Minimization approach to membership evaluation in fuzzy sets and error analysis

Evaluation of the degree of membership in fuzzy sets is a fundamental topic in fuzzy set theory. Saaty (Ref. 1) proposes a method for solving this problem that has been widely accepted. In this paper, we examine the problem from an error minimization point of view that attempts to reflect the real intentions of the decision maker. When this approach is used, the findings reveal that fuzzy sets of different cardinalities have dramatically different requirements in the consistency level of the input data as far as the error minimization criterion is concerned.     

粗集决策表简化理论研究

对粗集决策表简化理论进行研究 ,为了提高决策表简化算法效率 ,通过研究得出几个定理 ,并将其应用于决策表简化算法设计。     

On the existence of a finite invariant measure

A necessary and sufficient condition is given for a Borel automorphism on a standard Borel space to admit an invariant probability measure.     

基于粗糙集与层次分析法的组合预测方法

本文在改进的属性约简启发式算法 ,即应用加权平均的属性重要度对属性进行约简的基础上 ,将粗糙集理论和层次分析相结合 ,给出了一种全新的组合预测方法 .     

模糊粗糙集及粗糙模糊集的贴近度及其应用

本文研究了模糊粗糙集（FR集）及粗糙模糊集（RF集）的贴近度，是权衡两个FR集，两个RF集彼此糙近程度的一种标尺，进而研究了FR集，RF集的内积，外积，引进了FR集，RF集的格贴近度，并在此基础上提出一种新的属性约简的方法。     

The Index Set of Injectively Enumerable Classes of Recursively Enumerable Sets in ∑5-Complete

I introduce an effective enumeration of all effective enumerations of classes of r. e. sets and define with this the index set IE of injectively enumerable classes. It is easy to see that this set is ∑₅ in the Arithmetical Hierarchy and I describe a proof for the ∑₅-hardness of IE. Mathematics Subject Classification: 03D25, 03D45.     

New NCP-Functions and Their Properties

Recently, Luo and Tseng proposed a class of merit functions for the nonlinear complementarity problem (NCP) and showed that it enjoys several interesting properties under some assumptions. In this paper, adopting a similar idea to that of Luo and Tseng, we present new merit functions for the NCP, which can be decomposed into component functions. We show that these merit functions not only share many properties with the one proposed by Luo and Tseng but also enjoy additional favorable properties owing to their decomposable structure. In particular, we present fairly mild conditions under which these merit functions have bounded level sets.     

Ordering fuzzy sets over the real line: An approach based on decision making under uncertainty

The ordering of fuzzy sets over the real line is approached from the point of view of ordering intervals rather than ordering numbers. First, the maximax and maximin criteria which are commonly used for ordering intervals are expressed in terms of characteristic functions. These criteria and the Hurwicz criterion for decision making under complete ignorance are then reformulated in a manner that allows for their generalization to the fuzzy case. Transitivity is established for these ordering rules. A criterion based on the principle of diminishing marginal utility is also presented.     

Extremal Polygons with Minimal Perimeter

In this paper we will investigate an isoperimetric type problem in lattices. If K is a bounded O-symmetric (centrally symmetric with respect to the origin) convex body in En of volume v(K) = 2n det L which does not contain non-zero lattice points in its interior, we say that K is extremal with respect to the given lattice L. There are two variations of the isoperimetric problem for this class of polyhedra. The first one is: Which bodies have minimal surface area in the class of extremal bodies for a fixed n-dimensional lattice? And the second one is: Which bodies have minimal surface area in the class of extremal bodies with volume 1 of dimension n? We characterize the solutions of these two problems in the plane. There is a consequence of these results, the solutions of the above problems in the plane give the solution of the lattice-like covering problem: Determine those centrally symmetric convex bodies whose translated copies (with respect to a fixed lattice L) cover the space and have minimal surface area.