Integration of Interpolation and Inference with Multi-antecedent Rules

Nitin Naik*, Qiang Shen

*Corresponding author for this work

Research output: Chapter in Book/Published conference outputConference publication


The efficacious fuzzy rule based systems perform their tasks with either a dense rule base or a sparse rule base. The nature of the rule base decides on whether compositional rule of inference (CRI) or fuzzy rule interpolation (FRI) should be applied. Given a dense rule base where at least one rule exists for every observation, CRI can be effectively and sufficiently employed. For a sparse rule base where rules do not cover all possible observations, FRI is required. Nonetheless, certain observations may be matched partly or completely with any of the existing rules in the sparse rule-base. Such observations can be directly dealt with using CRI and the conclusion can be inferred via firing the matched rule, thereby avoiding extra overheads of interpolation. If no such matching can be found then correct rules should be selected to ensure the accuracy while performing FRI. This paper proposes a generalised approach for the integration of FRI and CRI. It utilises the notion of alpha-cut overlapping to determine the matching degree between rule antecedents and a given observation in order to determine if CRI is to be applied. In the event of no matching rules, the nearest rules will be chosen to derive conclusion using FRI based on the best suitable distance metric among possible alternatives such as the Centre of Gravity, Hausdorff Distance and Earth Mover’s Distance. Comparative results are presented to demonstrate the effectiveness of this integrated approach.

Original languageEnglish
Title of host publicationAdvances in Computational Intelligence Systems - Contributions Presented at the 19th UK Workshop on Computational Intelligence, 2019
Number of pages15
ISBN (Electronic)978-3-030-29933-0
ISBN (Print)9783030299323
Publication statusPublished - 30 Aug 2019
Event19th Annual UK Workshop on Computational Intelligence, UKCI 2019 - Portsmouth, United Kingdom
Duration: 4 Sept 20196 Sept 2019

Publication series

NameAdvances in Intelligent Systems and Computing
ISSN (Print)2194-5357
ISSN (Electronic)2194-5365


Conference19th Annual UK Workshop on Computational Intelligence, UKCI 2019
Country/TerritoryUnited Kingdom

Bibliographical note

© Springer Nature B.V. 2019. The final publication is available at Springer via


  • Computational rule of inference
  • Integration of interpolation and inference
  • Multi-antecedent rules
  • Rule extrapolation
  • Rule interpolation


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