Fuzzy representations need a careful design

Abstract

This paper tries to show, from a theoretical perspective, the importance of designing well the representation of fuzzy systems whose behaviour is described by a linguistic description. The way in which this design of the representation is done by means of fuzzy sets, connectives and relations marks a distinction between the fuzzy and the formal logic methodologies, two different disciplines whose design process and agendas are not coincidental.

Keywords:

• fuzzy logic
• linguistic descriptions
• fuzzy systems design
• semantics
• fuzzy representation
• system design

Acknowledgements

This work was partially supported by the Foundation for the Advancement of Soft Computing (Asturias, Spain) and MICINN (Spain) under project TIN2008-06890-C02-01.

Notes

^1. His work was supported by the Spanish Department of Science and Innovation (MICINN) under program Juan de la Cierva JCI-2008-3531 and the European Social Fund.

^2. S-implications (S stands for ‘strong’) are those implications whose proto-form comes from ‘not a or b’, that is .

^3. In algebraic logic, a conditional is called material when it is expressed by a formula with connectives. In this sense, in boolean algebras, also is material. We preferred to call them expressible by a protoform.

Additional information

Notes on contributors

Sergio Guadarrama

1. 1. His work was supported by the Spanish Department of Science and Innovation (MICINN) under program Juan de la Cierva JCI-2008-3531 and the European Social Fund.