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Advances in Fuzzy Systems
Volume 2018, Article ID 8458916, 16 pages
Research Article

A Method Based on Extended Fuzzy Transforms to Approximate Fuzzy Numbers in Mamdani Fuzzy Rule-Based System

1Università degli Studi di Napoli Federico II, Dipartimento di Architettura, Via Toledo 402, 80134 Napoli, Italy
2Università degli Studi di Napoli Federico II, Centro Interdipartimentale di Ricerca A. Calza Bini, Via Toledo 402, 80134 Napoli, Italy

Correspondence should be addressed to Ferdinando Di Martino; ti.aninu@itramidf

Received 9 April 2018; Accepted 25 July 2018; Published 12 September 2018

Academic Editor: Yasar Becerikli

Copyright © 2018 Ferdinando Di Martino and Salvatore Sessa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a new Mamdani fuzzy rule-based system in which the fuzzy sets in the antecedents and consequents are assigned in a discrete set of points and approximated by using the extended inverse fuzzy transforms, whose components are calculated by verifying that the dataset is sufficiently dense with respect to the uniform fuzzy partition. We test our system in the problem of spatial analysis consisting in the evaluation of the livability of residential housings in all the municipalities of the district of Naples (Italy). Comparisons are done with the results obtained by using trapezoidal fuzzy numbers in the fuzzy rules.