The idea of Sheffer stroke Hilbert algebra is studied from the perspective of the structure of the cubic structure. The filter and deductive system of the Sheffer stroke Hilbert algebra are defined and examined through the crossing cubic structure, which is an extension of the fuzziness of these substructures, verifying their many characteristics. Moreover, conditions suitable for the crossing cubic structure are established to be a crossing cubic filter and several characterization theorems are reached. Accordingly, the relationship between crossing cubic filters and filters of Sheffer stroke Hilbert algebras is explained such that the crossing cubic deductive system can handle all of the results for the crossing cubic filter covered above in the same way.
Al-Masarwah et al. (Fri,) studied this question.