Fuzzy representations need a careful design

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.

[1]  L. A. Jeffress,et al.  Cerebral Mechanisms in Behavior , 1953 .

[2]  M. Black.  Reasoning with Loose Concepts , 1963, Dialogue.

[3]  J. Neumann.  The General and Logical Theory of Au-tomata , 1963 .

[4]  E. Trillas.  Sobre funciones de negación en la teoría de conjuntos difusos. , 1979 .

[5]  Takeshi Yamakawa.  High-speed fuzzy controller hardware system: The mega-FIPS machine , 1988, Inf. Sci..

[6]  Witold Pedrycz,et al.  Fuzzy control and fuzzy systems , 1989 .

[7]  Siegfried Gottwald,et al.  Fuzzy Sets and Fuzzy Logic , 1993 .

[8]  Dimitar P. Filev,et al.  Fuzzy SETS AND FUZZY LOGIC , 1996 .

[9]  Dr. Hans Hellendoorn,et al.  An Introduction to Fuzzy Control , 1996, Springer Berlin Heidelberg.

[10]  Henri Prade,et al.  What are fuzzy rules and how to use them , 1996, Fuzzy Sets Syst..

[11]  Francisco Herrera,et al.  Applicability of the fuzzy operators in the design of fuzzy logic controllers , 1997, Fuzzy Sets Syst..

[12]  Enric Trillas,et al.  Searching for the roots of non-contradiction and excluded-middle , 2002, Int. J. Gen. Syst..

[13]  J. Gutiérrez,et al.  - A step towards conceptually improving Takagi-Sugeno's Approximation , 2003 .

[14]  Enric Trillas,et al.  Standard theories of fuzzy sets with the law (mu Lambda sigma) = (mu Lambda sigma) , 2004, Int. J. Approx. Reason..

[15]  Claudio Moraga,et al.  Multiple-Valued Logic and Artificial Intelligence Fundamentals of Fuzzy Control Revisited , 2003, Artificial Intelligence Review.

[16]  E. Vila-Matas.  Desde la ciudad nerviosa , 2004 .

[17]  E. Trillas,et al.  On MPT-implication functions for Fuzzy Logic , 2004 .

[18]  Siegfried Gottwald,et al.  Foundations of a set theory for fuzzy sets. 40 years of development , 2005, NAFIPS 2005 - 2005 Annual Meeting of the North American Fuzzy Information Processing Society.

[19]  S. Gottwald.  Foundations of a set theory for fuzzy sets. 40 years of development , 2005, NAFIPS 2005.

[20]  Sergio Guadarrama,et al.  What about fuzzy logic's linguistic soundness? , 2005, Fuzzy Sets Syst..

[21]  Sergio Guadarrama,et al.  Some Fuzzy Counterparts of the Language uses of And and Or , 2006 .

[22]  E. Trillas.  Why do fuzzy representations need a careful design , 2008 .

[23]  E. Trillas.  On some features of fuzzy logic , 2008, NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society.

[24]  Naiyao Zhang,et al.  Structure analysis and system design for a class of Mamdani fuzzy controllers , 2008, Int. J. Gen. Syst..

[25]  Pascual Campoy Cervera,et al.  Computational intelligence in decision and control , 2008, CDC 2008.

[26]  Sergio Guadarrama,et al.  Crisp sets as classes of discontinuous fuzzy sets , 2009, Int. J. Approx. Reason..

[27]  Joan Torrens,et al.  Conjecturing from consequences , 2009, Int. J. Gen. Syst..

[28]  Enric Trillas,et al.  Towards the dissolution of the sorites paradox , 2011, Appl. Soft Comput..