General decomposition of fuzzy relations: Semi-tensor product approach

Solvability of the matrix equation <inline-formula><tex-math id="M1">$ AX^{2} = B $</tex-math></inline-formula> with semi-tensor product

“…Recently, the solutions of the matrix equation AX = B in which the multiplication is semi-tensor product was discussed by Yao and Feng [21,7] in optimization and control analysis problems. The higher-order equation XX = R was also mentioned by Fan [6] in the investigation of fuzzy relation decomposition problems. In fact, high-order algebraic equations have important applications in file encryption and file transmission [17,18].…”

Multiobjective nonfragile fuzzy control for nonlinear stochastic financial systems with mixed time delays

“…Recently, T-S fuzzy systems have been used to efficient approximated nonlinear dynamic systems [1,9,15,28,30]. We also give an example to show that stochastic T-S fuzzy system (4) can effectively approximate nonlinear stochastic financial system (2) in the final simulation.…”

“…where U is the set of all the admissible control; the objective functional J 2 (u(t)) and J ∞ (u(t)) are defined in (9) and (10), respectively; the vector of the objective functionals (J 2 (u(t)), J ∞ (u(t))) is called objective vector of u(t).…”

On Solutions of the Matrix Equation A ∘ l X = B with respect to Jin1 2021Journal of Mathematics2000View full textAdd to dashboardCite

“…Matrix equations are a very important part of matrix theory [1], and they are often widely applied in many fields. For example, there have been a lot of researches about equations on economic theory [2], automation and information sciences [3][4][5], system and control theory [6][7][8], physics [9,10], and computing sciences [11,12]. For these fields, the numerical approximation solutions [13], least squares solutions [14], symmetric positive [15], and definite solutions [16] under various conditions can be obtained by direct or iterative methods.…”