In this paper, we propose a constructive method to develop a fuzzy system having a monotonic input–output relationship and prove that the developed fuzzy system can approximate any continuously differentiable monotonic function with any desired degree of accuracy. The fuzzy system is constructed with complete and consistent input membership functions and imposes special parametric constraints o...

‎In this paper‎, ‎we shall establish some extended Simpson-type inequalities‎ ‎for differentiable convex functions and differentiable concave functions‎ ‎which are connected with Hermite-Hadamard inequality‎. ‎Some error estimates‎ ‎for the midpoint‎, ‎trapezoidal and Simpson formula are also given‎.

In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on time scales. Usingthe derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. Wepresent some examples to illustrate our results.

Abstract In this paper, we introduce a new concept of sets and class functions called $$\alpha$$ α - E -invex V-E-preinvex functions. Furthermore, generalized convexity is introduced for (not necessarily) differentiable vector optimization problems. Namely, the V -type I defined -differentiable problem. A num...

In this paper, we obtain fuzzy approximations to fuzzy differentiable functions by means of fuzzy linear operators whose positivity condition and classical limits fail. In order to get more powerful results than the classical approach we investigate the effects of matrix summability methods on the fuzzy approximation. So, we mainly use the notion of A-statistical convergence from summability th...

Based on Colombeau’s theory of algebras of generalized functions we introduce the concepts of generalized functions taking values in differentiable manifolds as well as of generalized vector bundle homomorphisms. We study their basic properties, in particular with respect to some new point value concepts for generalized functions and indicate applications of the resulting theory in general rela...