In this paper we propose an approximation of piecewise linear membership functions with the help of sigmoid functions and certain arithmetic operations. The gradient-based tuning of piecewise linear membership functions can be achieved with the proposed efficient approximation because it has simple continuous derivatives. With this construction we can even approximate the Łukasiewicz operator f...

In this paper, a cooperative Continuous static game (F-CCSG) with fuzzy parameters in the cost function of the player is presented. Through the use of the ?-level sets of fuzzy numbers, the F-CCSG is converted to the corresponding ?-CCSG and an extended Pareto optimality concept called the ?-Pareto optimality is introduced. An algorithm for solving the ?-CCSG is suggested. The algorithm is base...

This is one of a series of papers examining the interplay between differentiation theory for Lipschitz maps, X → V , and bi-Lipschitz nonembeddability, where X is a metric measure space and V is a Banach space. Here, we consider the case V = L, where differentiability fails. We establish another kind of differentiability for certain X , including R and H, the Heisenberg group with its Carnot-Ca...

In this paper, the existence and uniqueness of the solution of a nonlinear fully fuzzy implicit integro-differential equation arising in the field of fluid mechanics is investigated. First, an equivalency lemma is presented by which the problem understudy is converted to the two different forms of integral equation depending on the kind of differentiability of the solution. Then, the conditions...

*Correspondence: [email protected] 1Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam Full list of author information is available at the end of the article Abstract In this paper the second-order random fuzzy differential equations (SRFDEs) under generalized Hukuhara differentiability are introduced. Un...

In this paper, dynamic behavior of a class of high-order fuzzy cellular neural networks (HFCNNs) with time-varying delays is investigated. Compared with the previous results in the literature, the restrictions are loosed, since we do not assume the boundedness and monotonicity on the activation functions, and the differentiability of time-varying delay functions. Some sufficient conditions are ...

This is one of a series of papers examining the interplay between differentiation theory for Lipschitz maps, X → V , and bi-Lipschitz nonembeddability, where X is a metric measure space and V is a Banach space. Here, we consider the case V = L, where differentiability fails. We establish another kind of differentiability for certain X , including R and H, the Heisenberg group with its Carnot-Ca...

We study a class of structured optimal control problems in which the main diagonal of the dynamic matrix is a linear function of the design variable. While such problems are in general challenging and nonconvex, for positive systems we prove convexity of the H2 and H∞ optimal control formulations which allow for arbitrary convex constraints and regularization of the control input. Moreover, we ...

Numerical study of various processes leads to the need clarification (extensions) limits applicability computational constructs and modeling tools. For dynamical systems, this question may be related with a generalization concept derivative, which keeps used constructions relevant. In article we introduce weak local differentiability in space Lebesgue integrable functions consider consistency s...