A classical question in the theory of functional equations is “when is it true that a mapping, which approximately satisfies a functional equation, must be somehow close to an exact solution of the equation?” Such a problem, called a stability problem of the functional equation, was formulated by Ulam 1 in 1940. In the next year, Hyers 2 gave a partial solution of Ulam’s problem for the case of...

This article shows how different functional interpretations can be combined into what we term hybrid functional interpretations. These hybrid interpretations work on the setting of a multi-modal linear logic. Functional interpretations of intuitionistic logic can be combined via Girard’s embedding of intuitionistic logic into linear logic. We first show how to combine the usual Kreisel’s modifi...

in this paper, a new method based on parametric form for approximate solu-tion of fuzzy linear matrix equations (flmes) of the form ax = b; where ais a crisp matrix, b is a fuzzy number matrix and the unknown matrix x one,is presented. then a numerical example is presented to illustrate the proposedmodel.

this paper deals with ridge estimation of fuzzy nonparametric regression models using triangular fuzzy numbers. this estimation method is obtained by implementing ridge regression learning algorithm in the la- grangian dual space. the distance measure for fuzzy numbers that suggested by diamond is used and the local linear smoothing technique with the cross- validation procedure for selecting t...

a‎s we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system's parameters are proposed as fuzzy numbers is very important in fuzzy set theory. for this reason, many researchers have used various numerical methods to solve fuzzy linear systems. in this paper, we define the concepts of midpoint a...

We give an example of a bounded discontinuous divergence-free solution of a linear elliptic system with measurable bounded coefficients in R and a corresponding example for a Stokes-like system.

This paper addresses the synthesis of a predictive controller for a nonlinear process based on a fuzzy model of the Takagi–Sugeno (T–S) type, resulting in a stable closed-loop control system. Conditions are given that guarantee closed-loop robust asymptotic stability for open-loop bounded-input–boundedoutput (BIBO) stable processes with an additive 1-norm bounded model uncertainty. The idea is ...

in the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. in particular, it isshown that the cauchy-schwarz inequality holds. moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy hilbert space has a complementary subspace.finally, the notions of fuzzy bo...

The rationality of a fuzzy choice function is a hot research topic in the study of fuzzy choice functions. In this paper, two common fuzzy sets are studied and analyzed in the framework of the Banerjee choice function. The complete rationality and bounded rationality of fuzzy choice functions are defined based on the two fuzzy sets. An assumption is presented to study the fuzzy choice function,...

The weak sequential compactness of reflexive Banach spaces is used to explain the fact that certain ill-posed, linear problems become well-posed if the solutions are required to satisfy a prescribed bound. Applications are made to the computability of solutions of ill-posed problems associated with elliptic and parabolic partial differential equations.