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  本文關鍵詞： MTL命題邏輯系統(tǒng) 真度 偽距離 三I算法 還原性　出處：《蘭州理工大學》2011年碩士論文　論文類型：學位論文

【摘要】：基于左連續(xù)三角模的MTL邏輯,也是基于正則蘊涵算子的邏輯,其中左連續(xù)三角模作為邏輯強合取算子的語義對應,與其伴隨的正則蘊涵算子作為邏輯蘊涵算子的語義對應.MTL邏輯作為模糊邏輯,具有很多良好的性質,同時,基于三I原則的模糊推理算法,其統(tǒng)一形式也是基于正則蘊涵算子給出的,因此三I算法和MTL邏輯之間存在著天然的聯(lián)系.三I原則和算法可以看做是模糊推理的一種數(shù)值實現(xiàn),但是在這種數(shù)值實現(xiàn)和邏輯的形式化推理之間,還存在著一定的距離,如果能為三I原則和算法提供一種邏輯上的解釋,那將會為模糊推理找到合適的邏輯基礎. 為了消除形式化的邏輯推理和數(shù)值計算之間的割裂,本世紀初,王國俊教授基于均勻概率的思想在經(jīng)典二值命題邏輯中引入了命題的真度概念,提出了計量邏輯理論,建立了一套近似推理模式之后,國內(nèi)外同行展開了廣泛的研究.相似的結論被推廣到n值Lukasiewicz命題邏輯系統(tǒng)和n值R0命題邏輯系統(tǒng)中.但是所有以上的結論都是建立在均勻概率測度空間上,由于實際應用中往往會對某些命題有所側重,所以針對非均勻分布情形進行研究會更適合于應用.本文在n值MTL命題邏輯系統(tǒng)的統(tǒng)一框架中,基于一般的概率測度,建立了真度的統(tǒng)一理論,給出了這種統(tǒng)一框架下公式真度的積分表示形式;證明了真度推理規(guī)則在所有的n值S-MTL命題邏輯系統(tǒng)中成立,定義了一種偽距離,為在n值MTL命題邏輯系統(tǒng)中建立近似推理理論給出了一種可能的框架.考慮到三I算法的統(tǒng)一形式也是基于正則蘊涵算子的,而還原性是判斷蘊涵算子與模糊推理方法配合效果的一個重要指標,只有蘊涵算子與推理方法搭配適當,才能使模糊推理有一個好的效果.因此本文還對三I算法的還原性進行了討論. 以下是本文所得到的主要結果: (1)提出了強正則蘊涵算子與S-MTL命題邏輯系統(tǒng)的概念,并且證明了Lukasiewicz蘊涵是最大的強正則蘊涵算子. (2)在n值MTL命題邏輯系統(tǒng)中基于一般的概率測度空間定義了公式的真度,給出了真度的積分表示形式,并在n值S-MTL命題邏輯系統(tǒng)中證明了這種基于一般概率測度的真度滿足真度推理規(guī)則.基于這種真度建立了S-MTL命題邏輯系統(tǒng)中公式之間的相似度及偽距離理論,進而為n值SMTL系統(tǒng)中建立了一種統(tǒng)一的近似推理機制. (3)對模糊推理三I算法具備還原性的條件進行了研究.當與蘊涵算子相伴隨的三角模為連續(xù)三角模時,給出并證明了FMP問題三I算法具有還原性的充要條件;當蘊涵算子為連續(xù)的正則蘊涵算子時,給出了FMT問題三I算法具有還原性的充要條件;最后,當正則蘊涵算子關于補運算滿足對合律時,給出了FMT問題三I算法滿足還原性的一個充分條件.
[Abstract]:The MTL logic based on the left continuous triangular module is also the logic based on the regular implication operator, in which the left continuous triangular module is used as the semantic correspondence of the strong combination operator of the logic. With its accompanying regular implication operator as the semantic correspondence of the logical implication operator, the MTL logic as fuzzy logic has many good properties. At the same time, the fuzzy reasoning algorithm based on the three I principle is proposed. The unified form is also based on the regular implication operator, so there is a natural relationship between the three I algorithm and the MTL logic, and the three I principle and algorithm can be regarded as a numerical realization of fuzzy reasoning. However, there is still a certain distance between the numerical realization and the formal reasoning of logic. If we can provide a logical explanation for the three-I principle and algorithm, we will find the appropriate logical basis for fuzzy reasoning. In order to eliminate the separation between formal logic reasoning and numerical calculation, Professor Wang Guojun introduced the concept of truth of proposition in classical binary propositional logic based on the idea of uniform probability at the beginning of this century, and put forward the theory of quantitative logic. After establishing a set of approximate reasoning models, Similar conclusions have been extended to n-valued Lukasiewicz propositional logic systems and n-valued R0 propositional logic systems. Because some propositions are often emphasized in practical applications, it is more suitable to study the case of non-uniform distribution. In this paper, in the unified framework of n-valued MTL propositional logic system, based on the general probability measure, The unified theory of truth degree is established, the integral representation of formula truth degree is given under this unified framework, it is proved that the truth degree reasoning rule holds in all n-valued S-MTL propositional logic systems, and a pseudo distance is defined. This paper presents a possible framework for establishing approximate reasoning theory in n-valued MTL propositional logic systems, considering that the unified form of the triple I algorithm is also based on regular implication operators. Reducibility is an important index to judge the effect of the combination of implication operator and fuzzy reasoning method. Therefore, the reducibility of the triple-I algorithm is also discussed in this paper. The following are the main results obtained in this paper:. 1) the concepts of strongly regular implication operator and S-MTL propositional logic system are proposed, and it is proved that Lukasiewicz implication is the largest strongly regular implication operator. (2) in the n-valued MTL propositional logic system, the true degree of the formula is defined based on the general probability measure space, and the integral representation of the truth degree is given. In the n-valued S-MTL propositional logic system, it is proved that the truth degree based on the general probability measure satisfies the truth degree inference rule. Based on this truth degree, the similarity degree and pseudo-distance theory among the formulas in S-MTL propositional logic system are established. Then a unified approximate reasoning mechanism is established for n-valued SMTL systems. In this paper, we study the condition that the triple-i algorithm of fuzzy reasoning has the reducibility. When the triangular module associated with the implication operator is a continuous triangular module, the sufficient and necessary conditions for the triple-I algorithm of the FMP problem to be reducible are given and proved. When the implication operator is a continuous regular implication operator, a sufficient and necessary condition for the reducibility of the three-I algorithm for the FMT problem is given, and finally, when the regular implication operator satisfies the involutive law about the complement operation, In this paper, a sufficient condition for the triple-I algorithm of FMT problem to satisfy the reducibility is given.
【學位授予單位】：蘭州理工大學
【學位級別】：碩士
【學位授予年份】：2011
【分類號】：O141.1

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本文編號：1542734