Longzhi Yang

Closed form fuzzy interpolation

Fuzzy interpolation enhances the robustness of fuzzy systems and helps to reduce systems complexity. Although a number of important fuzzy rule interpolation approaches have been proposed in the literature, most of these approaches cannot be expressed in a closed form. This is usually caused by the effort to avoid possible invalid interpolated results. This paper proposes a different fuzzy rule interpolation approach. It not only can be represented in a closed form but also guarantees that the interpolated results are valid fuzzy sets. This approach is based on a direct use of the extension principle which has been widely utilised for the development of a variety of fuzzy systems. The mathematical properties of the proposed approach are analysed by taking the advantage of the closed form representation. This approach has been applied to a practical problem of predicting diarrhoeal disease rates in remote villages. The results demonstrate the potential of the proposed work in enhancing the robustness of fuzzy interpolation.

Generalisation of scale and move transformation-based fuzzy interpolation

Q. Shen and L. Yang. Generalisation of scale and move transformation-based fuzzy interpolation. Advanced Computational Intelligence and Intelligent Informatics, 15(3):288-298, 2011.

Towards adaptive interpolative reasoning

Fuzzy interpolative reasoning has been extensively studied due to its ability to enhance the robustness of fuzzy systems and to reduce system complexity. However, during the interpolation process, it is possible that multiple object values for a common variable are inferred which may lead to inconsistency in interpolated results. Such inconsistencies may result from defective interpolated rules or incorrect interpolative transformations. This paper presents a novel approach for identification and correction of defective rules in transformations, thereby removing the inconsistencies. In particular, an assumption-based truth maintenance system (ATMS) is used to record dependencies between reasoning results and interpolated rules, while the underlying technique that the general diagnostic engine (GDE) employs for fault localization is adapted to isolate possible faulty interpolated rules and their associated interpolative transformations. From this, an algorithm is introduced to allow for the modification of the original linear interpolation to become first-order piecewise linear. The approach is applied to a carefully chosen practical problem to illustrate the potential in strengthening the power of interpolative reasoning.

Adaptive fuzzy interpolation and extrapolation with multiple-antecedent rules

Adaptive fuzzy interpolation strengthens the potential of fuzzy interpolative reasoning owning to its efficient identification and correction of defective interpolated rules during the interpolation process [11]. This approach assumes that: i) two closest adjacent rules which flank the observation or a previously inferred result are always available; ii) only single-antecedent rules are involved. In practice, however, variable values of these rules may lie just on one side of the observation or inferred result. Also, there may be certain rules with multiple antecedents in the rule base. This paper extends the adaptive approach, in order to cover fuzzy extrapolation and to support rule base with multiple-antecedent rules. Adaptive fuzzy interpolation and extrapolation complement each other, which jointly improve the applicability of fuzzy interpolative reasoning, as it significantly reduces the restriction over the given rule base.

Closed form fuzzy interpolation with interval type-2 fuzzy sets

Fuzzy rule interpolation enables fuzzy inference with sparse rule bases by interpolating inference results, and may help to reduce system complexity by removing similar (often redundant) neighbouring rules. In particular, the recently proposed closed form fuzzy interpolation offers a unique approach which guarantees convex interpolated results in a closed form. However, the difficulty in defining the required precise-valued membership functions still poses significant restrictions over the applicability of this approach. Such limitations can be alleviated by employing type-2 fuzzy sets as their membership functions are themselves fuzzy. This paper extends the closed form fuzzy rule interpolation using interval type-2 fuzzy sets. In this way, as illustrated in the experiments, closed form fuzzy interpolation is able to deal with uncertainty in data and knowledge with more flexibility.

Adaptive fuzzy interpolation with uncertain observations and rule base

Adaptive fuzzy interpolation strengthens the potential of fuzzy interpolative reasoning. It views interpolation procedures as artificially created system components, and identifies all possible sets of faulty components that may each have led to all detected contradictory results. From this, a modification procedure takes place, which tries to modify each of such components, termed candidates, in an effort to remove all the contradictions and thus restore consistency. This approach assumes that the employed interpolation mechanism is the only cause of contradictions, that is all given observations and rules are believed to be true and fixed. However, this may not be the case in certain real situations. It is common in fuzzy systems that each observation or rule is associated with a certainty degree. This paper extends the adaptive approach by taking into consideration both observations and rules also, treating them as diagnosable and modifiable components in addition to interpolation procedures. Accordingly, the modification procedure is extended to cover the cases of modifying observations or rules in a given rule base along with the modification of fuzzy reasoning components. This extension significantly improves the robustness of the existing adaptive approach.

