One of the useful methods of the singularity theory, the method of real morsifications [AC0, GZ] (see also [AGV]) reduces the study of discrete topological invariants of a critical point of a holomorphic function in two variables to the study of some real plane curves immersed into a disk with only simple double points of self-intersection. For the closed real immersed plane curves V.I.Arnold [...

The fuzzy extension principle has been widely used to extend the domain of mathematical functions and relations from elements of a referential set to fuzzy subsets of that referential set. However, there are restrictions associated with the fuzzy extension principle. This paper addresses the question how restricted is the family of “fuzzy set to fuzzy set mappings” obtained by the fuzzy extensi...

An important tool for the construction of tight wavelet frames is the Unitary Extension Principle first formulated in the Fourierdomain by Ron and Shen. We show that the time-domain analogue of this principle provides a unified approach to the construction of tight frames based on many variations of multiresolution analyses, e.g., regular refinements of bounded L-shaped domains, refinements of ...

Optimization problems in the fuzzy environment are widely studied literature. We restrict our attention to mathematical programming with coefficients and/or decision variables expressed by numbers. Since review of recent literature on shows that extension principle is present through arithmetic but much less involved foundations solution concepts, we believe efforts rehabilitate idea following ...