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基于核和灰度的區(qū)間灰數(shù)運(yùn)算法則

時(shí)間:2023-05-06 18:36:00 社會(huì)科學(xué)論文 我要投稿

基于核和灰度的區(qū)間灰數(shù)運(yùn)算法則

摘要:區(qū)間灰數(shù)運(yùn)算是灰色系統(tǒng)的理論基礎(chǔ),對(duì)灰色系統(tǒng)理論發(fā)展的影響舉足輕重.首先給出了灰數(shù)核的定義,基于核和灰數(shù)灰度建立了區(qū)間灰數(shù)運(yùn)算公理、運(yùn)算法則和新的灰代數(shù)系統(tǒng),并研究了運(yùn)算性質(zhì).至此,灰數(shù)運(yùn)算被轉(zhuǎn)化為實(shí)數(shù)運(yùn)算,區(qū)間灰數(shù)運(yùn)算的難題在一定程度上得到解決.定義的區(qū)間灰數(shù)運(yùn)算可以推廣到以區(qū)間灰數(shù)為基本元素的灰色代數(shù)方程、灰色微分方程、灰色矩陣運(yùn)算的情形,而且有助于由于受到區(qū)間灰數(shù)運(yùn)算困難的制約一直進(jìn)展緩慢的灰色投入產(chǎn)出和灰色規(guī)劃等方面的研究.Abstract:The algorithm of interval grey numbers is the theoretical basis of a grey system theory. It has very important significance in developing the grey system theory. A definition of Kernel is given first. Algorithm axioms, algorithm rules of interval grey numbers and new algebraic systems are built based on the Kernel and the degree of greyness of grey numbers. And the properties of the algorithm are studied. Up to now, the algorithm of interval grey numbers are transformed to the algorithm of real numbers, so the difficult problem for algorithm of interval grey numbers is solved to a certain degree. The algorithm of interval grey numbers is extended to the grey algebraic equation, grey differential equation and grey matrix algorithm including interval grey numbers. The algorithm system of interval grey numbers is helpful for research on grey input-output and grey programming. 作者: 劉思峰方志耕謝乃明 Author: LIU Si-feng  FANG Zhi-geng  XIE Nai-ming 作者單位: 南京航空航天大學(xué)灰色系統(tǒng)研究所,江蘇,南京,210016 期 刊: 系統(tǒng)工程與電子技術(shù)   ISTICEIPKU Journal: SYSTEMS ENGINEERING AND ELECTRONICS 年,卷(期): 2010, 32(2) 分類(lèi)號(hào): C931 N941.5 關(guān)鍵詞: 區(qū)間灰數(shù)    核    灰度    運(yùn)算法則    Keywords: interval grey numbers    Kernel    the degree of greyness of grey numbers    algorithm rules    機(jī)標(biāo)分類(lèi)號(hào): C93 O15 機(jī)標(biāo)關(guān)鍵詞: 灰數(shù)灰度    區(qū)間灰數(shù)    運(yùn)算法則    based    interval grey numbers    rules of    Kernel    數(shù)運(yùn)算    the grey system    differential equation    theoretical basis    灰色系統(tǒng)    灰色微分方程    significance    degree    運(yùn)算性質(zhì)    投入產(chǎn)出    理論基礎(chǔ)    理論發(fā)展    矩陣運(yùn)算 基金項(xiàng)目: 國(guó)家自然科學(xué)基金,哈爾濱工業(yè)大學(xué)校科研和教改項(xiàng)目,人文社會(huì)科學(xué)規(guī)劃基金,江蘇省高等學(xué)校優(yōu)秀創(chuàng)新團(tuán)隊(duì)基金,南京航空航天大學(xué)創(chuàng)新群體,特聘教授科研創(chuàng)新基金

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