Measuring the directional or non-directional distance between type-1 and type-2 fuzzy sets with complex membership functions

Fuzzy sets may have complex, non-normal or non-convex membership functions that occur, for example, in the output of a fuzzy logic system or when automatically generating fuzzy sets from data. Measuring the distance between such non-standard fuzzy sets can be challenging as there is no clear correct method of comparison and limited research currently exists that systematically compares existing distance measures for these fuzzy sets. It is useful to know the distance between these sets, which can tell us how much the results of a system change when the inputs differ, or the amount of disagreement between individual's perceptions or opinions on different concepts. In addition, understanding the direction of difference between such fuzzy sets further enables us to rank them, learning if one represents a higher output or higher ratings than another. This paper picks up previous functions of measuring directional distance and, for the first time, presents methods of measuring the directional distance between any type-1 and type-2 fuzzy sets with both normal/non-normal and convex/non-convex membership functions. In real-world applications where data-driven, non-convex, non-normal fuzzy sets are the norm, the proposed approaches for measuring the distance enables us to systematically reason about the real-world objects captured by the fuzzy sets

Novel methods of measuring the similarity and distance between complex fuzzy sets

This thesis develops measures that enable comparisons of subjective information that is represented through fuzzy sets. Many applications rely on information that is subjective and imprecise due to varying contexts and so fuzzy sets were developed as a method of modelling uncertain data. However, making relative comparisons between data-driven fuzzy sets can be challenging. For example, when data sets are ambiguous or contradictory, then the fuzzy set models often become non-normal or non-convex, making them difficult to compare. This thesis presents methods of comparing data that may be represented by such (complex) non-normal or non-convex fuzzy sets. The developed approaches for calculating relative comparisons also enable fusing methods of measuring similarity and distance between fuzzy sets. By using multiple methods, more meaningful comparisons of fuzzy sets are possible. Whereas if only a single type of measure is used, ambiguous results are more likely to occur. This thesis provides a series of advances around the measuring of similarity and distance. Based on them, novel applications are possible, such as personalised and crowd-driven product recommendations. To demonstrate the value of the proposed methods, a recommendation system is developed that enables a person to describe their desired product in relation to one or more other known products. Relative comparisons are then used to find and recommend something that matches a person's subjective preferences. Demonstrations illustrate that the proposed method is useful for comparing complex, non-normal and non-convex fuzzy sets. In addition, the recommendation system is effective at using this approach to find products that match a given query

Novel methods of measuring the similarity and distance between complex fuzzy sets

This thesis develops measures that enable comparisons of subjective information that is represented through fuzzy sets. Many applications rely on information that is subjective and imprecise due to varying contexts and so fuzzy sets were developed as a method of modelling uncertain data. However, making relative comparisons between data-driven fuzzy sets can be challenging. For example, when data sets are ambiguous or contradictory, then the fuzzy set models often become non-normal or non-convex, making them difficult to compare. This thesis presents methods of comparing data that may be represented by such (complex) non-normal or non-convex fuzzy sets. The developed approaches for calculating relative comparisons also enable fusing methods of measuring similarity and distance between fuzzy sets. By using multiple methods, more meaningful comparisons of fuzzy sets are possible. Whereas if only a single type of measure is used, ambiguous results are more likely to occur. This thesis provides a series of advances around the measuring of similarity and distance. Based on them, novel applications are possible, such as personalised and crowd-driven product recommendations. To demonstrate the value of the proposed methods, a recommendation system is developed that enables a person to describe their desired product in relation to one or more other known products. Relative comparisons are then used to find and recommend something that matches a person's subjective preferences. Demonstrations illustrate that the proposed method is useful for comparing complex, non-normal and non-convex fuzzy sets. In addition, the recommendation system is effective at using this approach to find products that match a given query

Modelling FTIR spectral sata with Type-I and Type-II fuzzy sets for breast cancer grading

Breast cancer is one of the most frequently occurring cancers amongst women throughout the world. After the diagnosis of the disease, monitoring its progression is important in predicting the chances of long term survival of patients. The Nottingham Prognostic Index (NPI) is one of the most common indices used to categorise the patients into different groups depending upon the severity of the disease. One of the key factors of this index is cancer grade which is determined by pathologists who examine cell samples under a microscope. This manual method has a higher chance of false classification and may lead to incorrect treatment of patients. There is a need to develop automated methods that employ advanced computational methods to help pathologists in making a decision regarding the classification of breast cancer grade. Fourier transform infra-red spectroscopy (FTIR) is one of the relatively new techniques that has been used for diagnosis of various cancer types with advanced computational methods in the literature. In this thesis we examine the use of advanced fuzzy methods with the FTIR spectral data sets to develop a model prototype that can help clinicians with breast cancer grading. Initial work is focussed on using the commonly used clustering algorithms k-means and fuzzy c-means with principal component analysis on different cancer spectral data sets to explore the complexities within them. After that, a novel model based on Type-II fuzzy logic is developed for use on a complex breast cancer FTIR spectral data set that can help clinicians classify breast cancer grades. The data set used for the purpose consists of multiple cases of each grade. We consider two types of uncertainty, one within the spectra of a single case of a grade (intra -case) and other when comparing it with other cases of same grade (inter-case). Features have been extracted in terms of interval data from various peaks and troughs. The interval data from the features has been used to create Type-I fuzzy sets for each case. After that the Type-I fuzzy sets are combined to create zSlices based General Type-II fuzzy sets for each feature for each grade. The created benchmark fuzzy sets are then used as prototypes for classification of unseen spectral data. Type-I fuzzy sets are created for unseen spectral data and then compared against the benchmark prototype Type-II fuzzy sets for each grade using a similarity measure. The best match based on the calculated similarity scores is assigned as the resultant grade. The novel model is tested on an independent spectral data set of oral cancer patients. Results indicate that the model was able to successfully construct prototype fuzzy sets for the data set, and provide in-depth information regarding the complexities of the data set as well as helping in classification of the data

