LR-fuzzy numbers are widely used in Fuzzy Set Theory applications based on the standard definition of convex fuzzy sets. However, in some empirical contexts such as, for example, human decision making and ratings, convex representations might not be capable to capture more complex structures in the data. Moreover, non-convexity seems to arise as a natural property in many applications based on fuzzy systems (e.g., fuzzy scales of measurement). In these contexts, the usage of standard fuzzy statistical techniques could be questionable. A possible way out consists in adopting ad-hoc data manipulation procedures to transform non-convex data into standard convex representations. However, these procedures can artificially mask relevant information carried out by the non-convexity property. To overcome this problem, in this article we introduce a novel computational definition of non-convex fuzzy number which extends the traditional definition of LR-fuzzy number. Moreover, we also present a new fuzzy regression model for crisp input/non-convex fuzzy output data based on the fuzzy least squares approach. In order to better highlight some important characteristics of the model, we applied the fuzzy regression model to some datasets characterized by convex as well as non-convex features. Finally, some critical points are outlined in the final section of the article together with suggestions about future extensions of this work.

Non-convex fuzzy data and fuzzy statistics: a first descriptive approach to data analysis / Calcagnì, Antonio; Lombardi, Luigi; E., Pascali. - In: SOFT COMPUTING. - ISSN 1432-7643. - 2014:8(2014), pp. 1575-1588. [10.1007/s00500-013-1164-x]

Non-convex fuzzy data and fuzzy statistics: a first descriptive approach to data analysis

Calcagnì, Antonio;Lombardi, Luigi;
2014-01-01

Abstract

LR-fuzzy numbers are widely used in Fuzzy Set Theory applications based on the standard definition of convex fuzzy sets. However, in some empirical contexts such as, for example, human decision making and ratings, convex representations might not be capable to capture more complex structures in the data. Moreover, non-convexity seems to arise as a natural property in many applications based on fuzzy systems (e.g., fuzzy scales of measurement). In these contexts, the usage of standard fuzzy statistical techniques could be questionable. A possible way out consists in adopting ad-hoc data manipulation procedures to transform non-convex data into standard convex representations. However, these procedures can artificially mask relevant information carried out by the non-convexity property. To overcome this problem, in this article we introduce a novel computational definition of non-convex fuzzy number which extends the traditional definition of LR-fuzzy number. Moreover, we also present a new fuzzy regression model for crisp input/non-convex fuzzy output data based on the fuzzy least squares approach. In order to better highlight some important characteristics of the model, we applied the fuzzy regression model to some datasets characterized by convex as well as non-convex features. Finally, some critical points are outlined in the final section of the article together with suggestions about future extensions of this work.
2014
8
Calcagnì, Antonio; Lombardi, Luigi; E., Pascali
Non-convex fuzzy data and fuzzy statistics: a first descriptive approach to data analysis / Calcagnì, Antonio; Lombardi, Luigi; E., Pascali. - In: SOFT COMPUTING. - ISSN 1432-7643. - 2014:8(2014), pp. 1575-1588. [10.1007/s00500-013-1164-x]
File in questo prodotto:
File Dimensione Formato  
8final_publication.pdf

Solo gestori archivio

Descrizione: final manuscript
Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 714.92 kB
Formato Adobe PDF
714.92 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/34514
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? ND
social impact