
12 July 2017

08:00AM  10:00AM

Room: Catalana

Chairs: Didier Dubois, Stephen E. Rodabaugh and Austin Melton
Fuzziness and the Mathematics of ManyValuedness
Abstract  Let Sup be the category of complete lattices and join preserving maps. The aim of this talk is to show that the theory of complete manyvalued lattices exists. For this purpose we recall the concept of manyvalued preordered sets and show that the category of manyvalued joincomplete lattices is isomorphic to the category of right modules in Sup  a theorem which goes back to I. Stubbe 2006 in a more general context given by quantaloid enriched categories. Finally, the presented theory will be explained by some natural examples.
Abstract  In the past there have been made various attempts to define the spectrum of a noncommutative Cstaralgebra. But all these definitions have certain drawbacks  e.g. C.J. Mulvey's definition does not coincide with the standard definition of the spectrum in the commutative case. The aim of our talk is to give an alternative definition of the spectrum which does not suffer under this deficit  i.e. coincides with the standard situation in the commutative setting. For this purpose we recall some properties of balanced and bisymmetric quantales, introduce a definition of the spectrum of a Cstaralgebra working for the general case and develop subsequently its topological representation.
Abstract  In this paper we define the Smarandache hoopalgebras and QSmarandache filters, we obtain some related results. After that, by considering the notions of these filters we determine relationships between filters in hoopalgebras and QSmarandache filters in hoopalgebras. Finally, we introduce the concept of Smarandache 2structure and Smarandache 2filter on hoopalgebras.
Abstract  In applications, for example in health care, many valuedness modelled using quantales plays an important role. The paper presents variations of the three chain modules over unitalization of the three chain quintile (three chain is the smallest possible quantale to model manyvaluedness), thus, variations of right actions are given. From application point of view, it is then possible to choose suitable modules when modelling, for example, the causalities between disease, intervention and functioning. Effects of drug interactions in presence of multiple diseases, and as affecting functioning, adds to this complexity. Health care communities and professionals comply with a range classifications and terminologies, also including scales to qualify strength or hierarchies of evidence (in the sense of evidencebased medicine) or interaction, or as related to levels of functioning. Such hierarchies adopted in health care are ad hoc as compared to the potentially algebraic and logic structures of terminology infused reasoning. In this paper we show how these hierarchies canonically derive as actions where transitions appear as levels in hierarchies of evidence. We will also see how threevaluedness related to health conditions, rather than twovaluedness, is the generator many valuedness related to strength of evidence.
Abstract  In this paper fuzzy (tied) relational systems are considered which are the objects of semicategories whose morphisms constitute a general variablebasis approach to fuzzy Galois connections and conjugated pairs. Useful applications to some kinds of algebraic structures are outlined.
Abstract  The purpose of this paper is to make a case for the value of manyvalued mathematics, often called fuzzy mathematics. We believe there may be a difference between manyvalued mathematics and fuzziness, as used by those who work with fuzzy logic and fuzzy set theory and applications thereof. We think that most, if not all, fuzzy mathematics is manyvalued. However, for this paper, the difference between manyvalued mathematics and fuzzy mathematics, if a difference exists, is not important. We are. in this paper, content to show that manyvalued mathematics can contribute to mathematics. We do understand that for those mathematicians who feel that manyvalued mathematics does not have a place in mathematics this paper will not cause them to embrace manyvalued mathematics, but we would like for some of them to consider that manyvalued mathematics might be able to contribute to mathematics. In this paper, we give an example of a mathematical construction which was created and defined in part to help computer scientists understand and be able to use topological ideas and concepts in their work as computer scientists. Thus, one would think that this construction, called topological systems, would be topological (as defined later). However, it seems that topological systems are clearly not topological. Thus, an interesting question is can topological systems be made topological, or said more mathematically, can topological systems be embedded into something which is topological.