Fuzzy Weirstrass theorem and convex fuzzy mappings

The convexity and continuity of fuzzy mappings are defined through a linear ordering and a metric on the set of fuzzy numbers. The local-global minimum property of real-valued convex functions is extended to convex fuzzy mappings. It is proved that a strict local minimizer of a quasiconvex fuzzy mapping is also a strict global minimizer. Characterizations for convex fuzzy mappings and quasiconvex fuzzy mappings are given. In addition, the Weirstrass theorem is extended from real-valued functions to fuzzy mappings.     

关于Smarandache可乘函数的均值研究

本文的主要目的是利用初等方法研究Smarandache可乘函数在简单数集中的均值性质,并给出一个有趣的渐近公式。     

企业专网号码的合理编制

号码是一种有限的资源,虽然企业专网的号码资源比较丰富,但也不能毫无规律随意编制,否则会为将来发展带来意想不到的麻烦,本文叙述了号码编制必须遵循的一些原则,希望对专网的管理人员有一些帮助。     

Linear interpolation in a fuzzy information space

An approach to solving a linear interpolation problem in a fuzzy information space is proposed. Two different schemes of interpolation are outlined: a heuristic one, based on the geometrical interpretation of operations, and an optimization one, based on the expansion principle. The results obtained allow performing fuzzy linear prediction. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 55–68, March–April 2006.     

A general class of simple majority decision rules based on linguistic opinions

In this paper we have introduced a class of decision rules related to simple majority, by considering individual intensities of preference. These intensities will be shown by means of linguistic labels. In order to compare the amount of opinion obtained by each alternative, we have considered the total ordered monoid generated by the sums of the original labels, according to an addition and an ordering. In this general framework different sets of linguistic labels can be employed and these sets can be represented by means of diverse mathematical objects. Moreover, on these mathematical representations of linguistic labels several orderings can be considered. Thus, flexibility is an important feature of this new class of group decision making procedures. Some examples of putting in practice the simple majority decision rules based on linguistic labels are provided, and the main properties of these voting systems are analyzed. It is worth emphasizing that these properties are satisfied for any total ordered monoid, regardless of the mathematical representation of linguistic labels or the ordering used to compare collective opinions.     

The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making

In this paper, we present the induced generalized intuitionistic fuzzy ordered weighted averaging (I-GIFOWA) operator. It is a new aggregation operator that generalized the IFOWA operator, including all the characteristics of both the generalized IFOWA and the induced IFOWA operators. It provides a very general formulation that includes as special cases a wide range of aggregation operators for intuitionistic fuzzy information, including all the particular cases of the I-IFOWA operator, GIFOWA operator and the induced intuitionistic fuzzy ordered geometric (I-IFOWG) operator. We also present the induced generalized interval-valued intuitionistic fuzzy ordered weighted averaging (I-GIIFOWA) operator to accommodate the environment in which the given arguments are interval-valued intuitionistic fuzzy sets. Further, we develop procedures to apply them to solve group multiple attribute decision making problems with intuitionistic fuzzy or interval-valued intuitionistic fuzzy information. Finally, we present their application to show the effectiveness of the developed methods.     

基于FANUC数控系统实现刀具寿命管理

文章结合HARDINGE数控车床实例，介绍了如何利用FANUC18T数控系统中提供的计数器跟踪刀具加工的次数，通过新增一个刀具寿命管理功能模块的PMC子程序，为用户提供一个友好、可视、便捷的刀具寿命管理功能。对今后类似的设备功能设计和改进都具有实际的指导意义和参考价值。     

氧化还原反应式配平中可能差错的几种情况

本文通过许多实例，指出了氧化还原反应式配平中可能出现的得失电子数不等或电荷数未配平、得失电子关系不对及反应式中酸碱性介质有错误等几种差错，并归纳了在酸碱性水溶液中平衡介质的方法。     

PRAND: GPU accelerated parallel random number generation library: Using most reliable algorithms and applying parallelism of modern GPUs and CPUs

The library PRAND for pseudorandom number generation for modern CPUs and GPUs is presented. It contains both single-threaded and multi-threaded realizations of a number of modern and most reliable generators recently proposed and studied in Barash (2011), Matsumoto and Tishimura (1998), L’Ecuyer (1999,1999), Barash and Shchur (2006) and the efficient SIMD realizations proposed in Barash and Shchur (2011). One of the useful features for using PRAND in parallel simulations is the ability to initialize up to 10¹⁹${10}^{19}$ independent streams. Using massive parallelism of modern GPUs and SIMD parallelism of modern CPUs substantially improves performance of the generators.