Constructing the FEEM sustainability index: A Choquet integral application
نویسندگان
چکیده
منابع مشابه
Extending the Choquet integral
In decision under uncertainty, the Choquet integral yields the expectation of a random variable with respect to a fuzzy measure (or non-additive probability or capacity). In general, for the discrete setting, this technique allows to integrate functions taking values on a finite n-set with respect to a (fuzzy) measure taking values on subsets of such a set. Yet, the integrand may well be treate...
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In this paper, we introduce the Choquet integral as a general tool for dealing with multiple criteria decision making. After a theoretical exposition giving the fundamental basis of the methodology, practical problems are addressed, in particular the problem of determining the fuzzy measure. We give an example of application, with two different approaches, together with their comparison.
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We consider a collection F of subsets of a finite set N together with a capacity v : F → R+ and call a function f : N → R measurable if its level sets belong to F . Only in this case, the classical definition of the Choquet integral works in our wider context. In this article, we provide a general framework for a Choquet integral that works also for non-measurable functions f and includes the i...
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Cumulative Prospect Theory of Tversky and Kahneman (1992) is the modern version of Prospect Theory (Kahneman and Tversky (1979)) and is nowadays considered a valid alternative to the classical Expected Utility Theory. Cumulative Prospect theory implies Gain-Loss Separability, i.e. the separate evaluation of losses and gains within a mixed gamble. Recently, some authors have questioned this assu...
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We show that the Choquet integral is the unique linear interpolator between vertices of the [0, 1] hypercube, using the least possible number of vertices. Related results by Lovász and Singer are discussed, as well as other interpolations. We show that the Choquet integral for bi-capacities can be also casted into this framework. Lastly, we discuss the case of Sugeno integral.
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ژورنال
عنوان ژورنال: Ecological Indicators
سال: 2014
ISSN: 1470-160X
DOI: 10.1016/j.ecolind.2013.12.012