【摘要】：模糊蘊涵作為重要的連接詞,是通過其單調(diào)性和邊界條件來定義的,在模糊決策,模糊控制等很多領(lǐng)域都有重要作用.對于模糊蘊涵的性質(zhì)及其應(yīng)用已經(jīng)有許多研究成果.在模糊控制領(lǐng)域,對任意輸入值,基于模糊規(guī)則庫,運用模糊推理機制輸出控制結(jié)論.模糊推理機制的核心技術(shù)之一是使用適當(dāng)?shù)哪：N涵.本文主要研究模糊蘊涵的生成方法,提出幾種將多個蘊涵組合在一起生成新蘊涵的方法,并考慮模糊蘊涵算子在模糊推理方面的應(yīng)用問題.本文的主要研究內(nèi)容與結(jié)論如下:提出一些生成模糊蘊涵的新方法,即通過對一個或多個選定的模糊蘊涵的第一變元和第二變元進行多重迭代,生成一些新的函數(shù)形式.經(jīng)分析得到,當(dāng)生成這些函數(shù)的原蘊涵具有某些性質(zhì)時,此函數(shù)為模糊蘊涵,本文稱其為多重模糊蘊涵.進一步,分析選定的模糊蘊涵具有某些好的性質(zhì)時,生成的多重模糊蘊涵仍保持這些性質(zhì),例如:冪等性,單位元,左邊界性等.接下來,又研究了一些多重模糊蘊涵滿足相互交換律,及與分配律相關(guān)的邏輯等式的問題,給出這些邏輯等式成立的充分必要條件.進一步,將以上生成的多重模糊蘊涵應(yīng)用于全蘊涵推理算法,得到了當(dāng)全蘊涵算法里面的蘊涵為多重模糊蘊涵時其解的形式.最后,受全蘊涵算法求解原理的啟發(fā),利用模糊相似度的概念,提出基于全蘊涵算法的模糊相似度推理算法,給出解的通式,并分析當(dāng)其中的蘊涵為一些重要蘊涵時其解的形式.這些結(jié)果將為模糊蘊涵在模糊推理,模糊控制及模糊決策等領(lǐng)域的應(yīng)用提供支持.
[Abstract]:As an important conjunction, fuzzy implication is defined by its monotonicity and boundary conditions. It plays an important role in many fields such as fuzzy decision making, fuzzy control and so on. There have been many research results on the properties and applications of fuzzy implication. In the field of fuzzy control, the fuzzy inference mechanism is used to output the control conclusion for any input value based on fuzzy rule base. One of the core technologies of fuzzy reasoning is the use of appropriate fuzzy implication. In this paper, the method of generating fuzzy implication is studied, and several methods of combining multiple implication to generate new implication are put forward, and the application of fuzzy implication operator in fuzzy reasoning is considered. The main contents and conclusions of this paper are as follows: some new methods for generating fuzzy implication are proposed, that is, by iterating the first variable and the second variable of one or more selected fuzzy implication, some new function forms are generated. It is obtained by analysis that when the original implication of generating these functions has some properties, the function is fuzzy implication, which is called multiple fuzzy implication in this paper. Furthermore, when the selected fuzzy implication has some good properties, the generated multiple fuzzy implication still retains these properties, such as idempotent, unit element, left boundary, etc. Then, we study some problems of multiple fuzzy implication satisfying the law of mutual exchange and the logical equality related to the distribution law, and give the necessary and sufficient conditions for these logical equalities to hold. Furthermore, the multiple fuzzy implication generated above is applied to the full implication reasoning algorithm, and the form of the solution is obtained when the implication in the full implication algorithm is multiple fuzzy implication. Finally, inspired by the principle of full implication algorithm, a fuzzy similarity reasoning algorithm based on full implication algorithm is proposed by using the concept of fuzzy similarity, and the general formula of the solution is given. The form of solution is analyzed when the implication is some important implication. These results will support the application of fuzzy implication in fuzzy reasoning, fuzzy control and fuzzy decision making.
【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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本文編號：2173902