Some Thoughts About Appealing Directions for the Future of Fuzzy Theory and Technologies Along the Path Traced by Lotfi Zadeh

摘要

Alas, it is always dangerous to prophesy, particularly, as the Danish proverb says, about the future. The quoted text is an interesting instance of a fuzzy object: it is currently known in slightly diversified forms, each rather different from the quoted one, which corresponds to the first known appearance in English of this adage1. Indeed, most of the times we are used to reading or hearing variations of the sentence 'it is difficult to make predictions, particularly about the future'. The fuzziness here also extends to the source of the aphorism, which over the years has been attributed, among others, to Mark Twain, Niels Bohr, and even Nostradamus. This induces a fortiori further uncertainty of about half a century on the time of introduction of this saying. Actually, the first written evidence of what we could call an academic proverb is found in the autobiography of a Danish politician (published in 1948, by the way, in Danish). Summing up, what we have here is a rather definite concept (a humorous, yet effective warning about the assertion of forecasts) exhibiting several forms of imprecision: in its statement, in its authorship and in its temporal origin. Having this warning in mind, the challenging idea of shaping the future of fuzzy logic and fuzzy sets fields one year after Lotfi Zadeh passed away looks like a venturesome and hazardous task. On the one hand, almost any scholar investigating the broad umbrella of soft computing knows the papers originating the rich veins of fuzzy sets and fuzzy logic [22,26]; however, the fact of having extended the basic brick of mathematical architecture (namely, the concept of set, along with the immediate application bringing to the definition of fuzzy numbers [8]) allowed Zadeh to publish more than forty years ago quite a number of seminal papers concerning the 'fuzzification' of several key fields in mathematics and informatics. The following list shows some interesting example of such fields~2, without any pretence of exhaustiveness: 1. the notion of fuzzy languages [12], introduced as fuzzy sets defined over the universe of strings induced by a finite alphabet;