Every lattice is the complete join of all its one-element sublattices. In this paper we address the question: Which lattices L have the property that L is finitely join reducible in SubL? That is, when do there exist proper sublattices A, B such that L = A∨B? In particular, could it be that every nontrivial lattice has this property, in which case every element of SubL would be finitely join re...

Let L be a finite distributive lattice. Let Sub0(L) be the lattice {S | S is a sublattice of L} ∪ {∅} and let ∗[Sub0(L)] be the length of the shortest maximal chain in Sub0(L). It is proved that if K and L are non-trivial finite distributive lattices, then ∗[Sub0(K × L)] = ∗[Sub0(K)] + ∗[Sub0(L)]. A conjecture from the 1984 Banff Conference on Graphs and Order is thus proved. 1 Motivation Let L...

we show that the lattice of all ideals of a ring $r$ can be embedded in the lattice of all its fuzzyideals in uncountably many ways. for this purpose, we introduce the concept of the generalizedcharacteristic function $chi _{s}^{r} (a)$ of a subset $a$ of a ring $r$ forfixed $r , sin [0,1] $ and show that $a$ is an ideal of $r$ if, and only if, its generalizedcharacteristic function $chi _{s}^{...

based on credibilistic value-at-risk (cvar) of regularfuzzy variable, we introduce a new cvar reduction method fortype-2 fuzzy variables. the reduced fuzzy variables arecharacterized by parametric possibility distributions. we establishsome useful analytical expressions for mean values and secondorder moments of common reduced fuzzy variables. the convex properties of second order moments with ...

In this paper, firstly, we gain some basic properties and characterization theorems of the differential and local sub-differential of the fuzzy mapping, obtain an important result that the local sub-differential of fuzzy mapping is an empty set or a convex set. Secondly, we generalize the concept of local differentiability of fuzzy mapping, and obtain some basic properties about the concept. At...

Based on credibilistic value-at-risk (CVaR) of regularfuzzy variable, we introduce a new CVaR reduction method fortype-2 fuzzy variables. The reduced fuzzy variables arecharacterized by parametric possibility distributions. We establishsome useful analytical expressions for mean values and secondorder moments of common reduced fuzzy variables. The convex properties of second order moments with ...

This paper presents the concept of partition of a nonempty fuzzy set in nonempty convex fuzzy subsets. We restrict our discussion when the universal set, where are defined the fuzzy sets, is the real n-dimensional Euclidean space. We also show that a nonempty fuzzy set has a least one partition in nonempty convex fuzzy subsets.

The paper presents the problem of decentralized state feedback control for nonlinear interconnected systems with time-varying delay in both states and inputs which is composed by a number of Takagi-Sugeno (T-S) fuzzy bilinear subsystems with interconnections. Based on the Lyapunov criterion and the parallel distribute compensation scheme, the delay-dependent stabilization sufficient conditions ...

We say that a C*-algebra A has the ‘sublattice property’ if the set P(A) of all projections in A is a sublattice of the projection lattice of its enveloping von Neumann algebra A∗∗. It is shown that this property is equivalent to the requirement that all pairs of projections have strictly positive ‘angle’. We discuss this property in relation to some results obtained by C. Akemann and by A. Laz...

This paper presents the problem of decentralized robust control for discrete-time fuzzy bilinear interconnected large-scale system. Based on the Lyapunov criterion and the parallel distribute compensation (PDC) scheme, the sufficient conditions are derived to guarantee the robust stability of the overall fuzzy system via bilinear matrix inequalities (BMIs). The V-K iteration algorithm is employ...