An effective similarity measurement under epistemic uncertainty

The epistemic uncertainty stems from the lack of knowledge and it can be reduced when the knowledge increases. Such inter-pretation works well with data represented as a set of possible states and therefore, multivalued similarity measures. Unfortunately, set-valued extensions of similarity measures are not computationally feasible even when the data is finite. Measures with properties that allow efficient calculation of their extensions, need to be found. Analysis of various similarity measures indicated logic-based (additive) measures as an excellent candidate. Their unique properties are discussed and efficient algorithms for computing set-valued extensions are given. The work presents results related to various classes of fuzzy set families: general ones, intervals of fuzzy sets, and their finite sums. The first case is related to the concept of the Fuzzy Membership Function Family, the second corresponds to the Interval-Valued Fuzzy Sets, while the third class is equivalent to the concept of Typical Interval-Valued Hesitant Fuzzy Sets

Similarity between interval-valued fuzzy sets taking into account the width of the intervals and admissible orders

In this work we study a new class of similarity measures between interval-valued fuzzy sets. The novelty of our approach lays, firstly, on the fact that we develop all the notions with respect to total orders of intervals; and secondly, on that we consider the width of intervals so that the uncertainty of the output is strongly related to the uncertainty of the input. For constructing the new interval-valued similarity, interval valued aggregation functions and interval-valued restricted equivalence functions which take into account the width of the intervals are needed, so we firstly study these functions, both in line with the two above stated features. Finally, we provide an illustrative example which makes use of an interval-valued similarity measure in stereo image matching and we show that the results obtained with the proposed interval-valued similarity measures improve numerically (according to the most widely used measures in the literature) the results obtained with interval valued similarity measures which do not consider the width of the intervals

A type-2 fuzzy logic based goal-driven simulation for optimising field service delivery

This thesis develops an intelligent system capable of incorporating the conditions that drive operational activity while implementing the means to handle unexpected factors to protect business sustainability. This solution aims to optimise field service operations in the utility-based industry, especially within one of the world's leading communications services companies, namely BT (British Telecom), which operates in highly regulated and competitive markets. Notably, the telecommunication sector is an essential driver of economic activity. Consequently, intelligent solutions must incorporate the ability to explain their underlying algorithms that power their final decisions to humans. In this regard, this thesis studies the following research gaps: the lack of integrated solutions that go beyond isolated monolithic architectures, the lack of agile end-to-end frameworks for handling uncertainty while business targets are defined, current solutions that address target-oriented problems do not incorporate explainable methodologies; as a result, limited explainability features result in inapplicability for highly regulated industries, and most tools do not support scalability for real-world scenarios. Hence, the need for an integrated, intelligent solution to address these target-oriented simulation problems. This thesis aims to reduce the gaps mentioned above by exploiting fuzzy logic capabilities such as mimicking human thinking and handling uncertainty. Moreover, this thesis also finds support in the Explainable AI field, particularly in the strategies and characteristics to deploy more transparent intelligent solutions that humans can understand. Hence, these foundations support the thesis to unlock explainability, transparency and interpretability. This thesis develops a series of techniques with the following features: the formalisation of an end-to-end framework that dynamically learns form data, the implementation of a novel fuzzy membership correlation analysis approach to enhance performance, the development of a novel fuzzy logic-based method to evaluate the relevancy of inputs, the modelling of a robust optimisation method for operational sustainability in the telecommunications sector, the design of an agile modelling approach for scalability and consistency, the formalisation of a novel fuzzy-logic system for goal-driven simulation for achieving specific business targets before being implemented in real-life conditions, and a novel simulation environment that incorporates visual tools to enhance interpretability while moving from conventional simulation to a target-oriented model. The proposed tool was developed based on data from BT, reflecting their real-world operational conditions. The data was protected and anonymised in compliance with BT’s sharing of information regulations. The techniques presented in the development of this thesis yield significant improvements aligned to institutional targets. Precisely, as detailed in Section 9.5, the proposed system can model a reduction between 3.78% and 5.36% of footprint carbon emission due to travel times for jobs completion on customer premises for specific geographical areas. The proposed framework allows generating simulation scenarios 13 times faster than conventional approaches. As described in Section 9.6, these improvements contribute to increased productivity and customer satisfaction metrics regarding keeping appointment times, completing orders in the promised timeframe or fixing faults when agreed by an estimated 2.6%. The proposed tool allows to evaluate decisions before acting; as detailed in Section 9.7, this contributes to the ‘promoters’ minus ‘detractors’ across business units measure by an estimated 1%

Similarity Measures of Interval-Valued Fuzzy Sets in Classification of Uncertain Data. Applications in Ovarian Tumor Diagnosis.

Wydział Matematyki i InformatykiRozprawa dotyczy problemu mierzenia podobieństwa w sytuacji, gdy wiedza na temat reprezentowanych przez przedziałowe zbiory rozmyte obiektów jest tylko częściowa i niepewna. Dokonano przeglądu literatury oraz porównania obecnych podejść do mierzenia podobieństwa klasycznych i przedziałowych zbiorów rozmytych. Okazuje się, że aby możliwe było pełne uwzględnienie niekompletności danych konieczne jest wyrażenie podobieństwa przy pomocy przedziału. Zbudowano teorię niezbędną do poprawnego modelowania przedziałowego podobieństwa. Sformułowane zostały podstawowe własności, jakie w takiej sytuacji powinna spełniać miara podobieństwa, a następnie zaproponowano metodę konstrukcji nieskończenie wielu takich miar. Metoda ta pozwala na skonstruowanie nowej miary na podstawie miary podobieństwa zbiorów rozmytych, o ile ta spełnia pewne warunki. Zbadano problem efektywnego obliczania nowych miar uzyskanych tą metodą. Szczególną uwagę poświęcono uogólnionej wersji indeksu Jaccarda. Korzystając z przedziałowych miar podobieństwa zaproponowano dwie metody klasyfikacji umożliwiające pełne wsparcie dla danych niepewnych zarówno na etapie budowy klasyfikatora, jak i jego stosowania. Dokonano obszernej ewaluacji jakości klasyfikacji z wykorzystaniem rzeczywistych danych medycznych. Jedna z zaproponowanych metod została wykorzystana w inteligentnym systemie wspomagania diagnostyki guzów jajnika - OvaExpert.The dissertation deals with the problem of measuring the similarity when knowledge about objects represented by the Interval-Valued Fuzzy Sets is incomplete and uncertain. Various current approaches to measuring similarity of classical and interval-valued fuzzy sets were investigated and compared. It appears that to be able to take full account of the data incompleteness, it is necessary to express the similarity as an interval. Theory necessary to properly model interval similarity was built. Basic properties, which in this case should be fulfilled by similarity measure were formulated, and a method of construction of infinitely many such measures was proposed. This method allows to construct a new interval measure from a similarity measure of fuzzy sets, as long as it meets certain conditions. Problem of effective calculation of the new measures obtained by this method was examined. Special attention was given to the generalized version of the Jaccard index. Using the interval similarity measures, two classification methods that allow full support for data uncertainty, both at the stage of building a classifier and its usage, were proposed. Comprehensive evaluation of the classification quality using real medical data was performed. One of the proposed methods was applied in the intelligent diagnosis support system for ovarian tumor - OvaExpert