Computing the variance of interval and fuzzy data

Massimo Spadoni; Luciano Stefanini

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Computing the variance of interval and fuzzy data

机译：计算区间和模糊数据的方差

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摘要

We propose an algorithm for the computation of the interval and fuzzy variance. In particular, based on the application of the max-min inequality, we obtain an upper bound to the maximization problem and we indicate how to obtain a feasible (heuristic) solution from the upper bound. The procedure requires the minimization of a unidimensional (continuous) convex function over a compact interval, for which efficient procedures exist. Having determined the upper bound, we are able to estimate the quality of any heuristic solution. Some computational results for problems of different dimensions are reported.

机译：我们提出了一种计算区间和模糊方差的算法。特别是，基于最大-最小不等式的应用，我们获得了最大化问题的上限，并指出了如何从上限获得可行的（启发式）解。该过程要求在一个紧凑的间隔内最小化一维（连续）凸函数，为此存在有效的过程。确定上限后，我们可以估算任何启发式解决方案的质量。报告了不同尺寸问题的一些计算结果。

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来源
《Fuzzy sets and systems》 |2011年第1期|p.24-36|共13页
作者
Massimo Spadoni; Luciano Stefanini;
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作者单位

MATEMATES (Department of Mathematics for Economic and Social Sciences), University of Bologna, Rimini branch, Italy;

DEMQ (Department of Economics and Quantitative Methods), University of Urbino"Carlo Bo ", Italy;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Interval variance; Interval uncertainty; Fuzzy uncertainty; Fuzzy variance;

机译：区间方差;区间不确定性;模糊不确定性;模糊方差;

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1. On-line algorithms for computing mean and variance of interval data, and their use in intelligent systems [J] . Kreinovich V, Nguyen HT, Wu BL Information Sciences: An International Journal . 2007,第16期

机译：在线计算区间数据均值和方差的算法及其在智能系统中的使用
2. Fast Algorithm for Computing the Upper Endpoint of Sample Variance for Interval Data: Case of Sufficiently Accurate Measurements [J] . GANG XIANG Reliable Computing . 2006,第1期

机译：快速计算间隔数据样本方差的上限算法：足够准确的测量结果
3. Computing variance for interval data in NP-hard [J] . Scott Ferson, Lev Ginzburg, Vlddik Kreinovich, SIGACT News . 2002,第2期

机译：在NP-hard中计算区间数据的方差
4. Interval-Valued and Fuzzy-Valued Random Variables: From Computing Sample Variances to Computing Sample Covariances [C] . Jan B. Beck, Vladik Kreinovich, Berlin Wu International Conference on Soft Methods in Probability and Statistics(SMPS'2004); 200405; Oviedo(ES) . 2004

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5. Comparative Analysis of Interval Type-2 Fuzzy PI Controllers with Different Antecedent Fuzzy Sets [D] . Yip, Chun Ming Tommy. 2018

机译：不同前一种模糊集的间隔类型2模糊PI控制器的比较分析
6. Incremental Interval Type-2 Fuzzy Clustering of Data Streams using Single Pass Method [O] . Sana Qaiyum, Izzatdin Aziz, Mohd Hilmi Hasan, 2020

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7. Interval-Valued and Fuzzy-Valued Random Variables: From Computing Sample Variances to Computing Sample Covariances [O] . Beck Jan B., Kreinovich Vladik, Wu Berlin 2004

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8. Confidence Intervals on a Ratio of Variances in the Two-Factor Crossed Components of Variance Model [R] . Graybill, F. A., Arteaga, C. E. 1980

机译：方差模型双因子交叉分量方差比的置信区间

Computing the variance of interval and fuzzy data

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