In this paper, we study the fuzzy differential equations in the quotient space of fuzzy numbers. We deal with the convergence of successive approximations of the initial value problem of the fuzzy differential equations under the general uniqueness assumption of Perron type utilizing the comparison functions that is rather instructive. We also discuss the approximate solutions and the error est...

This chapter addresses the issues in air interface designs for Cognitive Radios. Fuzzy logic system is used as one of the soft computing techniques to learn to sub optimality and vagueness. Many good, simple, and quick fuzzy based solutions have been developed since few decades in many diverse domains. Through this chapter, the authors first discuss the significance and need of soft computing t...

In this paper, the differential transformation method (DTM) was applied to solve fuzzy fractional heat equations. The elementary properties of this method were given. The approximate and exact solutions of these equations were calculated in the form of series with easily computable terms. The proposed method was also illustrated by some examples. The results revealed that DTM is a highly effect...

The hybrid fuzzy differential equations have a wide range of applications in science and engineering. We consider the problem of nding their numerical solutions by using a novel hybrid method based on fuzzy neural network. Here neural network is considered as a part of large eld called neural computing or soft computing. The proposed algorithm is illustrated by numerical examples and the result...

In the paper the problem of mathematical properties of B-operations and weak WB-operations introduced by the author for interpretation of connectives “and”, “or”, and “also” in fuzzy rules is considered. In previous author’s papers some interesting properties of fuzzy systems with these operations were shown. These operations are weaker than triangular norms used commonly for a fuzzy system des...

We study a class of semi-linear mean curvature equations −Mu = H + λf(u) where M is the mean curvature operator. We show that there exists an extremal parameter λ∗ such that this equation admits a minimal weak solutions for all λ ∈ [0, λ∗], while no weak solutions exists for λ > λ∗. In the radial case, we then show that minimal solutions are classical solutions for all λ ∈ [0, λ∗] and that anot...

We prove weak-strong uniqueness results for the isentropic compressible Navier-Stokes system on the torus. In other words, we give conditions on a strong solution so that it is unique in a class of weak solutions. Known weak-strong uniqueness results are improved. Classical uniqueness results for this equation follow naturally.

In this paper we study the existence and asymptotic stability of periodic solutions of the differential equation ẍ+ f (x)ẋ+g(x) = h(t), where h(t) is T -periodic, f (x) is positive and g(x) is strictly monotonically increasing and has one or two weak singularities. The method of proof relies on the construction of a positively invariant region of the flux. Mathematics subject classification (20...