抄録
We propose here a new theory of a multiple fuzzy set(MFS) defined on the frameworks(=dependent coordinates system as a support set) composed of vectors in a unit circle, which is taken out from a universe of static frameworks(set of support sets). And we propose another new concept of "fuzziness" concerning how to be seen through the spectacles applied to the frameworks. The measures of spectacles are constructed on the basis of relationship. Further, we propose a new methodology to express a MFS in the geometrically measurable form by using the reducing transformation technology. The diagram of transformed MFS(TMFS) is called by the name, COSMOS-DIAGRAM because of the close resemblance of the figures to the several appearances of natural objects such as trees, flowers, fireworks, constellations, cellular segmentations and so on. Lastly, we refer to its capability in several engineering fields as well as the mathematical interest.
