Fuzzy logic is an approach to computing based on "degrees of truth" rather than the usual "true or false" (1 or 0) Boolean logic on which the modern computer is based. 

The idea of fuzzy logic was first advanced by Dr. Lotfi Zadeh of the University of California at Berkeley in the 1960s.

Here is how, Prof Zadeh, father of fuzzy logic ,defined it in the attached document:

Fuzzy Logic is basically  a multi-valued logic that allows intermediate values to be defined between conventional evaluations like yes/no, true/false, black /white, etc.Notions like rather warm or pretty cold can be formulated  mathematically and processed with the computer. In this way, an attempt is made to apply a more humanlike way of thinking in the programming of computers.

Fuzzy logic is an extension of the classical propositional and predicate logic that rests on the principles of the binary truth functionality. Fuzzy logic is a multi-valued logic. However, the most pertinent feature of fuzzy logic for which it receives so much attention is ts scope of partial  matching. In any real world system, the inferences guided by a number of rules follow a middle decision trajectory over time.

Fuzzy logic is an approach to computing based on "degrees of truth" rather than the usual "true or false" (1 or 0) Boolean logic on which the modern computer is based. 

The idea of fuzzy logic was first advanced by Dr. Lotfi Zadeh of the University of California at Berkeley in the 1960s.

Here is how, Prof Zadeh, father of fuzzy logic ,defined it in the attached document:

Fuzzy Logic is basically  a multi-valued logic that allows intermediate values to be defined between conventional evaluations like yes/no, true/false, black /white, etc.Notions like rather warm or pretty cold can be formulated  mathematically and processed with the computer. In this way, an attempt is made to apply a more humanlike way of thinking in the programming of computers.

Fuzzy logic is an extension of the classical propositional and predicate logic that rests on the principles of the binary truth functionality. Fuzzy logic is a multi-valued logic. However, the most pertinent feature of fuzzy logic for which it receives so much attention is ts scope of partial  matching. In any real world system, the inferences guided by a number of rules follow a middle decision trajectory over time.

Dear Colleagues,

Good Day,

Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1, considered to be "fuzzy". By contrast, in Boolean logic, the truth values of variables may only be 0 or 1, often called "crisp" values.

Fuzzy logic has two different meanings. In a narrow sense, fuzzy logic is a logical system, which is an extension of multivalued logic. However, in a wider sense fuzzy logic (FL) is almost synonymous with the theory of fuzzy sets, a theory which relates to classes of objects with unsharp boundaries in which membership is a matter of degree. In this perspective, fuzzy logic in its narrow sense is a branch of FL. Even in its more narrow definition, fuzzy logic differs both in concept and substance from traditional multivalued logical systems.

In Fuzzy Logic Toolbox™ software, fuzzy logic should be interpreted as FL, that is, fuzzy logic in its wide sense. The basic ideas underlying FL are explained very clearly and insightfully in Foundations of Fuzzy Logic. What might be added is that the basic concept underlying FL is that of a linguistic variable, that is, a variable whose values are words rather than numbers. In effect, much of FL may be viewed as a methodology for computing with words rather than numbers. Although words are inherently less precise than numbers, their use is closer to human intuition. Furthermore, computing with words exploits the tolerance for imprecision and thereby lowers the cost of solution.

Another basic concept in FL, which plays a central role in most of its applications, is that of a fuzzy if-then rule or, simply, fuzzy rule. Although rule-based systems have a long history of use in Artificial Intelligence (AI), what is missing in such systems is a mechanism for dealing with fuzzy consequents and fuzzy antecedents. In fuzzy logic, this mechanism is provided by the calculus of fuzzy rules. The calculus of fuzzy rules serves as a basis for what might be called the Fuzzy Dependency and Command Language (FDCL). Although FDCL is not used explicitly in the toolbox, it is effectively one of its principal constituents. In most of the applications of fuzzy logic, a fuzzy logic solution is, in reality, a translation of a human solution into FDCL.

A trend that is growing in visibility relates to the use of fuzzy logic in combination with neurocomputing and genetic algorithms. More generally, fuzzy logic, neurocomputing, and genetic algorithms may be viewed as the principal constituents of what might be called soft computing. Unlike the traditional, hard computing, soft computing accommodates the imprecision of the real world. The guiding principle of soft computing is: Exploit the tolerance for imprecision, uncertainty, and partial truth to achieve tractability, robustness, and low solution cost. In the future, soft computing could play an increasingly important role in the conception and design of systems whose MIQ (Machine IQ) is much higher than that of systems designed by conventional methods.

