A New View on Fuzzy Hypermodules

We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy     

Algebras of Random Operators Associated to Delone Dynamical Systems

We carry out a careful study of operator algebras associated with Delone dynamical systems. A von Neumann algebra is defined using noncommutative integration theory. Features of these algebras and the operators they contain are discussed. We restrict our attention to a certain C ^*-subalgebra to discuss a Shubin trace formula.     

Stone代数的Cayley表示定理

首先通过集代数得到了Stone代数的表示定理,然后证明了每一个Stone代数均嵌入到某个集合X上的一个Stone映射类S中.     

L-型模糊格蕴涵代数

This paper introduced the concept of L-fuzzy sub lattice implication algebra and discussed its properties. Proved that the intersection set of a family of L-fuzzy sub lattice implication algebras is a L-fuzzy sub lattice implication algebra, that a L-fuzzy sub set of a lattice implication algebra is a L-fuzzy sub lattice implication algebra if and only if its every cut set is a sub lattice implication algebra, and that the image and original image of a L-fuzzy sub lattice implication algebra under a lattice implication homomorphism are both L-fuzzy sub lattice implication algebras.     

Ultra <Emphasis Type="Italic">LI</Emphasis>-ideals in lattice implication algebras and <Emphasis Type="Italic">MTL</Emphasis>-algebras

A mistake concerning the ultra LI-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an LI-ideal to be an ultra LI-ideal are given. Moreover, the notion of an LI-ideal is extended to MTL-algebras, the notions of a (prime, ultra, obstinate, Boolean) LI-ideal and an ILI-ideal of an MTL-algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in MTL-algebra: (1) prime proper LI-ideal and Boolean LI-ideal, (2) prime proper LI-ideal and ILI-ideal, (3) proper obstinate LI-ideal, (4) ultra LI-ideal. This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. Y605389) and K. C. Wong Magna Fund in Ningbo University.     

Representation of Cubic Lattices by Symmetric Implication Algebras

In this paper a cubic lattice L(S) is endowed with a symmetric implication structure and it is proved that L(S) \ {0} is a power of the three-element simple symmetric implication algebra. The Metropolis–Rota’s symmetries are obtained as partial terms in the language of symmetric implication algebras.     

Computing Aviation Sparing Policies: Solving a Large Nonlinear Integer Program

Deployed US Navy aircraft carriers must stock a large number of spare parts to support the various types of aircraft embarked on the ship. The sparing policy determines the spares that will be stocked on the ship to keep the embarked aircraft ready to fly. Given a fleet of ten or more aircraft carriers and a cost of approximately 50 million dollars per carrier plus the cost of spares maintained in warehouses in the United States, the sparing problem constitutes a significant portion of the Navy’s resources. The objective of this work is to find a minimum-cost sparing policy that meets the readiness requirements of the embarked aircraft. This is a very large, nonlinear, integer optimization problem. The cost function is piecewise linear and convex while the constraint mapping is highly nonlinear. The distinguishing characteristics of this problem from an optimization viewpoint are that a large number of decision variables are required to be integer and that the nonlinear constraint functions are essentially “black box” functions; that is, they are very difficult (and expensive) to evaluate and their derivatives are not available. Moreover, they are not convex. Integer programming problems with a large number of variables are difficult to solve in general and most successful approaches to solving nonlinear integer problems have involved linear approximation and relaxation techniques that, because of the complexity of the constraint functions, are inappropriate for attacking this problem. We instead employ a pattern search method to each iteration of an interior point-type algorithm to solve the relaxed version of the problem. From the solution found by the pattern search on each interior point iteration, we begin another pattern search on the integer lattice to find a good integer solution. The best integer solution found across all interations is returned as the optimal solution. The pattern searches are distributed across a local area network of non-dedicated, heterogeneous computers in an office environment, thus, drastically reducing the time required to find the solution.     

ON THE INCOMPLETENESS OF A DESCENDING CHAIN OF EXTENSIONS OF IMPLICATIONAL S5

C5.ω is obtained by adding, schematically, to the strict-implicational fragment C5 of S5 the axiom ((p → q) → (q → p)) → (q → p). This paper presents a fully general proof that neither C5.ω nor any of a descending chain of its extensions is complete with respect to any class of frames, correcting the garbled details of a version skeched in an earlier paper (same Zeitschrift 31 (1985), 201-208).     

On a Boolean-valued Model of the Strict Implication System(Continuous)

The reference [4] proved the consistency of S1 and S2 among Lewis' five strict implication systems in the modal logic by using the method of the Boolean-valued model. But, in this method, the consistency of S3, S4 and S5 in Lewis' five strict implication systems is not decided. This paper makes use of the properties: (1) the equivalence of the modal systems S3 and P3, S4 and P4; (2) the modal systems P3 and P4 all contained the modal axiom T(□p → p); (3) the modal axiom T is correspondence to the reflexive property in VB. Hence, the paper proves: (a) ‖As31‖ = 1; (b) ‖AS41‖ = 1; (c) ‖AS5l‖ = 1 in the model (where B is a complete Boolean algebra, R is reflexive property in VB). Therefore, the paper finally proves that the Boolean-valued model VB of the ZFC axiom system in set theory is also a Boolean-valued model of Lewis' the strict implication system S3, S4 and S5.