We define the stochastic integrals of a set-valued process and a fuzzy process with respect to a cylindrical Brownian motion on a Hilbert space. We also give their properties, which are useful for the study of fuzzy stochastic differential equations and stochastic differential inclusions with a set-valued diffusion term.

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In this paper, we propose an acoustic block for widening the bandwidth and modulating center frequency of airborne transducers to improve the ultrasound imaging or metrology system. When acoustic block is attached, the characteristics of the ultrasonic transducer are changed by the squeeze film effect. Extra elastic and damping force are generated by squeeze film damping and can be changed according to parameters of acoustic block. For impedance matching, a CMUT vibrating in bending mode was used. The CMUT's FBW is 3.18 % and the center frequency is 103.5 kHz. We changed the area ratio of the acoustic block and attached it to the CMUT. The FBW was changed to 7.14 to 9.14 % and the center frequency to 108.7 to 112.1 kHz. With acoustic block, conventional transducers can be transformed into transducers with better performance in areas such as non-destructive testing and ultrasonic imaging.