For more information you may consult the following link

http://www.mathworks.com/help/fuzzy/what-is-fuzzy-logic.html?requestedDomain=www.mathworks.com

Dear Colleagues,

Good Day,

"Almost any control system can be replaced with a fuzzy logic based control system. This may be overkill in many places however it simplifies the design of many more complicated cases. So fuzzy logic is not the answer to everything, it must be used when appropriate to provide better control. If a simple closed loop or PID controller works fine then there is no need for a fuzzy controller. There are many cases when tuning a PID controller or designing a control system for a complicated system is overwhelming, this is where fuzzy logic gets its chance to shine.

One of the most famous applications of fuzzy logic is that of the Sendai Subway system in Sendai, Japan. This control of the Nanboku line, developed by Hitachi, used a fuzzy controller to run the train all day long. This made the line one of the smoothest running subway systems in the world and increased efficiency as well as stopping time. This is also an example of the earlier acceptance of fuzzy logic in the east since the subway went into operation in 1988. For more information on this, see 1st & 2nd links...

The most tangible applications of fuzzy logic control have appeared commercial appliances. Specifically, but not limited to heating ventillation and air conditioning (HVAC) systems. These systems use fuzzy logic thermostats to control the heating and cooling, this saves energy by making the system more efficient. It also keeps the temperature more steady than a traditional thermostat. For more information on this application see 3rd link...

nother signifigant area of application of fuzzy control is in industrial automation. Fuzzy logic based PLCs have been developed by companies like Moeller. These PLCs, as well as other implementations of fuzzy logic, can be used to control any number of industrial processes. For some examples see 4th link...

As a final example of fuzzy logic, it can be used in areas other than simply control. Fuzzy logic can be used in any decision making process such as signal processing or data analysis. An example of this is a fuzzy logic system that analyzes a power system and diagnoses any harmonic disturbance issues. The system analyzes the fundamental voltage, as well as third, fifth and seventh harmonics as well as the temperature to determine if there is cause for concern in the operation of the system. A complete explanation of this project can be found in 5th link...."

http://sipi.usc.edu/~kosko/Scientific%20American.pdf

http://www.smart.sunderland.ac.uk/f_succ.htm

http://www.fuzzytech.com/e/e_a_esa.html

http://www.fuzzytech.com/e/e_a_plc.html

http://www.calvin.edu/~pribeiro/othrlnks/Fuzzy/pictures/fuzzy_paper.pdf

Dear Colleagues,

Good Day,

"Fuzzy logic

Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1, considered to be "fuzzy". By contrast, in Boolean logic, the truth values of variables may only be 0 or 1, often called "crisp" values. Fuzzy logic has been employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. Furthermore, when linguistic variables are used, these degrees may be managed by specific (membership) functions.

The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by Lotfi Zadeh. Fuzzy logic had however been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski.

Fuzzy logic has been applied to many fields, from control theory to artificial intelligence."....

Please, see the link for the rest of the article .....

https://en.wikipedia.org/wiki/Fuzzy_logic

Dear @Behrouz Ahmadi-Nedushan,

Thanks a lot for your perfect answers and useful links.

Regards, Shafagat

Dear @Hazim Hashim Tahir,

Thank you very much for opinion.

The links that you mentioned are rich and valuable. Thanks a lot.

Regards, Shafagat

Dear @Mahfuz Judeh,

Thank you very much. Your answer is highly appreciated.

Regards, Shafagat

Sometimes, its hard to determine whether a particular object fully belongs to or not to a given set. In such cases crisp measurement somewhat fails to answer this . Those problems can be dealt with assigning a membership grade to the objects that will determine how much the concerned object contributes towards the set..  E.g., in the image segmentation problems, sometimes we find that some pixels have the tendency  of showing properties of more than one segment (or clusters). In such cases, hard clustering can not efficiently determine the true clusters of such pixels..Then we need to adopt some fuzzy logic based techniques for correct segmentation results. 

