Settimo Termini

On Some Vagaries of Vagueness and Information

The presence of vagueness in scientific theories (in particular, to those related to and connected with the management of information) is briefly analyzed. We consider, firstly, the problem whether vague predicates can be adequately represented by existing formal theories. A negative answer to this question produces, as a by-product, the suggestion that a good semantics for fuzzy sets can be offered by the notion of “distance from idealized items”. Secondly, some questions connected with the adequacy of “theories of information” to the multifaceted informal notion of “information” suggest to afford this problem within an enlarged dynamical setting.

Fuzzy Set Theory as a Methodological Bridge between Hard Sciences and Humanities

In this paper, we will investigate the possible role of fuzzy set theory (FST), and more generally the ensemble of technologies and theoretical approaches known as soft computing, as a methodological bridge between hard sciences and humanities. We will try, building on previous works, to investigate the “family links” between these disciplines and show how FST may be of help in promoting a connection between the “two cultures”. We will discuss Carnap and his paradox of explication, the dilemma between imagination and rigor according to Bateson, the problem of interdisciplinarity, and the consequences of precision and exactness.

Some Reflections on Fuzzy Set Theory as an Experimental Science

The aim of this paper is to open a critical discussion on the claim, recently presented in the community and especially heralded by Enric Trillas, that fuzzy logic should be seen as an “experimental science”. The first interesting aspect of such remark is whether and in which way such position has consequences on the real development of the research, or if it is simply a (different) way of looking at the same phenomenon. As a consequence, we investigate the possible connection to Zadeh’s distiction between Fuzzy logic in a restricted sense and in a general sense. We shall argue that Trillas’s claim not only strongly supports the necessity for such a distinction, but provides a path of investigation which can preserve the conceptual innovativeness of the notion of fuzziness.

On Some “family resemblances” of Fuzzy Set Theory and Human Sciences

The aim of this paper is to underline the importance of detecting similarities or at least, ‘family resemblances’ among different fields of investigation. As a matter of fact, the attention will be focused mainly on fuzzy sets and a few features of human sciences; however, I hope that the arguments provided and the general context outlined will show that the problem of picking up (dis)similarities among different disciplines is of a more general interest. Usually strong dichotomies guide out attempts at understanding the paths along which scientific research proceed; i.e., soft versus hard sciences, humanities versus the sciences of nature, Naturwissenschaften versus Geisteswissenschaften, Kultur versus Zivilization, applied sciences and technology versus fundamental, basic (or, as has become recently fashionable to denote it, “curiosity driven”) research. However, the similarity or dissimilarity of different fields of investigation is - to quote Lotfi Zadeh - “a matter of degree”. This is particularly evident in the huge, composite, rich and chaotic field of the investigations having to do with the treatment of information, uncertainty, partial and revisable knowledge (and their application to different problems). The specific points treated in this paper can be then seen as case studies of a more general crucial question. A question which could be important in affording also the problems posed by interdisciplinarity. The specific point of the interaction between fuzzy sets and human sciences can be seen as an episode of a larger question. There is a long history, in fact, regarding the mutual relationship existing between the (so-called) humanities and the (so-called) hard sciences, that has produced the so-called question of the two Cultures. At the end of the paper possible epistemological similarities between the development of Fuzzy Set theory and new emerging disciplines, like Trust Theory, will be briefly discussed.

Varieties of Vagueness, Fuzziness and a few foundational (and ontological) questions

In this paper we discuss the multifaceted nature of vagueness, the limits of (standard) set theory in dealing with the foundational aspects that a really innovating theory of vagueness should manifest, and the difficulties in outlining the possible features that such a type of new formalism should exhibit in order to be able to deal with such innovative aspects. We shall highlight some aspects of the role that Fuzzy Set Theory (FST) can play in this process.

A Few Remarks on the Roots of Fuzziness Measures

In the forty years from the introduction of Fuzzy Entropy, fuzziness measures has been employed in many different fields pertaining both hard and soft sciences, from medicine to art, from engineering to linguistics. If we look back at the road traveled, we can safely state that on of the main reasons for this enduring presence, and maybe the most underrated, is the truly uniqueness of the concept of fuzziness. Far from a reminiscence, this consideration is more of a projection on the future of fuzziness: we strongly believe that the innovation implicit in the concept, while having sometime hindered in the past its perception as a powerful paradigm and tool for the hard science community, will maintain fuzziness measures topical and relevant. New developments of Fuzzy Sets Theory such as Computing with Words, will need new ways of measuring, and new fuzzy measures.

Fuzziness and social life: Informal notions, formal definitions

A clear bidirectional path exists between everyday social and cultural life and the formal notions of uncertainty. If in recent times there has been a resurgence of the contribution of the formal notions of fuzziness and vagueness to disciplines such as aesthetics, medicine and more generally humanities, it is also true that concepts and phenomena from everyday reality are continually and usefully reused in order to build formal definitions that are more akin to the essence of things. In this paper, some notions connected with the handling of uncertainty, and particularly with FST, are outlined with the aim of benefitting the spontaneous emergence of new paths toward an unified theory of uncertainty.

Do Uncertainty and Fuzziness Present Themselves (and Behave) in the Same Way in Hard and Human Sciences

In the present paper the question whether uncertainty and fuzziness present themselves and behave in the same way (or not) in hard and human sciences will be briefly discussed. This problem came out from the attempt to answer the question asked by Lotfi Zadeh on the (apparent) strangeness of a very limited use of fuzzy sets in human sciences.

Future Is Where Concepts, Theories and Applications Meet (also in Fuzzy Logic)

No one knows where the future lies, and the idea of serendipity in science is now raised to something of a tropism. This does not impede our will to predict, if not the exact events, at least the short–term trends in the disciplines we live and breathe, and to point at the (subjective) glaring chances for a bright future. This volume is a clear example of the need that any living scientific discipline has for constant regrouping and redirection, in a never–ending process of consolidating results and finding new paths. In this contribution we will try and focus on a number of areas of fuzzy logic and, by extension, in the whole word of uncertainty, where (in our opinion) a number of interesting future developments can and will happen. While our comments and ideas about the technical aspects of the evolution hereby forecasted are proper to the realm of Fuzziness and much dependent on our previous work and experience in the field, the knowledge we have amassed and our personal preferences and quirks, the general remarks of a more epistemological nature interspersed and concluding this paper should and could be applied, in our view, to the development of any scientific endeavour.

Experimental Modeling for a Natural Landing of Fuzzy Sets in New Domains

In this paper we plan to touch upon (and briefly discuss) some (out of the many) contributions done by Enric Trillas to Fuzzy Sets Theory. We have carefully chosen, from the abundant panorama we have been allowed to gaze at in the years, two different but intertwined topics of a more methodological character, which—as such—are, obviously, not only outside the topics massively developed by the scientific community in this field but also not in the mainstream of Enric’s investigations. We picked up them, however, since we believe that they are related to a crucial problem for the further developments of fuzzy research in the subsequent years. In this perspective, they represent a very significative element of the legacy that Enric Trillas has bestowed on Fuzzy Sets, besides his long-lasting and seminal specific scientific achievements.