5 research outputs found
Defuzzification of groups of fuzzy numbers using data envelopment analysis
Defuzzification is a critical process in the implementation of fuzzy systems that converts fuzzy numbers to crisp representations. Few researchers have focused on cases where the crisp outputs must satisfy a set of relationships dictated in the
original crisp data. This phenomenon indicates that these crisp outputs are mathematically dependent on one another. Furthermore, these fuzzy numbers may
exist as a group of fuzzy numbers. Therefore, the primary aim of this thesis is to develop a method to defuzzify groups of fuzzy numbers based on Charnes, Cooper, and Rhodes (CCR)-Data Envelopment Analysis (DEA) model by modifying the Center of Gravity (COG) method as the objective function. The constraints represent the relationships and some additional restrictions on the allowable crisp outputs with their dependency property. This leads to the creation of crisp values with preserved
relationships and/or properties as in the original crisp data. Comparing with Linear Programming (LP) based model, the proposed CCR-DEA model is more efficient, and also able to defuzzify non-linear fuzzy numbers with accurate solutions. Moreover, the crisp outputs obtained by the proposed method are the nearest points to the fuzzy numbers in case of crisp independent outputs, and best nearest points to the fuzzy numbers in case of dependent crisp outputs. As a conclusion, the proposed
CCR-DEA defuzzification method can create either dependent crisp outputs with preserved relationship or independent crisp outputs without any relationship. Besides, the proposed method is a general method to defuzzify groups or individuals
fuzzy numbers under the assumption of convexity with linear and non-linear membership functions or relationships
Robust ordinal regression in preference learning and ranking
Multiple Criteria Decision Aiding (MCDA) offers a diversity of approaches designed for providing the decision maker (DM) with a recommendation concerning a set of alternatives (items, actions) evaluated from multiple points of view, called criteria. This paper aims at drawing attention of the Machine Learning (ML) community upon recent advances in a representative MCDA methodology, called Robust Ordinal Regression (ROR). ROR learns by examples in order to rank a set of alternatives, thus considering a similar problem as Preference Learning (ML-PL) does. However, ROR implements the interactive preference construction paradigm, which should be perceived as a mutual learning of the model and the DM. The paper clarifies the specific interpretation of the concept of preference learning adopted in ROR and MCDA, comparing it to the usual concept of preference learning considered within ML. This comparison concerns a structure of the considered problem, types of admitted preference information, a character of the employed preference models, ways of exploiting them, and techniques to arrive at a final ranking
Mathematical programming models for classification problems with applications to credit scoring
Mathematical programming (MP) can be used for developing
classification models for the twoâgroup classification problem. An MP
model can be used to generate a discriminant function that separates the
observations in a training sample of known group membership into the
specified groups optimally in terms of a group separation criterion. The
simplest models for MP discriminant analysis are linear programming
models in which the group separation measure is generally based on the
deviations of misclassified observations from the discriminant function.
MP discriminant analysis models have been tested extensively over the
last 30 years in developing classifiers for the twoâgroup classification
problem. However, in the comparative studies that have included MP
models for classifier development, the MP discriminant analysis models
either lack appropriate normalisation constraints or they do not use the
proper data transformation. In addition, these studies have generally been
based on relatively small datasets. This thesis investigates the development
of MP discriminant analysis models that incorporate appropriate
normalisation constraints and data transformations. These MP models are
tested on binary classification problems, with an emphasis on credit scoring
problems, particularly application scoring, i.e. a twoâgroup classification
problem concerned with distinguishing between good and bad applicants for
credit based on information from application forms and other relevant data.
The performance of these MP models is compared with the performance of
statistical techniques and machine learning methods and it is shown that MP
discriminant analysis models can be useful tools for developing classifiers.
Another topic covered in this thesis is feature selection. In order to make
classification models easier to understand, it is desirable to develop
parsimonious classification models with a limited number of features.
Features should ideally be selected based on their impact on classification
accuracy. Although MP discriminant analysis models can be extended for
feature selection based on classification accuracy, there are computational
difficulties in applying these models to large datasets. A new MP heuristic
for selecting features is suggested based on a feature selection MP
discriminant analysis model in which maximisation of classification
accuracy is the objective. The results of the heuristic are promising in
comparison with other feature selection methods.
Classifiers should ideally be developed from datasets with
approximately the same number of observations in each class, but in practice
classifiers must often be developed from imbalanced datasets. New MP
formulations are proposed to overcome the difficulties associated with
generating discriminant functions from imbalanced datasets. These
formulations are tested using datasets from financial institutions and the
performance of the MP-generated classifiers is compared with classifiers
generated by other methods. Finally, the ordinal classification problem is
considered. MP methods for the ordinal classification problem are outlined
and a new MP formulation is tested on a small dataset