I have few papers, where I am discussing this fuzzy logic based clustering issues in details.. Links are given below :

1>A comparative study between fuzzy clustering algorithm and hard clustering algorithm

http://arxiv.org/abs/1404.6059

2> Impact of exponent parameter value for the partition matrix on the performance of fuzzy C means Algorithm

https://scholar.google.co.in/citations?view_op=view_citation&hl=en&user=FY7bIDsAAAAJ&citation_for_view=FY7bIDsAAAAJ:u-x6o8ySG0sC

3> COLOR IMAGE SEGMENTATION USING AN EFFICIENT FUZZY BASED WATERSHED APPROACH

http://www.academia.edu/download/40839530/6515sipij02.pdf

4>CLUSTERING APPROACH TOWARDS IMAGE SEGMENTATION: AN ANALYTICAL STUDY

http://arxiv.org/abs/1407.8121

Dear @Dibya jyoti Bora,

Thanks a lot for your useful answer. 

Regards, Shafagat

Apple Grading Using Fuzzy Logic

Classification is vital for the evaluation of agricultural produce. However, the high costs, subjectivity, tediousness and inconsistency associated with manual sorting have been forcing the post harvest industry to apply automation in sorting operations. Fuzzy logic (FL) was applied as a decision making support to grade apples in this study. Quality features such as the color, size and defects of apples were measured through different equipment

http://dergipark.ulakbim.gov.tr/tbtkagriculture/article/viewFile/5000028078/5000028315

FL is branch of mathematics which can capture uncertainties of non-statistical kind. Fuzzy logic also provides a tolerance for imprecision. By saying this , it doe't mean that it advocates inaccuracy, instead, it argues about the necessity of being accurate if things can be done approximately very well.

Crisply & mathematically, it is the super set of binary logic

Dear @Krishnan Umachandran,

Many thanks for your  opinion.

Regards, SHafagat

Dear @Jayaram M.A,

Thank you very much for answers.

Regards, Shafagat

Dear Shafagat,

I am not a mathematician, but come across the basic information. Very interesting to read

Fuzzy logic

https://en.wikipedia.org/wiki/Fuzzy_logic

Dear Shafagat,

   Thanks for your invitation to share our colleagues in this interesting and beautiful branch of mathematics that extends our knowledge and take us away from the classical theories and branches of science that sometimes disable to interpret many scientific phenomena and sometimes lack to have applications to modern technology.

May the following links and refrerences be helpful for further explanations about this topic.

Best regards

1-Hájek, Petr (1998). Metamathematics of fuzzy logic. Dordrecht: Kluwer. ISBN 0-7923-5238-6.

2-Ibrahim, Ahmad M. (1997). Introduction to Applied Fuzzy Electronics. Englewood Cliffs, N.J: Prentice Hall. ISBN 0-13-206400-6.

3-Klir, George J.; Yuan, Bo (1995). Fuzzy sets and fuzzy logic: theory and applications. Upper Saddle River, NJ: Prentice Hall PTR. ISBN 0-13-101171-5.

4-Kosko, Bart (1993). Fuzzy thinking: the new science of fuzzy logic. New York: Hyperion. ISBN 0-7868-8021-X.

5-Lohani, A.K.; Goel, N.K.; Bhatia K.K.S. (2011). "Comparative study of neural network, fuzzy logic and linear transfer function techniques in daily rainfall‐runoff modelling under different input domains". Hydrological Processes. 25 (2): 175–193. doi:10.1002/hyp.7831.

6-Novák, Vilém; Perfilieva, Irina; Močkoř, Jiří (1999). Mathematical principles of fuzzy logic. Dordrecht: Kluwer Academic. ISBN 0-7923-8595-0.

7-Santos, Eugene S. (1970). "Fuzzy Algorithms". Information and Control. 17 (4): 326–339. doi:10.1016/S0019-9958(70)80032-8.

http://plato.stanford.edu/entries/logic-fuzzy/

http://www.sfu.ca/~jeffpell/papers/ReviewHajek.pdf

I exactly don't know about that but through the below it can be understood i think.

http://whatis.techtarget.com/definition/fuzzy-logic

Fuzzy Logic is a branch discipline of mathematics that emerged in the decade of the 60s of the last century, and has now had a resurgence by researchers who were interested in describing, analyzing and evaluating information where the subject or object Linguistic study (semantic, semiotic, conceptual), because they are handled in particular terms, concepts, semantic fields; and in general phrases, verbs, and opinions.

