Fuzzy measures and integrals in MCDA

This chapter aims at a unified presentation of various methods of MCDA based onfuzzy measures (capacity) and fuzzy integrals, essentially the Choquet andSugeno integral. A first section sets the position of the problem ofmulticriteria decision making, and describes the various possible scales ofmeasurement (difference, ratio, and ordinal). Then a whole section is devotedto each case in detail: after introducing necessary concepts, the methodologyis described, and the problem of the practical identification of fuzzy measuresis given. The important concept of interaction between criteria, central inthis chapter, is explained in details. It is shown how it leads to k-additivefuzzy measures. The case of bipolar scales leads to thegeneral model based on bi-capacities, encompassing usual models based oncapacities. A general definition of interaction for bipolar scales isintroduced. The case of ordinal scales leads to the use of Sugeno integral, andits symmetrized version when one considers symmetric ordinal scales. Apractical methodology for the identification of fuzzy measures in this contextis given. Lastly, we give a short description of some practical applications.Choquet integral; fuzzy measure; interaction; bi-capacities

Axiomatizations of the Choquet integral on general decision spaces

PhDWe propose an axiomatization of the Choquet integral model for the general case of a heterogeneous product set X = X1 Xn. Previous characterizations of the Choquet integral have been given for the particular cases X = Y n and X = Rn. However, this makes the results inapplicable to problems in many fields of decision theory, such as multicriteria decision analysis (MCDA), state-dependent utility (SD-DUU), and social choice. For example, in multicriteria decision analysis the elements of X are interpreted as alternatives, characterized by criteria taking values from the sets Xi. Obviously, the identicalness or even commensurateness of criteria cannot be assumed a priori. Despite this theoretical gap, the Choquet integral model is quite popular in the MCDA community and is widely used in applied and theoretical works. In fact, the absence of a sufficiently general axiomatic treatment of the Choquet integral has been recognized several times in the decision-theoretic literature. In our work we aim to provide missing results { we construct the axiomatization based on a novel axiomatic system and study its uniqueness properties. Also, we extend our construction to various particular cases of the Choquet integral and analyse the constraints of the earlier characterizations. Finally, we discuss in detail the implications of our results for the applications of the Choquet integral as a model of decision making

Incomparability and incommensurability in choice : no common currency of value?

Models of decision-making typically assume the existence of some common currency of value, such as utility, happiness, or inclusive fitness. This common currency is taken to allow comparison of options and to underpin everyday choice. Here we suggest instead that there is no universal value scale, that incommensurable values pervade everyday choice, and hence that most existing models of decision-making in both economics and psychology are fundamentally limited. We propose that choice objects can be compared only with reference to specific but nonuniversal “covering values.” These covering values may reflect decision-makers’ goals, motivations, or current states. A complete model of choice must accommodate the range of possible covering values. We show that abandoning the common-currency assumption in models of judgment and decision-making necessitates rank-based and “simple heuristics” models that contrast radically with conventional utility-based approaches. We note that if there is no universal value scale, then Arrow’s impossibility theorem places severe bounds on the rationality of individual decision-making and hence that there is a deep link between the incommensurability of value, inconsistencies in human decision-making, and rank-based coding of value. More generally, incommensurability raises the question of whether it will ever be possible to develop single-quantity-maximizing models of decision-making

Prospect Theory and Choice Behaviour Strategies: Review and Synthesis of Concepts from Social and Transport sciences

Utility Theory is commonly considered as the most useful descriptive theory of human choice behaviour. Alternative concepts are only incidentally considered. This paper reviews alternative assumptions and empirical findings about human choice behaviour. To facilitate comparison and synthesis the review starts with the proposal of a generic framework of choice behaviour. The micro-economic assumptions of Utility Theory and Prospect Theory are then mapped onto this framework. These are compared with each other and other assumptions against the background of theoretical and empirical findings from behavioural economics, several other social disciplines and transport sciences. An extension of Prospect Theory with assumptions about the valuation of attributes and the employment of different decision rules yields a functional concept of choice behaviour that is able to describe most of the reviewed empirical findings to a larger extent than Utility Theory

The complementary use of IS technologies to support flexibility and integration needs in budgeting

