The Digital Phenomenon : From concept to practice
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The hypnotherapist Milton H. Erickson noted likewise that the conscious mind and the unconscious normally interact. Some psychologists and logicians argue that fuzzy concepts are a necessary consequence of the reality that any kind of distinction we might like to draw has limits of application. At a certain level of generality, a distinction works fine.
But if we pursued its application in a very exact and rigorous manner, or overextend its application, it appears that the distinction simply does not apply in some areas or contexts, or that we cannot fully specify how it should be drawn. An analogy might be, that zooming a telescope , camera , or microscope in and out, reveals that a pattern which is sharply focused at a certain distance becomes blurry at another distance, or disappears altogether.
Faced with any large, complex and continually changing phenomenon, any short statement made about that phenomenon is likely to be "fuzzy", i. A correct, precise statement would require a lot of elaborations and qualifiers. Nevertheless, the "fuzzy" description turns out to be a useful shorthand that saves a lot of time in communicating what is going on "you know what I mean". In psychophysics , it was discovered that the perceptual distinctions we draw in the mind are often more definite than they are in the real world. Thus, the brain actually tends to "sharpen up" or "enhance" our perceptions of differences in the external world.
If there are more gradations and transitions in reality, than our conceptual or perceptual distinctions can capture, then it could be argued that how those distinctions will actually apply, must necessarily become vaguer at some point.
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In interacting with the external world, the human mind may often encounter new, or partly new phenomena or relationships which cannot yet be sharply defined given the background knowledge available, and by known distinctions, associations or generalizations. At the outset, information is often vague , even contradictory. Events move so quickly that decision makers experience a sense of loss of control.
Often denial sets in, and managers unintentionally cut off information flow about the situation" - L. Paul Bremer. It also can be argued that fuzzy concepts are generated by a certain sort of lifestyle or way of working which evades definite distinctions, makes them impossible or inoperable, or which is in some way chaotic. To obtain concepts which are not fuzzy, it must be possible to test out their application in some way.
But in the absence of any relevant clear distinctions, lacking an orderly environment, or when everything is "in a state of flux " or in transition, it may not be possible to do so, so that the amount of fuzziness increases. Fuzzy concepts often play a role in the creative process of forming new concepts to understand something. In the most primitive sense, this can be observed in infants who, through practical experience, learn to identify, distinguish and generalise the correct application of a concept, and relate it to other concepts.
However, fuzzy concepts may also occur in scientific, journalistic, programming and philosophical activity, when a thinker is in the process of clarifying and defining a newly emerging concept which is based on distinctions which, for one reason or another, cannot yet be more exactly specified or validated.
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Fuzzy concepts are often used to denote complex phenomena, or to describe something which is developing and changing, which might involve shedding some old meanings and acquiring new ones. It could be argued that many concepts used fairly universally in daily life e. Yet despite this limitation, such concepts are not meaningless.
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People keep using the concepts, even if they are difficult to define precisely. It may also be possible to specify one personal meaning for the concept, without however placing restrictions on a different use of the concept in other contexts as when, for example, one says "this is what I mean by X" in contrast to other possible meanings. In ordinary speech, concepts may sometimes also be uttered purely randomly; for example a child may repeat the same idea in completely unrelated contexts, or an expletive term may be uttered arbitrarily.
A feeling or sense is conveyed, without it being fully clear what it is about. Happiness may be an example of a word with variable meanings depending on context or timing. Fuzzy concepts can be used deliberately to create ambiguity and vagueness , as an evasive tactic, or to bridge what would otherwise be immediately recognized as a contradiction of terms. They might be used to indicate that there is definitely a connection between two things, without giving a complete specification of what the connection is, for some or other reason.
This could be due to a failure or refusal to be more precise. But it could also be a prologue to a more exact formulation of a concept, or to a better understanding of it. Fuzzy concepts can be used as a practical method to describe something of which a complete description would be an unmanageably large undertaking, or very time-consuming; thus, a simplified indication of what is at issue is regarded as sufficient, although it is not exact. There is also such a thing as an "economy of distinctions", meaning that it is not helpful or efficient to use more detailed definitions than are really necessary for a given purpose.