It is fair to clarify that the discipline "Fuzzy Logic" is not inaccurate or "Blurry", but its purpose or field of study, as previously detailed; where terms axiológicos as moral values ​​and ethical principles that are expressed and write formally in written form, as an organized anti-thesis and conclusion, arguments qualifying for or against "something" or that are not entirely false or thesis text totally true, but they are in a "continuum" of truth;

It also refers to a listing of terms, answers and inventory of opinions, which by its qualitative linguistic expression does not give precise nor particularly numerical measurement, but if allowed to handle groups of terms and concepts related fields, after which they can handle with the set theory and vectors, same as if it can be expressed in mathematical and geometric shape.

All this is especially useful for qualitative research, such as sociological, educational and cultural research. There is already methodology and research instruments, measurement, analysis and qualitative assessment to perform statistical analysis of these results and to make technology decisions and practices in this regard. Internet, Artificial Intelligence and Information Technology, together with the "Statistical Programs Pre-programmed" and already marketed general scientific knowledge (eg SPSS) are useful for this purpose.

A recently developed computer technology (programming language, algorithms and software) using Artificial Intelligence, facilitate the description, analysis and evaluation of conceptual, semantic and linguistic information, called "Opinion Mining"

Greetings and expected to continue contributing further on this interesting question, I say goodbye for now of all participants.

Dr. Jose Luis Garcia Vigil

Dear @Dr. Jose Luis Garcia Vigil,

Thank you very much for useful opinion.

Regards, Shafagat

Dear @Aparna Murthy ,

Thanks for answer.

Regards, Shafagat

Classical or two valued logic takes 0 or 1 for logical decision making. There is nothing intermediate between them.  Fuzzy logic is the extension of classical logic that takes values from 0 to 1. Generally, we know that a variable takes numbers as their value. But in fuzzy logic the variable takes word as their value.

Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1, considered to be "fuzzy". By contrast, in Boolean logic, the truth values of variables may only be 0 or 1, often called "crisp" values. Fuzzy logic has been employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. Furthermore, when linguistic variables are used, these degrees may be managed by specific (membership) functions.

https://en.wikipedia.org/wiki/Fuzzy_logic

whatis.techtarget.com › Topics › Application Development › Programming

Dear Shafagat,

DEFINITION of 'Fuzzy Logic': A mathematical logic that attempts to solve problems by assigning values to an imprecise spectrum of data in order to arrive at the most accurate conclusion possible. Fuzzy logic is designed to solve problems in the same way that humans do: by considering all available information and making the best possible decision given the input.

I found the presentation below very helpful...

I generally encourage my students to interact in the class without worrying about the truth value of their answers. .according to me NO ans is incorrect, it is always correct with membership of correctness ranging between [0,1]…some of their answers may be 100% correct, some may be 90, 80,70, . .53,21, 9 . .or 0% correct but never wrong and I am  as young as they all (to be a friend of them) with the membership value, fortunately/ unfortunately, lowering year after year! This really encourages my students to come forward with new new opinions without hegitation. Thanks to Fuzzy theory for qualifying me to be a permanent member of the frriendly associations if my young friends!

Dear @Nizam Uddin Ahmed,

Thanks, for opinion.

Regards, Shafagat

Dear @Abhishek Raj,

Thank you very much for answer.

Regards, Shafagat

Dear @Minati Mishra,  dear@Jeanan Shafiq,

Thank you very much for opinion.

Regards, Shafagat 

@Jeanan Shafiq: nice ppt. Thanks!

'fuzzy logic is not logic that is fuzzy but logic that is used to describe fuzzy.'

- a good quote

Dear @Priyadarsini Mishra ,

Thank you very much.

Regards, Shafagat

In their book, Klir and his colleagues provide the following definition:

Fuzzy logic is derived from fuzzy set theory dealing with reasoning that is approximate rather than precisely deduced from classical predicate logic. It can be thought of as the application side of fuzzy set theory dealing with well thought out real world expert values for a complex problem (Klir et. al, 1997).

Klir, George J.; St Clair, Ute H.; Yuan, Bo (1997). Fuzzy set theory: foundations and applications. Englewood Cliffs, NJ: Prentice Hall. ISBN 0133410587.

