Fuzzy functions: a fuzzy extension of the category SET and some related categories
<p>In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -&gt; L is distinguished which could be considered as fuzzy functions from an L-valued set (X,Ex) to an L-valued set (Y,Ey). We study basic properties of these functions, consider some properties of the corresponding category of L-valued sets and fuzzy functions as well as briefly describe some categories related to algebra and topology with fuzzy functions in the role of morphisms.</p>
Uncertainty Measures, Realizations and Entropies*
This paper presents the axiomatic foundations of uncertainty theories arising in quantum theory and artificial intelligence. Plausibility measures and additive uncertainty measures are investigated. The representation of uncertainty measures by random sets in spaces of events forms a common base for the treatment of an appropriate integration theory as well as for a reasonable decision theory.
Axiomatic Foundations Of Fixed-Basis Fuzzy Topology
This paper gives the first comprehensive account on various systems of axioms of fixed-basis, L-fuzzy topological spaces and their corresponding convergence theory. In general we do not pursue the historical development, but it is our primary aim to present the state of the art of this field. We focus on the following problems: