Mathematical models in science and engineering often contain parameters that are uncertain. These parameters are usually represented by random numbers, fields or processes. However, when the stochastic characteristics of these parameters are not precisely known, an interval representation, or, more generally, a fuzzy representation may be more appropriate. This leads to so-called fuzzy differen...

The fuzzy differential and integral equations are important part of the fuzzy analysis theory and they have the important value of theory and application in control theory. Seikkala in [8] has defined the fuzzy derivative which is the generalization of the Hukuhara derivative in [7], the fuzzy integral which is the same as that of Dubois and prade [1], and by means of the extension principle of...

Adomian decomposition method has been applied to solve many functional equations so far. In this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. We interpret a fuzzy differential equation by using the strongly generalized differentiability. Also one concrete application for ordinary fuzzy differential equation with fuzzy input data...

LI, PINGKE. Fuzzy Relational Equations: Resolution and Optimization. (Under the direction of Professor Shu-Cherng Fang). Fuzzy relational equations play an important role as a platform in various applications of fuzzy sets and systems. The resolution and optimization of fuzzy relational equations are of our particular interests from both of the theoretical and applicational viewpoints. In this ...

Multi-dimensional Fuzzy differential equations driven by multi-dimensional Liu process, have been intensively applied in many fields. However, we can not obtain the analytic solution of every multi-dimensional fuzzy differential equation. Then, it is necessary for us to discuss the numerical results in most situations. This paper focuses on the numerical method of multi-dimensional fuzzy differ...

Abstract: We introduce some fuzzy set-valued functional equations, i.e. the generalized Cauchy type (in n variables), the Quadratic type, the Quadratic-Jensen type, the Cubic type and the Cubic-Jensen type fuzzy set-valued functional equations and discuss the Hyers-Ulam-Rassias stability of the above said functional equations. These results can be regarded as an important extension of stability...

In the literature, the solution set of a system of bipolar fuzzy relational equations with max-min composition can be characterized by a finite set of maximal and minimal solution pairs. However, some researches presented that determining the consistency of a system of bipolar fuzzy relational equations is NP-complete. Namely, the solution procedure for solving a system of bipolar fuzzy relatio...

in this paper, existence theorems for the fuzzy volterra-fredholm integral equations of mixed type (fvfiemt) involving fuzzy number valued mappings have been investigated. then, by using banach's contraction principle, sufficient conditions for the existence of a unique solution of fvfiemt are given. finally, illustrative examples are presented to validate the obtained results.

in this paper, we present gauss-sidel and successive over relaxation (sor) iterative methods for finding the approximate solution system of fuzzy sylvester equations (sfse), ax + xb = c, where a and b are two m*m crisp matrices, c is an m*m fuzzy matrix and x is an m*m unknown matrix. finally, the proposed iterative methods are illustrated by solving one example.

in this paper, we investigate the general fuzzy linear system of equations.  the  main aim of this paper is based on the embedding approach. we find the necessary and sufficient conditions for the existence of fuzzy solution of the mentioned systems.  finally, numerical examples are presented to more illustration of the proposed model.