Degrees of truth are often confused with probabilities. However, they are conceptually distinct; fuzzy truth represents membership in vaguely defined sets, not likelihood of some event or condition. 

FL allows for set membership values to range (inclusively) between 0 and 1, and in its linguistic form, imprecise concepts like "slightly", "quite" and "very". Specifically, it allows partial membership in a set. It is related to fuzzy sets and possibility theory.

@Behrouz Ahmadi-Nedushan: 'Degrees of truth are often confused with probabilities' - good point

I like to cite the following popular example in this regard:

a highly thirty man, in an isolated captivity, has  to choose to drink  from two available bottles of water. ONE of those two has been labeled  "it has  0.1 membership in the class of poisonous drinking water". The other has a label which reads "it has 10% probability of being poison". Which bottle should the prisoner choose?

The term “fuzzy logic” emerged in the development of the theory of fuzzy sets by Lotfi Zadeh (1965). A fuzzy subsetA of a (crisp) set X is characterized by assigning to each element x of X the degree of membership of x in A (e.g., X is a group of people, A the fuzzy set of old people in X). Now if X is a set of propositions then its elements may be assigned their degree of truth, which may be “absolutely true,” “absolutely false” or some intermediate truth degree: a proposition may be more true than another proposition. This is obvious in the case of vague (imprecise) propositions like “this person is old” (beautiful, rich, etc.).

In the analogy to various definitions of operations on fuzzy sets (intersection, union, complement, …) one may ask how propositions can be combined by connectives (conjunction, disjunction, negation, …) and if the truth degree of a composed proposition is determined by the truth degrees of its components, i.e. if the connectives have their corresponding truth functions (like truth tables of classical logic). Saying “yes” (which is the mainstream of fuzzy logic) one accepts the truth-functional approach; this makes fuzzy logic to something distinctly different from probability theory since the latter is not truth-functional (the probability of conjunction of two propositions is not determined by the probabilities of those propositions).

Two main directions in fuzzy logic have to be distinguished (cf. Zadeh 1994). Fuzzy logic in the broad sense (older, better known, heavily applied but not asking deep logical questions) serves mainly as apparatus for fuzzy control, analysis of vagueness in natural language and several other application domains. It is one of the techniques of soft-computing, i.e. computational methods tolerant to suboptimality and impreciseness (vagueness) and giving quick, simple and sufficiently good solutions. The monographs Novak 1989, Zimmermann 1991, Klir-Yuan 1996, Nguyen 1999 can serve as recommended sources of information.

Fuzzy logic in the narrow sense is symbolic logic with a comparative notion of truth developed fully in the spirit of classical logic (syntax, semantics, axiomatization, truth-preserving deduction, completeness, etc.; both propositional and predicate logic). It is a branch of many-valued logic based on the paradigm of inference under vagueness. This fuzzy logic is a relatively young discipline, both serving as a foundation for the fuzzy logic in a broad sense and of independent logical interest, since it turns out that strictly logical investigation of this kind of logical calculi can go rather far. A basic monograph is Hajek 1998, further recommended monographs are Turunen 1999, Novak et al. 2000; also recent monographs dealing with many-valued logic (not specifically oriented to fuzziness), namely Gottwald 2001, Cignoli et al. 2000a; are highly relevant.

http://plato.stanford.edu/entries/logic-fuzzy/

@Minati Mishra: I would suggest the person to go for bottle 1 because according to the label of the 2nd bottle -the water in it is poison with a probability of 10% which implies, out of 10 bottles 10bottle contains poison. So, if the person will be unfortunate then the bottle in hand will be containing pure poison and he will surely die but according to the label of the 1st bottle the water is not completely safe but also not pure poison so the person can take a little of that and quench his thirst and can still survive.

Am I right?

Hello

I studied many logics, but sincerely I'm not very expert of fuzzy logic.

I was born with a light bulb with only two states, on and off.

Now a bulb light has the light trimmer, so they have on-off, and all the possible light intensity between on-off. This is my first mental image associated with fuzzy logic.

Second image: there is a glass with inside liquid.

I think that Fuzzy logic helps to understand if it is half full or half empty (For me, today, it is only a function of goals or scopes).

I think that I'll look a bit to fuzzy logic during summer holidays.

