Improvements and critique on Sugeno's and Yasukawa's qualitative modeling

Investigates Sugeno's and Yasukawa's (1993) qualitative fuzzy modeling approach. We propose some easily implementable solutions for the unclear details of the original paper, such as trapezoid approximation of membership functions, rule creation from sample data points, and selection of important variables. We further suggest an improved parameter identification algorithm to be applied instead of the original one. These details are crucial concerning the method's performance as it is shown in a comparative analysis and helps to improve the accuracy of the built-up model. Finally, we propose a possible further rule base reduction which can be applied successfully in certain cases. This improvement reduces the time requirement of the method by up to 16% in our experiments

Using Fuzzy Set Similarity in Sentence Similarity Measures

Sentence similarity measures the similarity between two blocks of text. A semantic similarity measure between individual pairs of words, each taken from the two blocks of text, has been used in STASIS. Word similarity is measured based on the distance between the words in the WordNet ontology. If the vague words, referred to as fuzzy words, are not found in WordNet, their semantic similarity cannot be used in the sentence similarity measure. FAST and FUSE transform these vague words into fuzzy set representations, type-1 and type-2 respectively, to create ontological structures where the same semantic similarity measure used in WordNet can then be used. This paper investigates eliminating the process of building an ontology with the fuzzy words and instead directly using fuzzy set similarity measures between the fuzzy words in the task of sentence similarity measurement. Their performance is evaluated based on their correlation with human judgments of sentence similarity. In addition, statistical tests showed there is not any significant difference in the sentence similarity values produced using fuzzy set similarity measures between fuzzy sets representing fuzzy words and using FAST semantic similarity within ontologies representing fuzzy words

ADONiS - Adaptive Online Non-Singleton Fuzzy Logic Systems

Non-Singleton Fuzzy Logic Systems (NSFLSs) have the potential to capture and handle input noise within the design of input fuzzy sets. In this paper, we propose an online learning method which utilises a sequence of observations to continuously update the input Fuzzy Sets (FSs) of an NSFLS, thus providing an improved capacity to deal with variations in the level of input-affecting noise, common in real-world applications. The method removes the requirement for both a priori knowledge of noise levels or relying on offline training procedures to define input FS parameters. To the best of our knowledge, the proposed ADaptive, ONline Non-Singleton (ADONiS) Fuzzy Logic System (FLS) framework represents the first end-to-end framework to adaptively configure non-singleton input FSs. The latter is achieved through online uncertainty detection applied to a sliding window of observations. Since real-world environments are influenced by a broad range of noise sources, which can vary greatly in magnitude over time, the proposed technique for combining online determination of noise levels with associated adaptation of input FSs provides an efficient and effective solution which elegantly models input uncertainty in the FLS's input FSs, without requiring changes in any other part (e.g. antecedents, rules or consequents) of the FLS. In this paper, two common chaotic time series (Mackey-Glass, Lorenz) are used to perform prediction experiments to demonstrate and evaluate the proposed framework. Results indicate that the proposed adaptive NSFLS framework provides significant advantages, particularly in environments that include high variation in noise levels, which are common in real-world applications

Fuzzy natural language similarity measures through computing with words

A vibrant area of research is the understanding of human language by machines to engage in conversation with humans to achieve set goals. Human language is naturally fuzzy by nature, with words meaning different things to different people, depending on the context. Fuzzy words are words with a subjective meaning, typically used in everyday human natural language dialogue and often ambiguous and vague in meaning and dependent on an individual’s perception. Fuzzy Sentence Similarity Measures (FSSM) are algorithms that can compare two or more short texts which contain fuzzy words and return a numeric measure of similarity of meaning between them. The motivation for this research is to create a new FSSM called FUSE (FUzzy Similarity mEasure). FUSE is an ontology-based similarity measure that uses Interval Type-2 Fuzzy Sets to model relationships between categories of human perception-based words. Four versions of FUSE (FUSE_1.0 – FUSE_4.0) have been developed, investigating the presence of linguistic hedges, the expansion of fuzzy categories and their use in natural language, incorporating logical operators such as ‘not’ and the introduction of the fuzzy influence factor. FUSE has been compared to several state-of-the-art, traditional semantic similarity measures (SSM’s) which do not consider the presence of fuzzy words. FUSE has also been compared to the only published FSSM, FAST (Fuzzy Algorithm for Similarity Testing), which has a limited dictionary of fuzzy words and uses Type-1 Fuzzy Sets to model relationships between categories of human perception-based words. Results have shown FUSE is able to improve on the limitations of traditional SSM’s and the FAST algorithm by achieving a higher correlation with the average human rating (AHR) compared to traditional SSM’s and FAST using several published and gold-standard datasets. To validate FUSE, in the context of a real-world application, versions of the algorithm were incorporated into a simple Question & Answer (Q&A) dialogue system (DS), referred to as FUSION, to evaluate the improvement of natural language understanding. FUSION was tested on two different scenarios using human participants and results compared to a traditional SSM known as STASIS. Results of the DS experiments showed a True rating of 88.65% compared to STASIS with an average True rating of 61.36%. Results showed that the FUSE algorithm can be used within real world applications and evaluation of the DS showed an improvement of natural language understanding, allowing semantic similarity to be calculated more accurately from natural user responses. The key contributions of this work can be summarised as follows: The development of a new methodology to model fuzzy words using Interval Type-2 fuzzy sets; leading to the creation of a fuzzy dictionary for nine fuzzy categories, a useful resource which can be used by other researchers in the field of natural language processing and Computing with Words with other fuzzy applications such as semantic clustering. The development of a FSSM known as FUSE, which was expanded over four versions, investigating the incorporation of linguistic hedges, the expansion of fuzzy categories and their use in natural language, inclusion of logical operators such as ‘not’ and the introduction of the fuzzy influence factor. Integration of the FUSE algorithm into a simple Q&A DS referred to as FUSION demonstrated that FSSM can be used in a real-world practical implementation, therefore making FUSE and its fuzzy dictionary generalisable to other applications

