Non-monotonic fuzzy measures and the Choquet integral

Murofushi, Toshiaki; Sugeno, Michio; Machida, Motoya

doi:10.1016/0165-0114(94)90008-6

Cited by 194 publications

(77 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Yan, Wang and Chen [55] tackle a quite similar problem, albeit using another optimization criterion (which can be seen as a kind of relaxed class separability criterion). Besides, the authors define the Choquet integral based on a so-called signed non-additive measure [41].…”

Section: The Choquet Integral In Machine Learningmentioning

confidence: 99%

Preference Learning Using the Choquet Integral: The Case of Multipartite Ranking

Tehrani

Cheng

Hüllermeier

2012

IEEE Trans. Fuzzy Syst.

View full text Add to dashboard Cite

We propose a novel method for preference learning or, more specifically, learning to rank, where the task is to learn a ranking model that takes a subset of alternatives as input and produces a ranking of these alternatives as output. Just like in the case of conventional classifier learning, training information is provided in the form of a set of labeled instances, with labels or, say, preference degrees taken from an ordered categorical scale. This setting is known as multipartite ranking in the literature. Our approach is based on the idea of using the (discrete) Choquet integral as an underlying model for representing ranking functions. Being an established aggregation function in fields such as multiple criteria decision making and information fusion, the Choquet integral offers a number of interesting properties that make it attractive from a machine learning perspective, too. The learning problem itself comes down to properly specifying the fuzzy measure on which the Choquet integral is defined. This problem is formalized as a margin maximization problem and solved by means of a cutting plane algorithm. The performance of our method is tested on a number of benchmark datasets.

show abstract

Section: The Choquet Integral In Machine Learningmentioning

confidence: 99%

Preference Learning Using the Choquet Integral: The Case of Multipartite Ranking

Tehrani

Cheng

Hüllermeier

2012

IEEE Trans. Fuzzy Syst.

View full text Add to dashboard Cite

show abstract

“…The monotonicity and non-negativity of the fuzzy measure are too restrictive to apply for more problems. Thus, the signed fuzzy measure, which is a generalization of the fuzzy measure, has been defined (Murofushi et al, 1994;Grabisch et al, 2000) and adopted.…”

Section: Fuzzy Measurementioning

confidence: 99%

A fuzzy intelligent system for land consolidation – a case study in Shunde, China

Wang

et al. 2015

Solid Earth

View full text Add to dashboard Cite

Abstract. Traditionally, potential evaluation methods for farmland consolidation have depended mainly on the experts' experiences, statistical computations or subjective adjustments. Some biases usually exist in the results. Thus, computer-aided technology has become essential. In this study, an intelligent evaluation system based on a fuzzy decision tree was established, and this system can deal with numerical data, discrete data and symbolic data. When the original land data are input, the level of potential of the agricultural land for development will be output by this new model. The provision of objective proof for decision-making by authorities in rural management is helpful. Agricultural land data characteristically comprise large volumes, complex varieties and more indexes. In land consolidation, it is very important to construct an effective index system. A group of indexes need to be selected for land consolidation. In this article, a fuzzy measure was adopted to accomplish the selection of specific features. A fuzzy integral based on a fuzzy measure is a type of fusion tool. The optimal solution with the fewest non-zero elements was obtained for the fuzzy measure by solving a fuzzy integral. This algorithm provides a quick and optimal way to identify the land-index system when preparing to conduct land consolidation. This new research was applied to Shunde's "Three Old" consolidation project which provides the data. Our estimation system was compared with a conventional evaluation system that is still accepted by the public. Our results prove to be consistent, and the new model is more automatic and intelligent. The results of this estimation system are significant for informing decision-making in land consolidation.

show abstract

“…The aggregated Sustainability Index is constructed through a non-linear aggregation methodology, the Choquet integral, which accounts for the possible interactions among sustainability indicators (see Murofushi and Soneda 1993;Murofushi et al 1994;Grabisch 1995Grabisch , 1996Marichal and Roubens 2000;Grabisch et al 2003 for the detailed Choquet integral aggregation procedure and its characteristics). 5 For the aggregation, the decision tree should be read from bottom (leaves) to top (final node) and the tree respects the three main pillar structure which is quite standard in most sustainability studies (see e.g., UN CSD 2005; Global Reporting Initiative framework, GRI 2006GRI , 2010Krajnc and Glavic 2005), with the final node producing the aggregate index.…”

Section: Normalisation and Aggregation Proceduresmentioning

confidence: 99%

The FEEM Sustainability Index: An Integrated Tool for Sustainability Assessment

Carraro

Campagnolo

Eboli

et al. 2013

Sustainability Appraisal: Quantitative Methods and Mathematical Techniques for Environmental Performance Evaluation

View full text Add to dashboard Cite

The FEEM Sustainability Index (FEEM SI) proposes an integrated methodological approach to quantitatively assess sustainability performance across countries and over time. Three are the main features of this approach: (1) the index considers sustainability based on economic, environmental and social indicators simultaneously; (2) the framework used to compute the indicators, i.e. a Computable General Equilibrium (CGE) model, allows to generate projections on the future evolution of sustainability; and (3) the methodology used for the normalisation and aggregation of the indicators delivers a unique and comprehensive measure of sustainability. These features along with the multi-regional nature of the CGE model consent to perform policy evaluations and sustainability assessments for different countries or regions in the world. This chapter offers a methodological overview of the FEEM SI approach. To illustrate the potential of the methodology for the measurement of sustainability, the chapter also illustrates results from a climate policy scenario. In the mitigation scenario considered Annex I and Non-Annex I countries taking action towards climate change achieve the lower end of the pledges proposed at the 15th UNFCCC Conference of the Parties in Copenhagen. For countries putting into practice the policy, the environmental sphere more than offsets the related costs (economic pillar), leading to an overall improvement in sustainability. At world level, the outcome is positive even though carbon leakage in countries that are not acting reduces the effectiveness of the policy and the sustainability performance.

show abstract

Non-monotonic fuzzy measures and the Choquet integral

Cited by 194 publications

References 6 publications

Preference Learning Using the Choquet Integral: The Case of Multipartite Ranking

Preference Learning Using the Choquet Integral: The Case of Multipartite Ranking

A fuzzy intelligent system for land consolidation – a case study in Shunde, China

The FEEM Sustainability Index: An Integrated Tool for Sustainability Assessment

Contact Info

Product

Resources

About