Adaptive fuzzy interpolation with prioritized component candidates

Adaptive fuzzy interpolation strengthens the potential of fuzzy interpolative reasoning. It first identifies all possible sets of faulty fuzzy reasoning components, termed the candidates, each of which may have led to all the contradictory interpolations. It then tries to modify one selected candidate in an effort to remove all the contradictions and thus restore interpolative consistency. This approach assumes that all the candidates are equally likely to be the real culprit. However, this may not be the case in real situations as certain identified reasoning components may be more liable to resulting in inconsistencies than others. This paper extends the adaptive approach by prioritizing all the generated candidates. This is achieved by exploiting the certainty degrees of fuzzy reasoning components and hence of derived propositions. From this, the candidate with the highest priority is modified first. This extension helps to quickly spot the real culprit and thus considerably improves the approach in terms of efficiency.

Towards a Fuzzy Expert System on Toxicological Data Quality Assessment

Quality assessment (QA) requires high levels of domain‐specific experience and knowledge. QA tasks for toxicological data are usually performed by human experts manually, although a number of quality evaluation schemes have been proposed in the literature. For instance, the most widely utilised Klimisch scheme 1 defines four data quality categories in order to tag data instances with respect to their qualities; ToxRTool 2 is an extension of the Klimisch approach aiming to increase the transparency and harmonisation of the approach. Note that the processes of QA in many other areas have been automatised by employing expert systems. Briefly, an expert system is a computer program that uses a knowledge base built upon human expertise, and an inference engine that mimics the reasoning processes of human experts to infer new statements from incoming data. In particular, expert systems have been extended to deal with the uncertainty of information by representing uncertain information (such as linguistic terms) as fuzzy sets under the framework of fuzzy set theory and performing inferences upon fuzzy sets according to fuzzy arithmetic. This paper presents an experimental fuzzy expert system for toxicological data QA which is developed on the basis of the Klimisch approach and the ToxRTool in an effort to illustrate the power of expert systems to toxicologists, and to examine if fuzzy expert systems are a viable solution for QA of toxicological data. Such direction still faces great difficulties due to the well‐known common challenge of toxicological data QA that “five toxicologists may have six opinions”. In the meantime, this challenge may offer an opportunity for expert systems because the construction and refinement of the knowledge base could be a converging process of different opinions which is of significant importance for regulatory policy making under the regulation of REACH, though a consensus may never be reached. Also, in order to facilitate the implementation of Weight of Evidence approaches and in silico modelling proposed by REACH, there is a higher appeal of numerical quality values than nominal (categorical) ones, where the proposed fuzzy expert system could help. Most importantly, the deriving processes of quality values generated in this way are fully transparent, and thus comprehensible, for final users, which is another vital point for policy making specified in REACH. Case studies have been conducted and this report not only shows the promise of the approach, but also demonstrates the difficulties of the approach and thus indicates areas for future development.

Generalized Adaptive Fuzzy Rule Interpolation

As a substantial extension to fuzzy rule interpolation that works based on two neighboring rules flanking an observation, adaptive fuzzy rule interpolation is able to restore system consistency when contradictory results are reached during interpolation. The approach first identifies the exhaustive sets of candidates, with each candidate consisting of a set of interpolation procedures which may jointly be responsible for the system inconsistency. Then, individual candidates are modified such that all contradictions are removed, and thus, interpolation consistency is restored. It has been developed on the assumption that contradictions may only be resulted from the underlying interpolation mechanism, and that all the identified candidates are not distinguishable in terms of their likelihood to be the real culprit. However, this assumption may not hold for real-world situations. This paper, therefore, further develops the adaptive method by taking into account observations, rules, and interpolation procedures, all as diagnosable and modifiable system components. In addition, given the common practice in fuzzy systems that observations and rules are often associated with certainty degrees, the identified candidates are ranked by examining the certainty degrees of its components and their derivatives. From this, the candidate modification is carried out based on such ranking. This study significantly improves the efficacy of the existing adaptive system by exploiting more information during both the diagnosis and modification processes.

Towards sparse rule base generation for fuzzy rule interpolation

Fuzzy inference systems have been successfully applied to many real-world applications. Traditional fuzzy inference systems are only applicable to problems with dense rule bases by which the entire input domain is fully covered, whilst fuzzy rule interpolation (FRI) is also able to work with sparse rule bases that may not cover certain observations. Thanks to its ability to work with fewer rules, fuzzy rule interpolation approaches have also been utilised to reduce system complexity by removing those rules which can be approximated by their neighbouring ones for complex fuzzy models. A number of important fuzzy rule base generation approaches have been proposed in the literature, but the majority of these only target dense rule bases for traditional fuzzy inference systems. This paper proposes a novel sparse fuzzy rule base generation method to support FRI. The approach first identifies important rules that cannot be accurately approximated by their neighbouring ones to initialise the rule base. Then the raw rule base is optimised by fine-tuning the membership functions of the fuzzy sets. Experimentation is conducted to demonstrate the working principles of the proposed system, with results comparable to those of traditional methods.