A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid

The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a better interpretation of the models and a better use of the Choquet integral in multi-criteria decision aid. Parallel to these theoretical works, the Choquet integral has been applied to many new fields, and several softwares and libraries dedicated to this model have been developed.Choquet integral, Sugeno integral, capacity, bipolarity, preferences

Managing Interacting Criteria: Application to Environmental Evaluation Practices

The need for organizations to evaluate their environmental practices has been recently increasing. This fact has led to the development of many approaches to appraise such practices. In this paper, a novel decision model to evaluate company’s environmental practices is proposed to improve traditional evaluation process in different facets. Firstly, different reviewers’ collectives related to the company’s activity are taken into account in the process to increase company internal efficiency and external legitimacy. Secondly, following the standard ISO 14031, two general categories of environmental performance indicators, management and operational, are considered. Thirdly, since the assumption of independence among environmental indicators is rarely verified in environmental context, an aggregation operator to bear in mind the relationship among such indicators in the evaluation results is proposed. Finally, this new model integrates quantitative and qualitative information with different scales using a multi-granular linguistic model that allows to adapt diverse evaluation scales according to appraisers’ knowledge

A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package

The application of multi-attribute utility theory whose aggregation process is based on the Choquet integral requires the prior identification of a capacity. The main approaches to capacity identification proposed in the literature are reviewed and their advantages and inconveniences are discussed. All the reviewed methods have been implemented within the Kappalab R package. Their application is illustrated on a detailed example.Multi-criteria decision aiding; Multi-attribute utility theory; Choquet integral; Free software

Decision theory under uncertainty

We review recent advances in the field of decision making under uncertainty or ambiguity.Ambiguity ; ambiguity aversion ; uncertainty ; decision

Enhancing strategic management using a quantified VRIO: Adding value with the MCDA approach

The field of strategic management has been popularized since the 1960s, as an aid for the search of success factors amongst the internal and external surroundings of an organization. Strategic management has observed and created strategies that are considered as pillars in the present way of applying contemporary management operations. Even though strategic management relies on managers’ capability to comprehend the current economic trends, this area has left a variety of questions unanswered, especially regarding the analyses of the combination of quantitative and qualitative decision criteria. This dissertation aims to enhance strategic management by developing a quantified valuable, rare, inimitable and organized (VRIO) framework, with the aid of the multiple criteria decision analysis (MCDA) approach. To accomplish this objective, the VRIO framework is combined with the Choquet integral (CI) and a real-life application is carried out to support strategic management. The dual methodology used in this dissertation offers an innovative process for business improvement. The benefits and limitations are also presented and discussed

Objective Imprecise Probabilistic Information, Second Order Beliefs and Ambiguity Aversion: an Axiomatization

We axiomatize a model of decision under objective ambiguity or imprecise risk. The decision maker forms a subjective (non necessarily additive) belief aboutthe likelihood of probability distributions and computes the average expected utility of a given act with respect to this second order belief. We show that ambiguity aversion like the one revealed by the Ellsberg paradox requires that second order beliefs be nonadditive. Somespecial cases of the model are examined and different forms of ambiguity aversion are characterized.Imprecise probabilistic information, second order beliefs, non-additive probabilities, ambiguity aversion, Ellsberg paradox, Choquet integral

Robust competence assessment for job assignment

International audienceAllocating the right person to a task or job is a key issue for improving quality and performance of achievements, usually addressed using the concept of "competences". Nevertheless, providing an accurate assessment of the competences of an individual may be in practice a difficult task. We suggest in this paper to model the uncertainty on the competences possessed by a person using a possibility distribution, and the imprecision on the competences required for a task using a fuzzy constraint, taking into account the possible interactions between competences using a Choquet Integral. As a difference with comparable approaches, we then suggest to perform the allocation of persons to jobs using a Robust Optimisation approach, allowing to minimize the risk taken by the decision maker. We first apply this framework to the problem of selecting a candidate within n for a job, then extend the method to the problem of selecting c candidates for j jobs (c ≥ j) using the leximin criterion

RISK PRIORITY EVALUATION OF POWER TRANSFORMER PARTS BASED ON HYBRID FMEA FRAMEWORK UNDER HESITANT FUZZY ENVIRONMENT

The power transformer is one of the most critical facilities in the power system, and its running status directly impacts the power system's security. It is essential to research the risk priority evaluation of the power transformer parts. Failure mode and effects analysis (FMEA) is a methodology for analyzing the potential failure modes (FMs) within a system in various industrial devices. This study puts forward a hybrid FMEA framework integrating novel hesitant fuzzy aggregation tools and CRITIC (Criteria Importance Through Inter-criteria Correlation) method. In this framework, the hesitant fuzzy sets (HFSs) are used to depict the uncertainty in risk evaluation. Then, an improved HFWA (hesitant fuzzy weighted averaging) operator is adopted to fuse risk evaluation for FMEA experts. This aggregation manner can consider different lengths of HFSs and the support degrees among the FMEA experts. Next, the novel HFWGA (hesitant fuzzy weighted geometric averaging) operator with CRITIC weights is developed to determine the risk priority of each FM. This method can satisfy the multiplicative characteristic of the RPN (risk priority number) method of the conventional FMEA model and reflect the correlations between risk indicators. Finally, a real example of the risk priority evaluation of power transformer parts is given to show the applicability and feasibility of the proposed hybrid FMEA framework. Comparison and sensitivity studies are also offered to verify the effectiveness of the improved risk assessment approach

CAPACITIES AND PROBABILISTIC BELIEFS: A PRECARIOUS COEXISTENCE

This paper raises the problem of how to define revealed probabilistic beliefs in the context of the capacity/Choquet Expected Utility model. At the center of the analysis is a decision-theoretically axiomatized definition of ""revealed unambiguous events."" The definition is shown to impose surprisingly strong restrictions on the underlying capacity and on the set of unambiguous events; in particular, the latter is always an algebra. Alternative weaker definitions violate even minimal criteria of adequacy. Rather than finding fault with the proposed definition, we argue that our results indicate that the CEU model is epistemically restrictive, and point out that analogous problems do not arise within the Maximin Expected Utility model.