本文選題：模糊邏輯 + 模糊蘊涵��； 參考：《浙江理工大學(xué)》2017年碩士論文

【摘要】：模糊蘊涵作為一種重要的邏輯算子被廣泛應(yīng)用于諸多領(lǐng)域,如模糊推理,模糊控制,模糊圖像處理,詞計算,模糊數(shù)學(xué)形態(tài)學(xué),數(shù)據(jù)挖掘等.正是由于它的理論意義與應(yīng)用價值,近年來關(guān)于模糊蘊涵算子的研究受到關(guān)注,其研究熱點主要集中于:模糊蘊涵構(gòu)造方法的研究,模糊蘊涵性質(zhì)的分析與刻畫,以及模糊蘊涵與一些函數(shù)方程的關(guān)系.本文將提出模糊蘊涵新的構(gòu)造方法,并將研究由這些方法生成的模糊蘊涵的性質(zhì)與它們滿足一些函數(shù)方程的條件.全文的主要內(nèi)容如下:Vemuri與Jayaram提出了模糊蘊涵的兩種合成方法,但它們不保持序性質(zhì)與換質(zhì)位對稱性.為了彌補這一不足,我們提出模糊蘊涵另一種新的合成方法及其推廣,證明了這兩種合成方法都保持序性質(zhì)與換質(zhì)位對稱性.并對新生成的兩類模糊蘊涵具有的其它性質(zhì)也進行了討論.通過利用(0,1)中一組嚴(yán)格單調(diào)增序列,將模糊蘊涵水平e-閾值生成方法與垂直e-閾值生成方法作了有意義的推廣,我們分別稱這兩種方法為模糊蘊涵水平多閾值生成方法與垂直多閾值生成方法.分析水平多閾值生成的模糊蘊涵與垂直多閾值生成的模糊蘊涵的一些性質(zhì)且對它們進行了刻畫.討論水平多閾值生成的模糊蘊涵與一些函數(shù)方程之間的關(guān)系.通過利用T-模,T-余模與模糊否定N提出了模糊蘊涵三種換質(zhì)位對稱化的新方法,分別稱為(T,N)-換質(zhì)位對稱化,(S,N)-換質(zhì)位對稱化和(T,S,N)-換質(zhì)位對稱化.由這三種方法得到的三類模糊蘊涵分別關(guān)于強否定具有換質(zhì)位對稱性.此外對這三類模糊蘊涵所具有的其它性質(zhì)也進行了詳細(xì)討論.基于不滿足恒等原則與序性質(zhì)的模糊蘊涵,我們提出模糊蘊涵的兩種修正方法,使得修正后的模糊蘊涵分別滿足這兩個性質(zhì),并對修正后的模糊蘊涵所保持的其它性質(zhì)也進行探究.
[Abstract]:As an important logic operator, fuzzy implication is widely used in many fields, such as fuzzy reasoning, fuzzy control, fuzzy image processing, word computing, fuzzy mathematical morphology, data mining and so on. It is precisely because of its theoretical significance and application value that the research on fuzzy implication operators has attracted much attention in recent years. The research focus is mainly on the research of fuzzy implication construction methods, the analysis and characterization of fuzzy implication properties. And the relation between fuzzy implication and some functional equations. In this paper, a new construction method of fuzzy implication is proposed, and the properties of fuzzy implication generated by these methods and the conditions for them to satisfy some functional equations are studied. The main contents of this paper are as follows: 1. The composition methods of fuzzy implication proposed by: Vemuri and Jayaram, but they do not maintain the properties of order and the symmetry of transposition. In order to remedy this deficiency, we propose another new synthesis method with fuzzy implication and its generalization. It is proved that both of the two methods maintain the order property and the symmetry of transposition. The other properties of the two newly generated fuzzy implication are also discussed. By using a group of strictly monotone increasing sequences, this paper generalizes the fuzzy implication horizontal e- threshold generation method and the vertical e- threshold generation method. We refer to these two methods as fuzzy implication horizontal multi-threshold generation method and vertical multi-threshold generation method respectively. Some properties of fuzzy implication generated by horizontal multi-threshold and vertical multi-threshold are analyzed and characterized. The relationship between the fuzzy implication generated by horizontal multi-threshold and some functional equations is discussed. In this paper, three new methods of translocation symmetry of fuzzy implication are proposed by using T- mod T- comodules and fuzzy negative-N, which are called "T _ (T)" -T ~ (+) ~ (1) -S ~ (1) -N ~ (+) -N ~ (+) -N ~ (+) -T _ (1) -T _ (1) and T ~ (+) _ (S) _ (N) The three kinds of fuzzy implication obtained from these three methods are respectively about strong negation with transposable symmetry. In addition, the other properties of these three kinds of fuzzy implication are also discussed in detail. Based on the fuzzy implication which does not satisfy the identity principle and the order property, we propose two modified methods of fuzzy implication, so that the modified fuzzy implication satisfies these two properties respectively. The other properties of the modified fuzzy implication are also discussed.
【學(xué)位授予單位】：浙江理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O159

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