Here a is a positive semidefinite symmetric matrix for each t and x, and b is a d vector for each t and x. There are various ways of describing exactly what we mean by a diffusion process corresponding to the specified set of coefficients. We shall adopt the following approach. Let Q be the space of Rd valued continuous functions on [0, cc). The value of a function ow = x( ) in Q at time t will...

Following M. Krachounov ([5]), max and min operations with fuzzy sets are considered instead of Lukasiewicz ones ([6], [7], [8], [9]). Her the domain F of a probability m : F → [0, 1] consists on IF-events A = (μA, νA) i.e. mappings from a measurable space (Ω,S) to the unit square ([1]). Local representation of sequences of M -observables by random variables is constructed and three kinds of co...

Fuzzy clustering algorithm can not obtain good clustering effect when the sample characteristic is not obvious and need to determine the number of clusters firstly. For thi0s reason, this paper proposes an adaptive fuzzy kernel clustering algorithm. The algorithm firstly use the adaptive function of clustering number to calculate the optimal clustering number, then the samples of input space is...

In this paper, we study lacunary statistical convergence in intuition-istic fuzzy normed space. We also introduce here a new concept, that is, statistical completeness and show that IFNS is statistically complete but not complete.

This paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new...

We introduce a notion of topological quandle. Given a topological quandle Q we associate to every classical link L in R an invariant JQ(L) which is a topological space (defined up to a homeomorphism). The space JQ(L) can be interpreted as a space of colourings of a diagram of the link L with colours from the quandle Q.

In this note we obtain necessary and sufficient conditions for a convergence space to have a smallest Hausdorff compactification and to have a smallest regular compactification. Introduction. A Hausdorff convergence space as defined in [1] always has a Stone-Cech compactification which can be obtained by a slight modification of the result in [3]. But in general this need not be the largest Hau...

In this paper we start with a lattice (X,∨,∧) and define, in terms of ∨, a family of crisp hyperoperations tp (one hyperoperation for each p ∈ X). We show that, for every p, the hyperalgebra (X,tp) is a join space and the hyperalgebra (X,tp,∧) is very similar to a hyperlattice. Then we use the hyperoperations tp as p-cuts to introduce an L-fuzzy hyperoperation t and show that (X,t) is an L-fuzz...

We define interval valued (∈,∈∨q)-fuzzy k-ideals, interval valued (∈,∈∨q)-fuzzy k-quasi-ideals, interval valued (∈,∈∨q)-fuzzy k-bi-ideals and characterize k-regular and k-intra regular hemirings by the properties of interval valued (∈,∈∨q)-fuzzy k-ideals, interval valued (∈,∈∨q)-fuzzy k-quasi-ideals and interval valued (∈,∈∨q)-fuzzy k-bi-ideals. 2010 mathematics subject classification: 16Y60 • ...