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 multi-fuzzy 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.

Abstract. In this paper, the theoretical aspects of calculating the similarity between sets, and its generalizations multisets, fuzzy sets and fuzzy multisets, is presented. Afterwards, this theory is applied to enhance the facilities for accessing a multimedia system, namely when searching for correspondence between multi-valued attributes, which are coupled with a thesaurus. Furthermore, to allow flexibility in this search, thesauri with similarities defined between the thesaurus terms are considered. As a possible application, the DEKKMMA project is introduced, a project about an audio archive of African music. 1

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

Fuzzy set theory opens new vistas in computability theory and here I show this by defining a new computational metaphor—the fuzzy chemical metaphor. This metaphor is an extension of the chemical metaphor. In particular, I introduce the idea of a state of a system as a solution of fuzzy molecules, that is molecules that are not just different but rather similar, that react according to a set of fuzzy reaction rules. These notions become precise by introducing fuzzy labeled transition systems. Solutions of fuzzy molecules and fuzzy reaction rules are used to define the general notion of a fuzzy chemical abstract machine, which is a realization of the fuzzy chemical metaphor. Based on the idea that these machines can be used to describe the operational semantics of process calculi and algebras that include fuzziness as a fundamental property, I present a toy calculus that is a fuzzy equivalent of the π-calculus. 1

In this paper an attempt is made to extend the concept of topological spaces in the context of multisets (mset, for short). The paper begins with basic definitions and operations on msets. The mset space [X] w is the collection of msets whose elements are from X such that no element in the mset occurs more than finite number (w) of times. Different types of collections of msets such as power msets, power whole msets and power full msets which are submsets of the mset space and operations under such collections are defined. The notion of M-topological space and the concept of open msets are introduced. More precisely, an M-topology is defined as a set of msets as points. Furthermore the notions of basis, sub basis, closed sets, closure and interior in topological spaces are extended to M-topological spaces and many related theorems have been proved. The paper concludes with the definition of continuous mset functions and related properties, in particular the comparison of discrete topology and discrete M-topology are established.