In business controllers’ work on budgeting, considered as a classic decision-making process in organisations, it is consistently indicated that enterprise resource planning (ERP) systems, business intelligence (BI) and spreadsheets are commonly applied to assist the process. An academic research contribution on this topic is few. Most available research concentrates on ERP systems but it mentions neither BI nor spreadsheets. A further review of budgeting literature designates that budgeting characterises both flexibility and integration needs to accomplish decision-making. Given the limited understanding as to how IS technologies are used in budgeting, this dissertation aims to describe and explain how business controllers can complementarily use IS technologies to support the flexibility and integration needs in a budgeting process. Two research questions addressed are: RQ1- how do business controllers perceive IS technologies in relation to the need for both flexibility and integration in budgeting? And RQ2 - why do business controllers use IS technologies to support the need for both flexibility and integration in budgeting? The analysis employs conceptual ideas pertaining to structuration theory. Empirical data was collected through interviews, observations and documentations with twenty-six business controllers in sixteen companies in Thailand. It is concluded that business controllers perceive IS technologies to enable and constrain their flexibility and integration needs in budgeting. Spreadsheets are the main IS technology used in budgeting despite an existent of ERP systems and BI because of the flexibility that spreadsheets offer. Business controllers use spreadsheets to support both the flexibility and integration domains but they use ERP systems and BI to support the integration function alone. It is necessary for business controllers to rethink their IS technology use practice because spreadsheets cause errors and frauds. The insights generated create a framework to describe how the three IS technologies should be complementarily used to support specific budgeting activities in respect of the flexibility and integration needs

Learning nonlinear monotone classifiers using the Choquet Integral

In der jüngeren Vergangenheit hat das Lernen von Vorhersagemodellen, die eine monotone Beziehung zwischen Ein- und Ausgabevariablen garantieren, wachsende Aufmerksamkeit im Bereich des maschinellen Lernens erlangt. Besonders für flexible nichtlineare Modelle stellt die Gewährleistung der Monotonie eine große Herausforderung für die Umsetzung dar. Die vorgelegte Arbeit nutzt das Choquet Integral als mathematische Grundlage für die Entwicklung neuer Modelle für nichtlineare Klassifikationsaufgaben. Neben den bekannten Einsatzgebieten des Choquet-Integrals als flexible Aggregationsfunktion in multi-kriteriellen Entscheidungsverfahren, findet der Formalismus damit Eingang als wichtiges Werkzeug für Modelle des maschinellen Lernens. Neben dem Vorteil, Monotonie und Flexibilität auf elegante Weise mathematisch vereinbar zu machen, bietet das Choquet-Integral Möglichkeiten zur Quantifizierung von Wechselwirkungen zwischen Gruppen von Attributen der Eingabedaten, wodurch interpretierbare Modelle gewonnen werden können. In der Arbeit werden konkrete Methoden für das Lernen mit dem Choquet Integral entwickelt, welche zwei unterschiedliche Ansätze nutzen, die Maximum-Likelihood-Schätzung und die strukturelle Risikominimierung. Während der erste Ansatz zu einer Verallgemeinerung der logistischen Regression führt, wird der zweite mit Hilfe von Support-Vektor-Maschinen realisiert. In beiden Fällen wird das Lernproblem imWesentlichen auf die Parameter-Identifikation von Fuzzy-Maßen für das Choquet Integral zurückgeführt. Die exponentielle Anzahl von Freiheitsgraden zur Modellierung aller Attribut-Teilmengen stellt dabei besondere Herausforderungen im Hinblick auf Laufzeitkomplexität und Generalisierungsleistung. Vor deren Hintergrund werden die beiden Ansätze praktisch bewertet und auch theoretisch analysiert. Zudem werden auch geeignete Verfahren zur Komplexitätsreduktion und Modellregularisierung vorgeschlagen und untersucht. Die experimentellen Ergebnisse sind auch für anspruchsvolle Referenzprobleme im Vergleich mit aktuellen Verfahren sehr gut und heben die Nützlichkeit der Kombination aus Monotonie und Flexibilität des Choquet Integrals in verschiedenen Ansätzen des maschinellen Lernens hervor