Keynote 1 - Enric Trillas

ICFMsquare 2016

A Reflection on the Words Uncertain and Probable 


The words uncertain and probable, like all words, are only well comprehended, and communicated, once their respective meanings are captured, and seen as coincidental, analogous, or different. Nevertheless, in Science these words are often and practically   taken as synonymous; a identification that, in general, affects the measure of the uncertainty of those statements that can be qualified either as uncertain, or as probable, even by not differentiating between random and not random events. This is a serious problem that, actually, comes from an unclear philosophical understanding of what meaning is, how it can be represented, and what is a measure of meaning; in short, from a lack of ‘scientific domestication’ of meaning. Since both words belong to Natural Language but were translated into the Artificial Language of Science, it seems interesting to reflect on their linguistic primary uses, and the mathematical characteristics and differences of their respective measures.

Such reflection will be done through the interpretation, introduced few years ago and coming from Fuzzy Logic, of the linguistic meaning of a predicate as a quantity. Hence, its roots are in a ‘scientific concept’ of the (linguistic) meaning under which, and for instance, it can be shown that the uncertainty of a statement does not seem to be always measurable by a probability. The subject seems to actually deserve a reflection based on a new point of view that, perhaps not conclusive but even linked with the controversies between the competing ‘Frequentist’ and ‘Bayesian’ interpretations of probability, concerns the development of Zadeh’s ‘Computing with Words’.




Enric Trillas (Barcelona, 1940), got his Ph.D in Sciences by the University of Barcelona. Full professor in 1974, with a chair in Mathematics at the Technical University of Catalonia, served there up to 1988, when he moved into the Department of Artificial Intelligence at the Technical University of Madrid. Retired in 2006, and up to the beginning of 2016 he was an Emeritus Researcher at the European Centre for Soft Computing (Mieres, Spain), and currently is an Honorary Emeritus Professor at the University of Oviedo. He is recognized as who introduced Fuzzy Logic in Spain.

Formerly working in Ordered Semigroups and Probabilistic and Generalized Metrics, from 1976 is active in Fuzzy Logic, having received several international distinctions and honors. Doctor ‘Honoris Causa’ by the Public University of Navarra and the University of Santiago de Compostela in Spain, is a ‘Distinguished Visiting Professor’ at the University of Córdoba (Argentina).

He published over 400 papers in National and International   journals, conferences and edited books, as well as is editor or author of some other books in English, Spanish and Catalan.  His work in Fuzzy Logic began by studying fuzzy entropies, shifted to logical connectives where he characterized strong negations, introduced t-norms and t-conorms, did the first analysis of the ‘Modus Ponens’ inequality, introduced T-Indistinguishabilities, and the concept of conjecture. Currently, he mainly works in the analysis of conjecturing in Ordinary Reasoning, the representation of the meaning of words, the linguistic roots of fuzzy sets, the creative speculation, and is deeply interested in the philosophical reflection on these subjects. He did stays and seminars in several universities and research centers in Spain, France, Germany, Italy, United States, Japan, Argentina and Chile.

Between 1983 and 1996 served in the Spanish Government being, for instance, the President of the High Council for Scientific Research (CSIC), and the Director General of the National Institute for Aerospace Technology (INTA).

Holds several civil and military decorations from Spain and  other countries, like Italy and the Republic of Peru. Fellow of IFSA, and Honorary Member of EUSFLAT, was distinguished with the EUSFLAT’s ‘European Fuzzy Pioneer Award’, the IEEE-CIS’ ‘Fuzzy Pioneer Award’, the ‘Kampé de Fériet’ Award, the Medal of the Polish Academy of Sciences, and the IFSA’s ‘Outstanding Achievement Award’. He also holds the Spanish ‘Cajal’ and ‘Monturiol’ Medals, as well as a National Award in Computer Science.


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Tutorial FMsquare 2017
28 September 2017
Fribourg, Switzerland

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