In this sense, Karl Popper rejected pedantry and commented that:.
I might perhaps state my position as follows. Every increase in clarity is of intellectual value in itself; an increase in precision or exactness has only a pragmatic value as a means to some definite end The provision of "too many details" could be disorienting and confusing, instead of being enlightening, while a fuzzy term might be sufficient to provide an orientation. The reason for using fuzzy concepts can therefore be purely pragmatic, if it is not feasible or desirable for practical purposes to provide "all the details" about the meaning of a shared symbol or sign.
Thus people might say "I realize this is not exact, but you know what I mean" — they assume practically that stating all the details is not required for the purpose of the communication. Zadeh picked up this point, and drew attention to a "major misunderstanding" about applying fuzzy logic. It is true that the basic aim of fuzzy logic is to make what is imprecise more precise. Yet in many cases, fuzzy logic is used paradoxically to "imprecisiate what is precise", meaning that there is a deliberate tolerance for imprecision for the sake of simplicity of procedure and economy of expression.
In such uses, there is a tolerance for imprecision, because making ideas more precise would be unnecessary and costly, while "imprecisiation reduces cost and enhances tractability" tractability means "being easy to manage or operationalize". Zadeh calls this approach the "Fuzzy Logic Gambit" a gambit means giving up something now, to achieve a better position later.
In the Fuzzy Logic Gambit, "what is sacrificed is precision in [quantitative] value, but not precision in meaning", and more concretely, "imprecisiation in value is followed by precisiation in meaning". Zadeh cited as example Takeshi Yamakawa 's programming for an inverted pendulum , where differential equations are replaced by fuzzy if-then rules in which words are used in place of numbers.
Common use of this sort of approach combining words and numbers in programming , has led some logicians to regard fuzzy logic merely as an extension of Boolean logic a two-valued logic or binary logic is simply replaced with a many-valued logic. However, Boolean concepts have a logical structure which differs from fuzzy concepts. An important feature in Boolean logic is, that an element of a set can also belong to any number of other sets; even so, the element either does, or does not belong to a set or sets.
By contrast, whether an element belongs to a fuzzy set is a matter of degree, and not always a definite yes-or-no question. All the same, the Greek mathematician Costas Drossos suggests in various papers that, using a "non-standard" mathematical approach, we could also construct fuzzy sets with Boolean characteristics and Boolean sets with fuzzy characteristics. For a simplified example, we might be able to state, that a concept X is definitely applicable to a finite set of phenomena, and definitely not applicable to all other phenomena.
Following ordinary set theory, this generates logical problems, if e.
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In mathematical logic , computer programming , philosophy and linguistics fuzzy concepts can be analyzed and defined more accurately or comprehensively, by describing or modelling the concepts using the terms of fuzzy logic or other substructural logics. More generally, clarification techniques can be used such as:. In this way, we can obtain a more exact understanding of the meaning and use of a fuzzy concept, and possibly decrease the amount of fuzziness.
It may not be possible to specify all the possible meanings or applications of a concept completely and exhaustively, but if it is possible to capture the majority of them, statistically or otherwise, this may be useful enough for practical purposes. A process of defuzzification is said to occur, when fuzzy concepts can be logically described in terms of fuzzy sets , or the relationships between fuzzy sets, which makes it possible to define variations in the meaning or applicability of concepts as quantities. Effectively, qualitative differences are in that case described more precisely as quantitative variations, or quantitative variability.
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Assigning a numerical value then denotes the magnitude of variation along a scale from zero to one. The difficulty that can occur in judging the fuzziness of a concept can be illustrated with the question "Is this one of those?
http://chronograffle.co.uk/map40.php If it is not possible to clearly answer this question, that could be because "this" the object is itself fuzzy and evades definition, or because "one of those" the concept of the object is fuzzy and inadequately defined. Thus, the source of fuzziness may be in 1 the nature of the reality being dealt with, 2 the concepts used to interpret it, or 3 the way in which the two are being related by a person. From Wikipedia, the free encyclopedia. Main article: Fuzzy logic. Main article: Defuzzification. Chicago: University of Chicago Press, Vagueness, Its Nature, and Its Logic.