Modelling FTIR spectral sata with Type-I and Type-II fuzzy sets for breast cancer grading

Breast cancer is one of the most frequently occurring cancers amongst women throughout the world. After the diagnosis of the disease, monitoring its progression is important in predicting the chances of long term survival of patients. The Nottingham Prognostic Index (NPI) is one of the most common indices used to categorise the patients into different groups depending upon the severity of the disease. One of the key factors of this index is cancer grade which is determined by pathologists who examine cell samples under a microscope. This manual method has a higher chance of false classification and may lead to incorrect treatment of patients. There is a need to develop automated methods that employ advanced computational methods to help pathologists in making a decision regarding the classification of breast cancer grade. Fourier transform infra-red spectroscopy (FTIR) is one of the relatively new techniques that has been used for diagnosis of various cancer types with advanced computational methods in the literature. In this thesis we examine the use of advanced fuzzy methods with the FTIR spectral data sets to develop a model prototype that can help clinicians with breast cancer grading. Initial work is focussed on using the commonly used clustering algorithms k-means and fuzzy c-means with principal component analysis on different cancer spectral data sets to explore the complexities within them. After that, a novel model based on Type-II fuzzy logic is developed for use on a complex breast cancer FTIR spectral data set that can help clinicians classify breast cancer grades. The data set used for the purpose consists of multiple cases of each grade. We consider two types of uncertainty, one within the spectra of a single case of a grade (intra -case) and other when comparing it with other cases of same grade (inter-case). Features have been extracted in terms of interval data from various peaks and troughs. The interval data from the features has been used to create Type-I fuzzy sets for each case. After that the Type-I fuzzy sets are combined to create zSlices based General Type-II fuzzy sets for each feature for each grade. The created benchmark fuzzy sets are then used as prototypes for classification of unseen spectral data. Type-I fuzzy sets are created for unseen spectral data and then compared against the benchmark prototype Type-II fuzzy sets for each grade using a similarity measure. The best match based on the calculated similarity scores is assigned as the resultant grade. The novel model is tested on an independent spectral data set of oral cancer patients. Results indicate that the model was able to successfully construct prototype fuzzy sets for the data set, and provide in-depth information regarding the complexities of the data set as well as helping in classification of the data

Fuzzy Transfer Learning

The use of machine learning to predict output from data, using a model, is a well studied area. There are, however, a number of real-world applications that require a model to be produced but have little or no data available of the specific environment. These situations are prominent in Intelligent Environments (IEs). The sparsity of the data can be a result of the physical nature of the implementation, such as sensors placed into disaster recovery scenarios, or where the focus of the data acquisition is on very defined user groups, in the case of disabled individuals. Standard machine learning approaches focus on a need for training data to come from the same domain. The restrictions of the physical nature of these environments can severely reduce data acquisition making it extremely costly, or in certain situations, impossible. This impedes the ability of these approaches to model the environments. It is this problem, in the area of IEs, that this thesis is focussed. To address complex and uncertain environments, humans have learnt to use previously acquired information to reason and understand their surroundings. Knowledge from different but related domains can be used to aid the ability to learn. For example, the ability to ride a road bicycle can help when acquiring the more sophisticated skills of mountain biking. This humanistic approach to learning can be used to tackle real-world problems where a-priori labelled training data is either difficult or not possible to gain. The transferral of knowledge from a related, but differing context can allow for the reuse and repurpose of known information. In this thesis, a novel composition of methods are brought together that are broadly based on a humanist approach to learning. Two concepts, Transfer Learning (TL) and Fuzzy Logic (FL) are combined in a framework, Fuzzy Transfer Learning (FuzzyTL), to address the problem of learning tasks that have no prior direct contextual knowledge. Through the use of a FL based learning method, uncertainty that is evident in dynamic environments is represented. By combining labelled data from a contextually related source task, and little or no unlabelled data from a target task, the framework is shown to be able to accomplish predictive tasks using models learned from contextually different data. The framework incorporates an additional novel five stage online adaptation process. By adapting the underlying fuzzy structure through the use of previous labelled knowledge and new unlabelled information, an increase in predictive performance is shown. The framework outlined is applied to two differing real-world IEs to demonstrate its ability to predict in uncertain and dynamic environments. Through a series of experiments, it is shown that the framework is capable of predicting output using differing contextual data