This paper shows the best operators for sumof-products expressions. We first describe conditions of functions for product and sum operations. We examine all two-variable functions and select those that meet the conditions and then evaluate the number of product terms needed in the minimum sum-of-products expressions when each combination of selected product and sum functions is used. As a resul...

it is firstly proved that the multi-input-single-output (miso) fuzzy systems based on interval-valued $r$- and $s$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  a formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

We prove that a valued field of positive characteristic [Formula: see text] has only finitely many distinct Artin–Schreier extensions (which is property infinite NTP 2 fields) dense in its perfect hull. As consequence, it deeply ramified and text]-divisible value group residue field. Further, we partial analogue for fields mixed observe an open problem about 1-units this setting. Finally, fill ...