criteria levels. The presented method is illustrated with some examples.