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

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

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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Decision blocks: A tool for automating decision making in CLIPS

The human capability of making complex decision is one of the most fascinating facets of human intelligence, especially if vague, judgemental, default or uncertain knowledge is involved. Unfortunately, most existing rule based forward chaining languages are not very suitable to simulate this aspect of human intelligence, because of their lack of support for approximate reasoning techniques needed for this task, and due to the lack of specific constructs to facilitate the coding of frequently reoccurring decision block to provide better support for the design and implementation of rule based decision support systems. A language called BIRBAL, which is defined on the top of CLIPS, for the specification of decision blocks, is introduced. Empirical experiments involving the comparison of the length of CLIPS program with the corresponding BIRBAL program for three different applications are surveyed. The results of these experiments suggest that for decision making intensive applications, a CLIPS program tends to be about three times longer than the corresponding BIRBAL program

A Comparison of Type-1 and Type-2 Fuzzy Logic Controllers in Robotics: A review

Most real world applications face high levels of uncertainties that can affect the operations of such applications. Hence, there is a need to develop different approaches that can handle the available uncertainties and reduce their effects on the given application. To date, Type-1 Fuzzy Logic Controllers (FLCs) have been applied with great success to many different real world applications. The traditional type-1 FLC which uses crisp type-1 fuzzy sets cannot handle high levels of uncertainties appropriately. Nevertheless it has been shown that a type-2 FLC using type-2 fuzzy sets can handle such uncertainties better and thus produce a better performance. As such, type-2 FLCs are considered to have the potential to overcome the limitations of type-1 FLCs and produce a new generation of fuzzy controllers with improved performance for many applications which require handling high levels of uncertainty. This paper will briefly introduce the interval type-2 FLC and its benefits. We will also present briefly some of the type-2 FLC real world applications

Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology

Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted. The concept of L-fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov’s intuitionistic fuzzy set. In addition, the class of L-fuzzy sets forms a complete lattice whenever the underlying set L constitutes a complete lattice. Based on these observations, we develop a general approach towards L-fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of L-fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction techniques in terms of interval-valued fuzzy image processing