B. S. U. Mendis

Generalised Weighted Relevance Aggregation Operators for Hierarchical Fuzzy Signatures

Hierarchical Fuzzy Signatures are generalizations of the Vector Valued Fuzzy Set concept introduced in the 1970s. A crucial question in the Fuzzy Signature context is what kinds of aggregations are applicable for combining data with partly different substructures. Our earlier work introduced the Weighted Relevance Aggregation method to enhance the accuracy of the final results of calculations based on Hierarchical Fuzzy Signature Structures. In this paper, we further generalise the weights and the aggregation into a new operator called Weighted Relevance Aggregation Operator (WRAO). WRAO enhances the adaptability of the fuzzy signature model to different applications and simplifies the learning of fuzzy signature models from data. We also show the methodology of learning these aggregation operators from data.

Learning Generalized Weighted Relevance Aggregation Operators Using Levenberg-Marquardt Method

We previously introduced the generalized Weighted Relevance Aggregation Operators (WRAO) for hierarchical fuzzy signatures. WRAO enhances the ability of the fuzzy signature model to adapt to different applications and simplifies the learning of fuzzy signature models from data. In this paper we overcome the practical issues which occur when learning WRAO from data. This paper discuss an algorithm for learning WRAO using the Levenberg- Marquardt (LM) method, which is one of the most sophisticated and widely used gradient based optimization method. Also, this paper shows the successful results of applying the proposed algorithm to extract WRAO for two real world problems namely High Salary Selection and SARS Patient Classification.

On The Issue of Learning Weights from Observations for Fuzzy Signatures

We investigate the issue of obtaining weights, which are associated with aggregation in fuzzy signatures, from real world data. Our approach will provide a way to extract the relevance of lower levels to the higher levels of the hierarchical fuzzy signature structure. We also handle the non-differentiability of max-min aggregation functions for gradient based learning. A mathematically proved method, which is found in the literature to approximate the derivatives of max-min functions, has been used.

A comparison: Fuzzy signatures and Choquet Integral

Fuzzy signatures are hierarchical multi aggregative descriptors of objects. They have reduced computational complexity compared to formal fuzzy rule based systems. Weighted relevance aggregation enhances the performance of hierarchical fuzzy signatures. Thus, they are very robust and flexible under perturbed input data. On the other hand the Choquet integral, which is based on fuzzy measures, is a powerful aggregation tool in multi-criteria decision making. We compared fuzzy signatures and the Choquet integral as practical applications for hierarchical and non-hierarchical data aggregation/organization methods.

Complex Structured Decision Making Model: A hierarchical frame work for complex structured data

We introduce a hierarchical framework we call Complex Structured Decision Making model for complexly structured knowledge representation in intelligent decision making. We show that our model extends non-hierarchical (flat) decision making models to hierarchical decision making models that are similar to comprehensible human decision making processes. Further, we make an argument that hierarchial representation of knowledge in a Complex Structured Decision Making Model simplifies the approximation of aggregation functions to easily adapt to the underline relation of the system. Additionally, using a real world complex structured data set, we show that hierarchically organized Fuzzy Integrals, e.g. Choquet Integral, and Sugeno Integral and Fuzzy Signatures outperform these non-hierarchical Fuzzy Integrals.

Polymorphic fuzzy signatures

The fuzzy signature [1], [2] approach is aimed at finding a hierarchically decomposed solutions by adding new elements to Zadehs approach [3]. It tackles the problem by splitting the problem into hierarchically organized local sub-models and by applying more complex and heterogenous descriptors, more fit for the identification of extremely complex models. However, the computational time complexity still affects the fuzzy signatures as we were attempt to create an atomic fuzzy signature for each data point we get. Importantly, the atomic fuzzy signatures we store has properties we can make use of to make search over this structure computationally efficient. In this paper we introduce a new approach that uses the metadata about a set of fuzzy signatures to extract a Polymorphic Fuzzy Signature. Productively, a polymorphic fuzzy signature represents its base set of fuzzy signatures in a higher meta level which also allows search/inference, and so can reduce the computational time complexity of the inference process.

Finding input sub-spaces for Polymorphic Fuzzy Signatures

A significant feature of fuzzy signatures is its applicability for complex and sparse data. To create Polymorphic Fuzzy Signatures (PFS) for sparse data, sparse input sub-spaces (ISSs) should be considered. Finding the optimal ISSs manually is not a simple task as it is time consuming; moreover, some knowledge about the dataset is necessary. Fuzzy C-Means (FCM) clustering employed with a trapezoidal approximation method is needed to find ISSs automatically. Furthermore, dealing with sparse data, we should be mindful about choosing a reliable trapezoidal approximation method. This facilitates the optimal ISS creation for the data. In our experiment, two trapezoidal approximation methods were used to find optimal ISSs. The results demonstrate that our version of trapezoidal approximation for creating ISSs result in an PFS with lower mean square error compared to the original trapezoidal approximation method.

WRAO and OWA learning using Levenberg–Marquardt and genetic algorithms

The generalized Weighted Relevance Aggregation Operator (WRAO) is a non-additive aggregation function. The Ordered Weighted Aggregation Operator (OWA) (or its generalized form: Generalized Ordered Weighted Aggregation Operator (GOWA)) is more restricted with the additivity constraint in its weights. In addition, it has an extra weights reordering step making it hard to learn automatically from data. Our intension here is to compare the efficiency (or effectiveness) of learning these two types of aggregation functions from empirical data. We employed two methods to learn WRAO and GOWA: Levenberg–Marquardt (LM) and a Genetic Algorithm (GA) based method. We use UCI (University of California Irvine) benchmark data to compare the aggregation performance of non-additive WRAO and additive GOWA. We found that the non-constrained aggregation function WRAO was learnt well automatically and produced consistent results, while GOWA was learnt less well and quite inconsistently.

Improvements in Sugeno-Yasukawa modelling algorithm

A modified version of Sugeno-Yasukawa (SY) modelling algorithm is presented. We have employed a new method for parameter identification phase based on genetic algorithms (GA). Moreover, we have modified the modelling sequence by applying parameter identification on intermediate models. Models created with this method had lower mean square errors (MSE) compared to original algorithm. A case study on breast cancer survival prediction is also presented that demonstrates a thorough comparison of the new modelling algorithm with several other methods such as SVM, C5 decision tree, ANFIS and the original SY method. The modified SY method had the highest average of accuracies among all models. Moreover, it had significantly higher accuracy compared to the original SY method and ANFIS. 10-fold cross validation approach was employed for all evaluations.

Estimation of Possibility-Probability Distributions

We demonstrate a theory for evaluating the likelihood of a probability by way of possibility distributions. This theory derives from the standard probability distribution theory by using the possibility to define an arbitrary function whose values are bounded by [0,1] that represents the confidence that one may have in the outcomes. In other words, when in classic probability theory the probability of an event is represented by an integral of the probability mass over this event, in possibility theory the probability of an event is the integral of the probability mass times the confidence function over the whole space. This theory is then extended in order to define a similar notion to probability distributions, namely Possibility-Probability distributions, which represent, as for probabilities, the possibilities of a calculated probability for a given fuzzy event. In this context, we aim to define an estimation method of such a Possibility-Probability distribution in the case of experimental samples and the corresponding distribution.