Abstract: This paper presents the analysis of six different classes of Petri nets: fuzzy Petri nets (FPN), generalized fuzzy Petri nets (GFPN), parameterized fuzzy Petri nets (PFPN), T2GFPN, flexible generalized fuzzy Petri nets (FGFPN), binary Petri nets (BPN). These classes were simulated in the special software PNeS® for the analysis of its pros and cons on the example of models which are dedicated to the decision-making process of passenger transport logistics. The paper includes the analysis of two approaches: when input values are filled with the experts’ knowledge; when fuzzy expectations represented by output values are added to the point. These approaches fulfill the possibilities of triples of functions which are replaced with different combinations of t-/s-norms.
Abstract: This paper presents three new methodologies for the
basic operations, which aim at finding new ways of computing union
(maximum) and intersection (minimum) membership values by
taking into effect the entire membership values in a fuzzy set. The
new methodologies are conceptually simple and easy from the
application point of view and are illustrated with a variety of
problems such as Cartesian product of two fuzzy sets, max –min
composition of two fuzzy sets in different product spaces and an
application of an inverted pendulum to determine the impact of the
new methodologies. The results clearly indicate a difference based on
the nature of the fuzzy sets under consideration and hence will be
highly useful in quite a few applications where different values have
significant impact on the behavior of the system.
Abstract: In this paper, The T-G-action topology on a set acted
on by a fuzzy T-neighborhood (T-neighborhood, for short) group is
defined as a final T-neighborhood topology with respect to a set of
maps. We mainly prove that this topology is a T-regular Tneighborhood
topology.