Uncertainty Measurement for the Interval Type-2 Fuzzy Set

In this paper, two measures of uncertainty for interval type-2 fuzzy sets are presented, evaluated, compared and contrasted. Wu and Mendel regard the length of the type-reduced set as a measure of the uncertainty in an interval set. Green eld and John argue that the volume under the surface of the type-2 fuzzy set is a measure of the uncertainty relating to the set. For an interval type-2 fuzzy set, the volume measure is equivalent to the area of the footprint of uncertainty of the set. Experiments show that though the two measures give di erent results, there is considerable commonality between them. The concept of invariance under vertical translation is introduced; the uncertainty measure of a fuzzy set has the property of invariance under vertical translation if the value it generates remains constant under any vertical translation of the fuzzy set. It is left unresolved whether invariance under vertical translation is an essential property of a type-2 uncertainty measure

Exploration of Subjective Color Perceptual-Ability by EEG-Induced Type-2 Fuzzy Classifiers

Perceptual-ability informally refers to the ability of a person to recognize a stimulus. This paper deals with color perceptual-ability measurement of subjects using brain response to basic color (red, green and blue) stimuli. It also attempts to determine subjective ability to recognize the base colors in presence of noise tolerance of the base colors, referred to as recognition tolerance. Because of intra- and inter-session variations in subjective brain signal features for a given color stimulus, there exists uncertainty in perceptual-ability. In addition, small variations in the color stimulus result in wide variations in brain signal features, introducing uncertainty in perceptual-ability of the subject. Type-2 fuzzy logic has been employed to handle the uncertainty in color perceptual-ability measurements due to a) variations in brain signal features for a given color, and b) the presence of colored noise on the base colors. Because of limited power of uncertainty management of interval type-2 fuzzy sets and high computational overhead of its general type-2 counterpart, we developed a semi-general type-2 fuzzy classifier to recognize the base color. It is important to note that the proposed technique transforms a vertical slice based general type-2 fuzzy set into an equivalent interval type-2 counterpart to reduce the computational overhead, without losing the contributions of the secondary memberships. The proposed semi-general type-2 fuzzy sets induced classifier yields superior performance in classification accuracy with respect to existing type-1, type-2 and other well-known classifiers. The brain-understanding of a perceived base or noisy base colors is also obtained by exact low resolution electromagnetic topographic analysis (e-LORETA) software. This is used as the reference for our experimental results of the semi-general type-2 classifier in color perceptual-ability detection. Statistical tests undertaken confirm the superiority of the proposed classifier over its competitors. The proposed technique is expected to have interesting applications in identifying people with excellent color perceptual-ability for chemical, pharmaceutical and textile industries

Formulation of linguistic regression model based on natural words

When human experts express their ideas and thoughts, human words are basically employed in these expressions. That is, the experts with much professional experiences are capable of making assessment using their intuition and experiences. The measurements and interpretation of characteristics are taken with uncertainty, because most measured characteristics, analytical result, and field data can be interpreted only intuitively by experts. In such cases, judgments may be expressed using linguistic terms by experts. The difficulty in the direct measurement of certain characteristics makes the estimation of these characteristics imprecise. Such measurements may be dealt with the use of fuzzy set theory. As Professor L. A. Zadeh has placed the stress on the importance of the computation with words, fuzzy sets can take a central role in handling words [12, 13]. In this perspective fuzzy logic approach is offten thought as the main and only useful tool to deal with human words. In this paper we intend to present another approach to handle human words instead of fuzzy reasoning. That is, fuzzy regression analysis enables us treat the computation with words. In order to process linguistic variables, we define the vocabulary translation and vocabulary matching which convert linguistic expressions into membership functions on the interval [0–1] on the basis of a linguistic dictionary, and vice versa. We employ fuzzy regression analysis in order to deal with the assessment process of experts from linguistic variables of features and characteristics of an objective into the linguistic expression of the total assessment. The presented process consists of four portions: (1) vocabulary translation, (2) estimation, (3) vocabulary matching and (4) dictionary. We employed fuzzy quantification theory type 2 for estimating the total assessment in terms of linguistic structural attributes which are obtained from an expert

Adaptive Non-singleton Type-2 Fuzzy Logic Systems: A Way Forward for Handling Numerical Uncertainties in Real World Applications

Real world environments are characterized by high levels of linguistic and numerical uncertainties. A Fuzzy Logic System (FLS) is recognized as an adequate methodology to handle the uncertainties and imprecision available in real world environments and applications. Since the invention of fuzzy logic, it has been applied with great success to numerous real world applications such as washing machines, food processors, battery chargers, electrical vehicles, and several other domestic and industrial appliances. The first generation of FLSs were type-1 FLSs in which type-1 fuzzy sets were employed. Later, it was found that using type-2 FLSs can enable the handling of higher levels of uncertainties. Recent works have shown that interval type-2 FLSs can outperform type-1 FLSs in the applications which encompass high uncertainty levels. However, the majority of interval type-2 FLSs handle the linguistic and input numerical uncertainties using singleton interval type-2 FLSs that mix the numerical and linguistic uncertainties to be handled only by the linguistic labels type-2 fuzzy sets. This ignores the fact that if input numerical uncertainties were present, they should affect the incoming inputs to the FLS. Even in the papers that employed non-singleton type-2 FLSs, the input signals were assumed to have a predefined shape (mostly Gaussian or triangular) which might not reflect the real uncertainty distribution which can vary with the associated measurement. In this paper, we will present a new approach which is based on an adaptive non-singleton interval type-2 FLS where the numerical uncertainties will be modeled and handled by non-singleton type-2 fuzzy inputs and the linguistic uncertainties will be handled by interval type-2 fuzzy sets to represent the antecedents’ linguistic labels. The non-singleton type-2 fuzzy inputs are dynamic and they are automatically generated from data and they do not assume a specific shape about the distribution associated with the given sensor. We will present several real world experiments using a real world robot which will show how the proposed type-2 non-singleton type-2 FLS will produce a superior performance to its singleton type-1 and type-2 counterparts when encountering high levels of uncertainties.</jats:p

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

Performance Measurement Under Increasing Environmental Uncertainty In The Context of Interval Type-2 Fuzzy Logic Based Robotic Sailing

Performance measurement of robotic controllers based on fuzzy logic, operating under uncertainty, is a subject area which has been somewhat ignored in the current literature. In this paper standard measures such as RMSE are shown to be inappropriate for use under conditions where the environmental uncertainty changes significantly between experiments. An overview of current methods which have been applied by other authors is presented, followed by a design of a more sophisticated method of comparison. This method is then applied to a robotic control problem to observe its outcome compared with a single measure. Results show that the technique described provides a more robust method of performance comparison than less complex methods allowing better comparisons to be drawn.Comment: International Conference on Fuzzy Systems 2013 (Fuzz-IEEE 2013

Managing uncertainty in sound based control for an autonomous helicopter

In this paper we present our ongoing research using a multi-purpose, small and low cost autonomous helicopter platform (Flyper ). We are building on previously achieved stable control using evolutionary tuning. We propose a sound based supervised method to localise the indoor helicopter and extract meaningful information to enable the helicopter to further stabilise its flight and correct its flightpath. Due to the high amount of uncertainty in the data, we propose the use of fuzzy logic in the signal processing of the sound signature. We discuss the benefits and difficulties using type-1 and type-2 fuzzy logic in this real-time systems and give an overview of our proposed system

Distributed localized contextual event reasoning under uncertainty

We focus on Internet of Things (IoT) environments where sensing and computing devices (nodes) are responsible to observe, reason, report and react to a specific phenomenon. Each node captures context from data streams and reasons on the presence of an event. We propose a distributed predictive analytics scheme for localized context reasoning under uncertainty. Such reasoning is achieved through a contextualized, knowledge-driven clustering process, where the clusters of nodes are formed according to their belief on the presence of the phenomenon. Each cluster enhances its localized opinion about the presence of an event through consensus realized under the principles of Fuzzy Logic (FL). The proposed FLdriven consensus process is further enhanced with semantics adopting Type-2 Fuzzy Sets to handle the uncertainty related to the identification of an event. We provide a comprehensive experimental evaluation and comparison assessment with other schemes over real data and report on the benefits stemmed from its adoption in IoT environments