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 ...

We extend Hardy’s uncertainty principle for a square integrable function ψ and its Fourier transform to the n-dimensional case using a symplectic diagonalization. We use this extension to show that Hardy’s uncertainty principle is equivalent to a statement on the Wigner distribution Wψ of ψ. We give a geometric interpretation of our results in terms of the notion of symplectic capacity of an el...

The extension principle defines the arithmetic operations on fuzzy numbers. In the extension principle one can use any t-norm for modeling the conjunction operator. It is therefore important to know, which t-norms are consistent with a particular type of fuzzy number. We call a t-norm consistent, if the arithmetic operation is closed. In this paper we investigate the addition of sigmoid and two...

We investigate leading order deviations from general relativity that violate the Einstein equivalence principle in the gravitational standard model extension. We show that redshift experiments based on matter waves and clock comparisons are equivalent to one another. Consideration of torsion balance tests, along with matter-wave, microwave, optical, and Mössbauer clock tests, yields comprehensi...

This paper surveys the progress made on pairwise orthogonal wavelet frames and comments on the construction methods. There are a few known constructions based on the unitary extension principle, a paraunitary matrix and a given modulation matrix. A polyphase matrix based construction method has been presented which satisfies the condition of unitary extension principle yielding pairwise orthogo...

We discuss some optimization problems for fuzzy variable functions and show two interesting results. First result is related to conditions for existence of global optimal solutions for some general class of optimization problems on E, the space of compacts, upper semicontinuous and normal fuzzy sets of R. The second result is about preservation of local optimality points, via Zadeh’s principle ...

One of the major driven forces in the area of applied and computational harmonic analysis over the last decade or longer is the development of redundant systems that have sparse approximations of various classes of functions. Such redundant systems include framelet (tight wavelet frame), ridgelet, curvelet, shearlet and so on. This paper mainly focuses on a special class of such redundant syste...