Osmo Kaleva

The Cauchy problem for fuzzy differential equations

Abstract We characterize those subsets of fuzzy sets in which the Peano theorem is valid for fuzzy differential equations.

Interpolation of fuzzy data

Abstract We will consider the interpolation of fuzzy data by a continuous fuzzy-valued function and give some numerical methods for calculating the fuzzy interpolant.

On the convergence of fuzzy sets

Three kind of convergences are defined on a space of fuzzy sets. Relationships between these convergences are studied. Some comments on the fixed point property are represented.

The calculus of fuzzy valued functions

Abstract We show that the notions of differentiability and integrability, which generalize those of Hukuhara-differentiability and Aumann-integrability, are consistent with the corresponding concepts introduced by Bobylev.

The Peano theorem for fuzzy differential equations revisited

In Kaleva [Fuzzy Sets and Systems 35 (1990) 389] we proved a Peano theorem for fuzzy differential equations. Recently, Friedman et al. [Fuzzy Sets and Systems 86 (1997) 331] provided a counterexample for the theorem. Here we refute this counterexample.

A comment on the completion of fuzzy metric spaces

We argue that in some recent papers discussing the completion of fuzzy metric and fuzzy normed spaces proper credit is not given to earlier works on the subject.

Nonlinear iteration semigroups of fuzzy Cauchy problems

In this paper we introduce an iteration semigroup of a nonlinear fuzzy-valued function. We show that the iterates converge and the limit function, called the fuzzy exponential function, is a solution to an autonomous fuzzy Cauchy problem.

A characterization of level-continuous fuzzy numbers

In this note we show that a fuzzy number is level-continuous if and only if it is semistrictly quasiconcave. Furthermore, we show that a level-continuous fuzzy set defined in R^n,n>1, is not necessarily semistrictly quasiconcave.

A note on compactness in a fuzzy metric space

We study the compactness in a fuzzy metric space. We also give a generalization of Niemytzki-Tychonoff theorem for a fuzzy metric space.

Stress–strain behavior of polyamide 6 staple fibers of punch-needled press felts under simulated wet-pressing conditions

This study evaluates the specific stress (tenacity) and strain (elongation) of polyamide 6 staple fibers, which were virgin, punch-needled on the press felt, and worn on the press felt under simulated wet-pressing conditions. The staple fibers were distinguished by molecular weights. The fiber deformation and defects were microscopically characterized after the felt preparation and aging. We discovered that the tensile breaking force and elongation of the polyamide 6 staple fibers decreased markedly during the felt preparation and aging. The mechanical reduction of staple fibers reflected their tenacity, work, and modulus values. Surprisingly, the linear density of staple fibers remained unchanged – although fibers strongly deformed and lost their mechanical properties after the felt aging. The results indicate that an increase in molecular weight improves the mechanical durability of staple fibers, the preparation of the press felt (punch-needling) decreases the tenacity and elongation of staple fibers, and humidity provokes their degradation.