Data-informed fuzzy measures for fuzzy integration of intervals and fuzzy numbers

The fuzzy integral (FI) with respect to a fuzzy measure (FM) is a powerful means of aggregating information. The most popular FIs are the Choquet and Sugeno, and most research focuses on these two variants. The arena of the FM is much more populated, including numerically derived FMs such as the Sugeno λ-measure and decomposable measure, expert-defined FMs, and data-informed FMs. The drawback of numerically derived and expert-defined FMs is that one must know something about the relative values of the input sources. However, there are many problems where this information is unavailable, such as crowdsourcing. This paper focuses on data-informed FMs, or those FMs that are computed by an algorithm that analyzes some property of the input data itself, gleaning the importance of each input source by the data they provide. The original instantiation of a data-informed FM is the agreement FM, which assigns high confidence to combinations of sources that numerically agree with one another. This paper extends upon our previous work in datainformed FMs by proposing the uniqueness measure and additive measure of agreement for interval-valued evidence. We then extend data-informed FMs to fuzzy number (FN)-valued inputs. We demonstrate the proposed FMs by aggregating interval and FN evidence with the Choquet and Sugeno FIs for both synthetic and real-world data

A novel framework for predicting patients at risk of readmission

Uncertainty in decision-making for patients’ risk of re-admission arises due to non-uniform data and lack of knowledge in health system variables. The knowledge of the impact of risk factors will provide clinicians better decision-making and in reducing the number of patients admitted to the hospital. Traditional approaches are not capable to account for the uncertain nature of risk of hospital re-admissions. More problems arise due to large amount of uncertain information. Patients can be at high, medium or low risk of re-admission, and these strata have ill-defined boundaries. We believe that our model that adapts fuzzy regression method will start a novel approach to handle uncertain data, uncertain relationships between health system variables and the risk of re-admission. Because of nature of ill-defined boundaries of risk bands, this approach does allow the clinicians to target individuals at boundaries. Targeting individuals at boundaries and providing them proper care may provide some ability to move patients from high risk to low risk band. In developing this algorithm, we aimed to help potential users to assess the patients for various risk score thresholds and avoid readmission of high risk patients with proper interventions. A model for predicting patients at high risk of re-admission will enable interventions to be targeted before costs have been incurred and health status have deteriorated. A risk score cut off level would flag patients and result in net savings where intervention costs are much higher per patient. Preventing hospital re-admissions is important for patients, and our algorithm may also impact hospital income

Validation of Soft Classification Models using Partial Class Memberships: An Extended Concept of Sensitivity & Co. applied to the Grading of Astrocytoma Tissues

We use partial class memberships in soft classification to model uncertain labelling and mixtures of classes. Partial class memberships are not restricted to predictions, but may also occur in reference labels (ground truth, gold standard diagnosis) for training and validation data. Classifier performance is usually expressed as fractions of the confusion matrix, such as sensitivity, specificity, negative and positive predictive values. We extend this concept to soft classification and discuss the bias and variance properties of the extended performance measures. Ambiguity in reference labels translates to differences between best-case, expected and worst-case performance. We show a second set of measures comparing expected and ideal performance which is closely related to regression performance, namely the root mean squared error RMSE and the mean absolute error MAE. All calculations apply to classical crisp classification as well as to soft classification (partial class memberships and/or one-class classifiers). The proposed performance measures allow to test classifiers with actual borderline cases. In addition, hardening of e.g. posterior probabilities into class labels is not necessary, avoiding the corresponding information loss and increase in variance. We implement the proposed performance measures in the R package "softclassval", which is available from CRAN and at http://softclassval.r-forge.r-project.org. Our reasoning as well as the importance of partial memberships for chemometric classification is illustrated by a real-word application: astrocytoma brain tumor tissue grading (80 patients, 37000 spectra) for finding surgical excision borders. As borderline cases are the actual target of the analytical technique, samples which are diagnosed to be borderline cases must be included in the validation.Comment: The manuscript is accepted for publication in Chemometrics and Intelligent Laboratory Systems. Supplementary figures and tables are at the end of the pd

Interval-valued fuzzy decision trees with optimal neighbourhood perimeter

This research proposes a new model for constructing decision trees using interval-valued fuzzy membership values. Most existing fuzzy decision trees do not consider the uncertainty associated with their membership values, however, precise values of fuzzy membership values are not always possible. In this paper, we represent fuzzy membership values as intervals to model uncertainty and employ the look-ahead based fuzzy decision tree induction method to construct decision trees. We also investigate the significance of different neighbourhood values and define a new parameter insensitive to specific data sets using fuzzy sets. Some examples are provided to demonstrate the effectiveness of the approach

Extension of the fuzzy integral for general fuzzy set-valued information

The fuzzy integral (FI) is an extremely flexible aggregation operator. It is used in numerous applications, such as image processing, multicriteria decision making, skeletal age-at-death estimation, and multisource (e.g., feature, algorithm, sensor, and confidence) fusion. To date, a few works have appeared on the topic of generalizing Sugeno's original real-valued integrand and fuzzy measure (FM) for the case of higher order uncertain information (both integrand and measure). For the most part, these extensions are motivated by, and are consistent with, Zadeh's extension principle (EP). Namely, existing extensions focus on fuzzy number (FN), i.e., convex and normal fuzzy set- (FS) valued integrands. Herein, we put forth a new definition, called the generalized FI (gFI), and efficient algorithm for calculation for FS-valued integrands. In addition, we compare the gFI, numerically and theoretically, with our non-EP-based FI extension called the nondirect FI (NDFI). Examples are investigated in the areas of skeletal age-at-death estimation in forensic anthropology and multisource fusion. These applications help demonstrate the need and benefit of the proposed work. In particular, we show there is not one supreme technique. Instead, multiple extensions are of benefit in different contexts and applications

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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