Regards

Dear @Giorgio Demontis,

Thank you very much for interesting answer.

Regards, Shafagat

Dear Shafagat,

Thank you for sharing very interesting question,

Fuzzy logic is an approach to computing based on "degrees of truth" rather than the usual "true or false" (1 or 0) Boolean logic on which the modern computer is based. The idea of fuzzy logic was first advanced by Dr. Lotfi Zadeh of the University of California at Berkeley in the 1960s.Fuzzy logic is an approach to computing based on "degrees of truth" rather than the usual "true or false" (1 or 0) Boolean logic on which the modern computer is based.  Dr. Zadeh was working on the problem of computer understanding of natural language. Natural language (like most other activities in life and indeed the universe) is not easily translated into the absolute terms of 0 and 1. (Whether everything is ultimately describable in binary terms is a philosophical question worth pursuing, but in practice much data we might want to feed a computer is in some state in between and so, frequently, are the results of computing.)

Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1, considered to be "fuzzy". By contrast, in Boolean logic, the truth values of variables may only be 0 or 1, often called "crisp" values. Fuzzy logic has been employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. Furthermore, when linguistic variables are used, these degrees may be managed by specific (membership) functions.

A type of logic that recognizes more than simple true and false values. With fuzzy logic, propositions can be represented with degrees of truthfulness and falsehood. For example, the statement,today is sunny,might be 100% true if there are no clouds, 80% true if there are a few clouds, 50% true if it's hazy and 0% true if it rains all day.Fuzzy logic has proved to be particularly useful in expert systemand other artificial intelligence applications. It is also used in somespell checkers to suggest a list of probable words to replace a misspelled one.

 with best regards,

Prem Baboo

Dear @Prem Baboo,

Thanks a lot for your perfect answers and useful links.

Regards, Shafagat

HI

Fuzzy logic is presented by Prof. Zadeh and he is a Iranian and American scientist.you can see following links:

https://en.wikipedia.org/wiki/Fuzzy_logic

https://people.eecs.berkeley.edu/~zadeh/

Dear Colleagues,

Good Day,

Please, watch this interesting short Youtube, entitled "An Introduction to Fuzzy Logic", It is (3:48 minutes in length).

https://www.youtube.com/watch?v=rln_kZbYaWc

I believe science is the foundation of human existance. Nobody has the right take it lightly.

Zadeh  (1965) observed that most of the concepts with which humans wrestle and label experience are imprecise or "fuzzy." This is both a necessity and an advantage. For example, consider comparatively simple labels, such as tall and very tall. There is no precise boundary between these two labels; people do not carry around in their heads numeric values to distinguish the concept very tall from tall. These are what Zadeh (1973) identified as fuzzy variables because of their gradual progression from membership to non-membership in a fuzzy set.

Thus, the central notion of fuzzy logic is that “truth values” or “membership values” can vary continuously from, by convention, 0 to 1. In contrast, when bivalent logic is used, there are only two possible “truth values”: 0 (false) and 1 (true).

For example, consider the statement:

“Bob is old.”

Using bivalent logic, this statement would be either true or false: Bob is either old or he is not. With fuzzy logic, its truth value can be any number between 0 and 1. If Bob’s age is 75, we might assign the statement a truth value of .80. It is tempting to interpret this truth value as meaning, “There is an 80% chance that Bob is old.” A fuzzy logician would interpret the .80 truth value as meaning, “Bob’s degree of membership within the set of old people is .80.” The semantic difference is significant: the first interpretation assumes that Bob is or is not old (still caught in the law of the excluded middle); it is just that we only have an 80% chance of knowing which set he is in. By contrast, fuzzy logic supposes that Bob is “more or less” old, or some other term corresponding to the value of .80. This allows Bob to also be a member of other age groups at the same time. For instance, we might say that his degree of membership in the set of middle-aged people is .40 and his degree of membership in the set of young people is .10. In bivalent logic, this simply is not allowed.

It is based on the observation that people make decisions based on imprecise and non-numerical information, fuzzy models or sets are mathematical means of representing vagueness and imprecise information, hence the term fuzzy. These models have the capability of recognising, representing, manipulating, interpreting, and utilising data and information that are vague and lack certainty.

For more details:

https://mechanicalsite.com/157/what-is-fuzzy-logic