In this paper, we further investigate the constructions of fuzzy connectives on a complete lattice. We firstly illustrate the concepts of left (right) semi-uninorms and implications satisfying the order property by means of some examples. Then we give out the formulas for calculating the upper and lower approximation implications, which satisfy the order property, of a binary operation.

We recover the rays in the tensor product of Hilbert spaces within a larger class of so called ‘states of compoundness’, structured as a complete lattice with the ‘state of separation’ as its top element. At the base of the construction lies the assumption that the cause of actuality of a property of one individual entity is actuality of a property of the other.

We evaluated some particular type of functional integral over the local gauge group C(R, U(1)) by going to a discretized lattice. The results explicitly violates the property of the Haar measure. We also analysed the FaddeevPopov method through a toy example. The results also violates the property of the Haar measure. PACS numbers:11.15.-q; 12.20.-m Typeset using REVTEX

This paper establishes a new preservation property of supermodularity in a class of two dimensional parametric optimization problems, where the constraint set may not be a lattice. This property and its extensions include several existing results in the literature as special cases, and provide powerful tools as we illustrate their applications to several operations models.

We prove a Fredholm alternative theorem for a class of asymptotically hyperbolic linear diierential diierence equations of mixed type. We also establish the cocycle property and the spectral ow property for such equations, providing an eeective means of calculating the Fredholm index. Such systems can arise from equations which describe traveling waves in a spatial lattice.

The Congruence Lattice Problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of a lattice. It was hoped that a positive solution would follow from E. T. Schmidt’s construction or from the approach of P. Pudlák, M. Tischendorf, and J. Tůma. In a previous paper, we constructed a distributive algebraic lattice A with א2 compact elements that cannot be ob...

In this note we prove: If a subdirect product of ̄nitely many ̄nite projective geometries has the cover-preserving embedding property, then so does each factor. In what follows all the lattices will be ̄nite modular ones. A ̄nite lattice K has the cover-preseving embedding property, abbreviated as CPEP with respect a variety V of lattices if whenever K can be embedded into a ̄nite lattice L in ...

In this paper, we introduce the property (h) on Banach lattices and present its characterization in terms of disjoint sequences. Then, an example is given to show that order-to-norm continuous operator may not be σ-order continuous. Suppose T:E→F order-bounded from Dedekind σ-complete lattice E into complete F. We prove T σ-order-to-norm if only both order weakly compact addition, can represent...