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With the expansion of the field of philosophy and social sciences and the diversification of the research problems，Gradually there are many "fuzzy quantities" that cannot be calculated by classic quantitative analysis methods。For example，Evaluation of family financial ability in a certain field，can often be divided into a wealthy type、Well -off type、Food and clothing type, etc.; Evaluation of the physical quality of people，Height is often divided into high、Middle、Dwarf，etc.。These are the fuzzyness of quantity，That is the vague concept。In order to solve the contradiction between the concept of vague concept and the classic quantitative treatment，There is a fuzzy thinking method that blur the accurate concept。

　　The use of fuzzy concept is human wealth

Examine from the objective world，Classic collection founded by German scientist Conte in 1871，The concept described is only this is the concept，or the two extremes of things are portrait，that is 0,1 Two -value logic。and things from one extreme to another，Usually there is a process of intermediary transition。In this process，The state of "This is also the same" is objective，is [0,1] Multi -value logic of any value on the closed range。But the description of things is absolutely described by the classic collection，No full picture of things，Bet365 app download Multi Bet365 lotto review -value logic in the state of "this is also the same" state is helpless。and the classic quantitative method when discussing problems，Often is a clear relationship such as "belonging" and "not belonging" or "true" or "fake" between elements and collection。Because it cannot meet the treatment of the above problems，The emergence of the bottleneck of the classic thinking method。

The fuzzy collection created by Chad, an expert in the United States Control theory in 1965, objectively described the original appearance of things，Make fuzzy thinking methods can exhibit style between the vast scientific world。From classic to blur，After a century of vicissitudes，is the major development of human thinking methods。Chad said，"We will find that human beings can use the concept of vague concepts as a huge wealth rather than burden"。

Current，The application of fuzzy technology and the development of fuzzy products is very extensive，Like a washing machine、Microwave oven、Camera、The vacuum cleaner、Air conditioner、Electric refrigerator、TV、video recorder, etc.，All labels with vaguely controlled control。other，Vaguely controlled driverless model，Successfully applied vague logic to many cutting -edge technologies such as the docking and posture control of aerospace aircraft and attitude control and interstellar tracking system。

　　Vague thinking methods have rich connotations

Vague thinking method is the learning of quantitative research on the phenomenon of uncertainty。This uncertainty refers to the "scope uncertainty" caused by the inability Bet365 lotto review to Bet365 lotto review quantitatively quantitatively quantitatively quantitative "。1965，Professor Chad published the papers "Blog Collection" in the "Information and Control" magazine，It marks the birth of fuzzy thinking methods。Vague concept，refers to the unclear boundary、Concepts with unclear extension。Vague set is a reflection of the vague concept of objective existence。Whether the objective elements that exist are blurry collection, is not the other that is,。We can neither think that these elements belong to this collection，It can’t be considered that it does not belong to this collection，but often in a kind of one another、Ambiguous state，This is the so -called vagueness。

The word "fuzzy" is translated from the English "fuzzy"，Except for the meaning of "fuzzy" in the dictionary，There is also the meaning of "unclear" and "unclear boundaries"。Vagueness is a common phenomenon presented by objective things，Mainly refers to the "irregularity" of the intermediary transition in the differences between objectives.，or the uncertainty of the class or sexuality of the research object。Although there is no absolute boundary although fuzzy things，But there are still relative standards and rationality。At the same time，Allowing the existence of subjectivity in fuzzy，Because the boundaries in each person's minds of fuzzy things will not be exactly the same，Acknowledge that certain subjectivity is a feature of fuzzy。other，The boundaries in people's minds form a certain distribution，There are certain rules，Therefore, Bet365 app download bet365 best casino games bet365 live casino games it is objective。3454_3473。

The idea of ​​affiliation is the basic thought of vague thinking。For example，We describe the degree of belonging to the vague concept of "young people"，When facing the question of how old people are young people，You can give a vague range。This，100 people may give a fuzzy collection of 100 age range。For example，Some people think that the 18 to 45 years old is a young man，Some people think that 20 to 48 years old is a young man，etc.。Suppose there is a 40 -year -old person: within the range of possible 100 age，Some include 40 years old，Some do not include 40 years old，This state is described as "intermediary state"。If there are 80 areas containing 40 years old，Then the 40 -year -old person is "young man". It can be understood as 80%or 0.8。

The decomposition theorem of the fuzzy collection、The three basic laws of performance theorem and expansion theorem can establish a bridge between vague thinking and classic thinking，Use classic methods to handle fuzzy objects。These three basic laws have formed the most basic research technology in the theory。

Because most things are blurred，This requires us to adopt multi -value logical thinking when judging value judgment of things，is the past 0,1 The two -value logic is promoted to [0,1] Multi -value logic of any value on the closed range。It can be said，Vagueness is the promotion and extension of accuracy，and accuracy are vague extremes。So say，The relationship between accuracy and vagueness is very close。When studying the vagueness of things，bet365 live casino games bet365 Play online games Do not ignore the accuracy of things。The relationship between correcting and processing accuracy and fuzzyness is very important。

Many phenomena of the objective world are blurred，If these vague concepts still adopt traditional methods，The so -called classic thinking method to handle and study，Some unreasonable、Uncle's conclusion，Not to promote fuzzy control robots、Vague control car、The emergence of products such as subway。So，When dealing with the problem，To figure out which is precise phenomenon，Which is a fuzzy phenomenon，Then according to different situations，Use different methods to deal with。

　　Vague thinking methods are applied in the field of social sciences

Fluggish cluster analysis、Fluggish model recognition、Vague evaluation、Vague decision、Flugked linear plan、Vague control and other methods，It constitutes an important means of vague thinking method applications。

Current，Vague thinking methods have been applied in the field of philosophy and social sciences，and achieved specific research results。For example，Application of fuzzy thinking methods in soil evaluation，Application of fuzzy thinking methods in the comprehensive evaluation of economic benefits。other，In industry and agriculture、Economy、Ecological civilization、National governance、Policy evaluation and other aspects，Application of vague thinking methods。

Vague comprehensive evaluation method，It is an important aspect of the application of vague thinking methods。Specific speaking，Vague comprehensive evaluation is to unclear the border、Quantitative factors that bet365 Play online games Bet365 app download are not easy to quantitative，A method of comprehensive evaluation of the rally of the evaluation of the evaluation from multiple factors。

Another aspect that is widely valued in the fuzzy theory，It is a fuzzy neural network。It brings together the advantages of neural network and fuzzy theory，Collection Learning、Lenovo、Identification、Adaptive and fuzzy information processing in one。During the past few years，Fluggish neural network theory and application have developed rapidly，Research on the proposal of various new fuzzy neural network models and the study of learning algorithms that are compatible with it，Not only does it accelerate the improvement of fuzzy neural network theory，And blurred identification、Vague control、Vague control、Criminals such as image coding and mode recognition are successfully applied。

In recent years，With artificial intelligence、5g、The development of information technology such as the Internet，The development of fuzzy control technology is also very rapid。And the fuzzy control technology is also the theory of fuzzy collection、Based on the fuzzy language variables and vague logic reasoning。Apply fuzzy thinking method in the control field，Can simulate human brain thinking and judgment，Select and control the product production process，to promote the development of new technologies in intelligence。

　　(Author Unit: Institute of Quantitative Economics and Economics of the Chinese Academy of Social Sciences)