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Fuzzifying P Systems
, 2003
"... Uncertainty is an inherent property of all living systems. Curiously enough, computational models inspired by biological systems do not take, in general, under consideration this essential aspect of living systems. In this paper, after introducing the notion of a multifuzzy set (i.e., multisets ..."
Abstract

Cited by 5 (2 self)
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Uncertainty is an inherent property of all living systems. Curiously enough, computational models inspired by biological systems do not take, in general, under consideration this essential aspect of living systems. In this paper, after introducing the notion of a multifuzzy set (i.e., multisets where objects are repeated to some degree), we introduce two variants of P systems with fuzzy components: P systems with fuzzy data and P systems with fuzzy multiset rewriting rules. By silently assuming that fuzzy data are not the result of some fuzzification process, P systems with fuzzy data are shown to be a step towards real hypercomputation.
Mathematics of Multisets Apostolos Syropoulos
 In Multiset Processing
, 2001
"... This paper is an attempt to summarize most things that are related to multiset theory. We begin by describing multisets and the operations between them. Then we present hybrid sets and their operations. We continue with a categorical approach to multisets. Next, we present fuzzy multisets and their ..."
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This paper is an attempt to summarize most things that are related to multiset theory. We begin by describing multisets and the operations between them. Then we present hybrid sets and their operations. We continue with a categorical approach to multisets. Next, we present fuzzy multisets and their operations. Finally, we present partially ordered multisets. 1
Preface
, 2000
"... in a series devoted to explicitlyand coherentlydeveloping the FMT, the “Formal Multiset Theory”, following the experience and the model of FLT, the Formal Language Theory. It starts from two observations: (1) multisets appear “everywhere ” (this is also proved bya series of papers in the present vol ..."
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in a series devoted to explicitlyand coherentlydeveloping the FMT, the “Formal Multiset Theory”, following the experience and the model of FLT, the Formal Language Theory. It starts from two observations: (1) multisets appear “everywhere ” (this is also proved bya series of papers in the present volume), and (2) Membrane Computing is a sort of distributed multiset rewriting framework, without having equallywell developed the nondistributed multiset rewriting (whatever “rewriting ” means when dealing with multisets). This is in contrast with what happened in formal language theory, where the grammar system branch has appeared manyyears after extensivelydealing with single grammars and single automata. As an immediate scope, the workshop is intended to gather together people interested in multiset processing (from a mathematical or a computer science point of view) and in membrane computing (P systems), grounding the development of the latter on the “theory” of the former (although this theorylooks rather scattered in this moment, spread in many papers, without anysystematic/monographic presentation). Taking seriouslythe etymology, the workshop will mean not onlypresentations, but also
True Platonic Heaven: A Scientific Fiction on the Limits of
"... Uncertainty is an inherent property of all living systems. Curiously enough, computational models inspired by biological systems do not take, in general, under consideration this essential aspect of living systems. In this paper, after introducing the notion of a multifuzzy set (i.e. an orthogonal ..."
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Uncertainty is an inherent property of all living systems. Curiously enough, computational models inspired by biological systems do not take, in general, under consideration this essential aspect of living systems. In this paper, after introducing the notion of a multifuzzy set (i.e. an orthogonal approach to the fuzzification of multisets), we introduce two variants of P systems with fuzzy components: P systems with fuzzy data and P systems with fuzzy multiset rewriting rules. By silently assuming that fuzzy data are not the result of some fuzzification process, P systems with fuzzy data are shown to be a promising step towards real hypercomputation. On the other hand, P systems with fuzzy multiset rewriting rules are shown to be equivalent to fuzzy Turing machines. The paper concludes with remarks concerning the present work and future research. In science we try to tell people things in such a way that they understand something that nobody knew before. In art, one takes something everyone knows and tries to express it in ways nobody ever thought before. Based on a dialogue from John L. Casti (2003), The One