本文選題：模糊集　切入點(diǎn)：直覺模糊集　出處：《陜西師范大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：為了研究與人類思維模式更相近的模糊推理方法,美國學(xué)者K.T.Atanassov定義了直覺模糊集這一概念.由于直覺模糊集在實(shí)際應(yīng)用中展現(xiàn)出巨大的潛力,因此得到了眾多學(xué)者的親睞,在短短的幾十年間,有關(guān)直覺模糊集的理論取得了累累碩果.直覺模糊集的研究已經(jīng)涉及到?jīng)Q策分析、人工智能、拓?fù)�、邏輯代�?shù)等諸多領(lǐng)域.其中在邏輯代數(shù)領(lǐng)域里,有關(guān)學(xué)者把模糊濾子和直覺模糊集結(jié)合在一起,引入了直覺模糊濾子的概念.本文的第一部分在FI代數(shù)中引入了直覺模糊濾子的概念,并利用直覺模糊濾子誘導(dǎo)出FI代數(shù)上的一種同余關(guān)系,進(jìn)一步研究了它的基本性質(zhì),期待這些工作對(duì)FI代數(shù)結(jié)構(gòu)的研究起到一定的促進(jìn)作用.自從Menger于1942年引入T-模的概念以后,它已經(jīng)被應(yīng)用到多個(gè)領(lǐng)域,其中包括概率度量空間、半群理論、函數(shù)方程理論、模糊邏輯理論等.本文的第二部分將在裴崢研究的格蘊(yùn)涵代數(shù)中的直覺模糊濾子的基礎(chǔ)上,將直覺模糊濾子與T-模相結(jié)合,引入了T1,T2直覺模糊濾子和T1,T2直覺模糊關(guān)聯(lián)濾子的概念,分別研究了T1,T2直覺模糊濾子和T1,T2直覺模糊關(guān)聯(lián)濾子的相關(guān)性質(zhì)并給出了等價(jià)刻畫,期待這些工作為進(jìn)一步研究格蘊(yùn)涵代數(shù)上的其他濾子提供了一定的參考.本文主要內(nèi)容及安排如下：第一章預(yù)備知識(shí).主要介紹了本文所涉及的與FI代數(shù)和格蘊(yùn)涵代數(shù)相關(guān)的概念、例子和結(jié)論.第二章FI代數(shù)上的直覺模糊濾子和同余關(guān)系.在FI代數(shù)上引入了直覺模糊濾子的概念,給出了FI代數(shù)上直覺模糊濾子的一個(gè)等價(jià)刻畫,并由直覺模糊濾子出發(fā)定義了它上的一個(gè)同余關(guān)系,并討論了它的一些簡(jiǎn)單性質(zhì).第三章格蘊(yùn)涵代數(shù)上的兩種直覺模糊濾子.將直覺模糊濾子與T-模相結(jié)合應(yīng)用到格蘊(yùn)涵代數(shù)中,給出了兩種直覺模糊濾子的定義,分別研究了它們的性質(zhì)并給出了等價(jià)刻畫.
[Abstract]:In order to study the fuzzy reasoning method which is more similar to the human thinking mode, the American scholar K.T. Atanassov defined the concept of intuitionistic fuzzy set. Because of the great potential of intuitionistic fuzzy set in practical application, it has been favored by many scholars. In just a few decades, the theory of intuitionistic fuzzy sets has made a lot of achievements. The research of intuitionistic fuzzy sets has been related to many fields, such as decision analysis, artificial intelligence, topology, logic algebra and so on. Some scholars combine fuzzy filter with intuitionistic fuzzy set and introduce the concept of intuitionistic fuzzy filter. The first part of this paper introduces the concept of intuitionistic fuzzy filter in fi algebra. A congruence relation on fi algebras is induced by using intuitionistic fuzzy filters, and its basic properties are further studied. Since Menger introduced the concept of T-norm in 1942, it has been applied to many fields, including probabilistic metric space, semigroup theory, function equation theory. The second part of this paper combines intuitionistic fuzzy filters with T-modules on the basis of intuitionistic fuzzy filters in lattice implication algebras studied by Pei Zheng. The concepts of T 1 T 2 intuitionistic fuzzy filter and T 1 T 2 intuitionistic fuzzy correlation filter are introduced. The correlation properties of T 1 T 2 intuitionistic fuzzy filter and T 1 T 2 intuitionistic fuzzy correlation filter are studied and the equivalent characterizations are given. It is expected that these works will provide a certain reference for the further study of other filters on lattice implication algebras. The main contents and arrangements of this paper are as follows: the first chapter is the preparatory knowledge. The concepts associated with algebra, In chapter 2, we introduce the concept of intuitionistic fuzzy filters on fi algebras, and give an equivalent characterization of intuitionistic fuzzy filters on fi algebras. A congruence relation on the intuitionistic fuzzy filter is defined. Some simple properties of it are discussed. In the third chapter, two kinds of intuitionistic fuzzy filters on lattice implication algebras are discussed. The combination of intuitionistic fuzzy filters and T-modules is applied to lattice implication algebras, and the definitions of two intuitionistic fuzzy filters are given. Their properties are studied and the equivalent characterizations are given.
【學(xué)位授予單位】：陜西師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O159;O144

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本文編號(hào)：1641013