Static and Dynamic TSK Inference Systems Supported by Fuzzy Rule Interpolation

  • Pu Zhang

Student thesis: Doctoral ThesisDoctor of Philosophy


Fuzzy rule-based inference systems are successful representatives of knowledge based systems. Takagi-Sugeno-Kang (TSK) systems are one of the conventional and most exploited of such systems, providing an effective approach for performing prediction and regression tasks. However, when the input domain is not fully covered, it is possible for an observation to match no rule in the given rule base. In such a case, no conclusion can be drawn when using traditional rule-firing mechanisms. Fuzzy rule interpolation (FRI) has been introduced to deal with this problem. Whilst offering a potentially powerful inference mechanism, most existing FRI methodologies in the current literature are not developed for TSK inference models. In addition, several that are relevant may introduce an undesirable bias into the results while incurring significant computational overheads. Motivated by the above observation, this thesis presents a novel FRI approach through the use of comparatively few neighbour rules to derive interpolative results with TSK models. Compared with existing methods, the proposed approach helps reduce the computational overheads of the inference process while avoiding the adverse impact caused by rules with low similarity to the new, unmatched observation. More importantly, to deal with largesized sparse rule bases, where neighbourhood rules may be similar to each other, a rule-clustering-based method is introduced. In particular, a clustering algorithm is first employed to cluster rules into different groups, and the final interpolated conclusion is computed using the closest rules selected from a small number of closest rule clusters. The efficacy of the proposed approach is verified via systematic experimental examinations in comparison with existing methods, over a range of benchmark regression problems, whilst utilising different clustering algorithms. Particularly, to verify and demonstrate its potential, the proposed FRI approach is systematically adopted to conduct missing value imputation tasks for a real-world dataset, the water treatment plant dataset, in which features with missing values are regarded as the output of the system while others are used as inputs. The success of such a realistic application indicates the practicality of the proposed interpolation approach. In more real-world applications, the inputs are usually time-dependent, thereby requiring dynamic management of the rule base to maintain and possibly improve the efficacy of such a system. Situations may become more complicated if the training data does not sufficiently cover the problem space. FRI systems may help, whilst most of them follow a static approach, tending to process a large number of interpolated rules which are generally discarded once the results have been derived. Nonetheless, the interpolated rules may contain potentially useful information. This thesis presents a dynamic TSK system by exploiting such rules to support subsequent inference and promote rule bases. The obtained intermediate rules supplement the initial rule base, allowing it to expand to a larger set size. Afterwards, a clustering algorithm is employed to categorise rules into different groups so that an interpolated conclusion can be computed using the closest rules selected from a small number of the nearest rule clusters. Through systematic experimental comparisons with the conventional static approach, the proposed dynamic TSK system not only improves the overall reasoning accuracy but also reduces interpolation overheads by avoiding the need to interpolate similar observations.
Date of Award2021
Original languageEnglish
Awarding Institution
  • Aberystwyth University
SupervisorQiang Shen (Supervisor) & Neil Mac Parthalain (Supervisor)

Cite this