Towards Better Performance in the Face of Input Uncertainty while Maintaining Interpretability in AI

Uncertainty is a pervasive element of many real-world applications and very often existing sources of uncertainty (e.g. atmospheric conditions, economic parameters or precision of measurement devices) have a detrimental impact on the input and ultimately results of decision-support systems. Thus, the ability to handle input uncertainty is a valuable component of real-world decision-support systems. There is a vast amount of literature on handling of uncertainty through decision-support systems. While they handle uncertainty and deliver a good performance, providing an insight into the decision process (e.g. why or how results are produced) is another important asset in terms of having trust in or providing a ‘debugging’ process in given decisions. Fuzzy set theory provides the basis for Fuzzy Logic Systems which are often associated with the ability for handling uncertainty and possessing mechanisms for providing a degree of interpretability. Specifically, Non-Singleton Fuzzy Logic Systems are essential in dealing with uncertainty that affects input which is one of the main sources of uncertainty in real-world systems. Therefore, in this thesis, we comprehensively explore enhancing non-singleton fuzzy logic systems capabilities considering both capturing-handling uncertainty and also maintaining interpretability. To that end the following three key aspects are investigated; (i) to faithfully map input uncertainty to outputs of systems, (ii) to propose a new framework to provide the ability for dynamically adapting system on-the-fly in changing real-world environments. (iii) to maintain level of interpretability while leveraging performance of systems. The first aspect is to leverage mapping uncertainty from input to outputs of systems through the interaction between input and antecedent fuzzy sets i.e. firing strengths. In the context of Non-Singleton Fuzzy Logic Systems, recent studies have shown that the standard technique for determining firing strengths risks information loss in terms of the interaction of the input uncertainty and antecedent fuzzy sets. This thesis explores and puts forward novel approaches to generating firing strengths which faithfully map the uncertainty affecting system inputs to outputs. Time-series forecasting experiments are used to evaluate the proposed alternative firing strength generating technique under different levels of input uncertainty. The analysis of the results shows that the proposed approach can also be a suitable method to generate appropriate firing levels which provide the ability to map different uncertainty levels from input to output of FLS that are likely to occur in real-world circumstances. The second aspect is to provide dynamic adaptive behaviours to systems at run-time in changing conditions which are common in real-world environments. Traditionally, in the fuzzification step of Non-Singleton Fuzzy Logic Systems, approaches are generally limited to the selection of a single type of input fuzzy sets to capture the input uncertainty, whereas input uncertainty levels tend to be inherently varying over time in the real-world at run-time. Thus, in this thesis, input uncertainty is modelled -where it specifically arises- in an online manner which can provide an adaptive behaviour to capture varying input uncertainty levels. The framework is presented to generate Type-1 or Interval Type-2 input fuzzy sets, called ADaptive Online Non-singleton fuzzy logic System (ADONiS). In the proposed framework, an uncertainty estimation technique is utilised on a sequence of observations to continuously update the input fuzzy sets of non-singleton fuzzy logic systems. Both the type-1 and interval type-2 versions of the ADONiS frameworks remove the limitation of the selection of a specific type of input fuzzy sets. Also this framework enables input fuzzy sets to be adapted to unknown uncertainty levels which is not perceived at the design stage of the model. Time-series forecasting experiments are implemented and results show that our proposed framework provides performance advantages over traditional counterpart approaches, particularly in environments that include high variation in noise levels, which are common in real-world applications. In addition, the real-world medical application study is designed to test the deployability of the ADONiS framework and to provide initial insight in respect to its viability in replacing traditional approaches. The third aspect is to maintain levels of interpretability, while increasing performance of systems. When a decision-support model delivers a good performance, providing an insight of the decision process is also an important asset in terms of trustworthiness, safety and ethical aspects etc. Fuzzy logic systems are considered to possess mechanisms which can provide a degree of interpretability. Traditionally, while optimisation procedures provide performance benefits in fuzzy logic systems, they often cause alterations in components (e.g. rule set, parameters, or fuzzy partitioning structures) which can lead to higher accuracy but commonly do not consider the interpretability of the resulting model. In this thesis, the state of the art in fuzzy logic systems interpretability is advanced by capturing input uncertainty in the fuzzification -where it arises- and by handling it the inference engine step. In doing so, while the performance increase is achieved, the proposed methods limit any optimisation impact to the fuzzification and inference engine steps which protects key components of FLSs (e.g. fuzzy sets, rule parameters etc.) and provide the ability to maintain the given level of interpretability

Geometric Compatibility Modification

Compatibility modification is a rule-based inference strategy that uses the similarity of the input with the antecedent of a rule to modify the consequent. Existing compatibility modification inference techniques have employed a set theoretic assessment of compatibility. In this paper, a distance-based compatibility measure is derived from a generalization of the dissemblance index for fuzzy sets. This measure is then used to develop an inference technique based on geometric compatibility. This geometric approach is compared with two other distance-based inference techniques: linear rule interpolation and bound dependent linear revision

Geometric Compatibility Modification

Compatibility modification is a rule-based inference strategy that uses the similarity of the input with the antecedent of a rule to modify the consequent. Existing compatibility modification inference techniques have employed a set theoretic assessment of compatibility. In this paper, a distance-based compatibility measure is derived from a generalization of the dissemblance index for fuzzy sets. This measure is then used to develop an inference technique based on geometric compatibility. This geometric approach is compared with two other distance-based inference techniques: linear rule interpolation and bound dependent linear revision