Fuzzy concept

A fuzzy concept is a concept of which the content, value, or boundaries of application can vary according to context or conditions, instead of being fixed once and for all.

Usually this means the concept is vague, lacking a fixed, precise meaning, without however being meaningless altogether. It does have a meaning, or rather multiple meanings (it has different semantic associations). But these can become clearer only through further elaboration and specification, including a closer definition of the context in which they are used. Fuzzy concepts (Markusen, 2003) "lack clarity and are difficult to test or operationalize". In logic, fuzzy concepts are often regarded as concepts which in their application are neither completely true or completely false, or which are partly true and partly false. A fuzzy variable (such as "the temperature", "hot" or "cold") is a value which could lie in a probable range defined by quantitative limits or parameters and can be usefully described with imprecise categories (such as "high", "medium" or "low").

Fuzzy concepts may generate uncertainty (they do not provide a clear orientation for action or decision-making) and reducing fuzziness may generate more certainty. However, this is not necessarily always so, insofar as a concept, although it is not fuzzy at all and very exact, could equally well fail to capture the meaning of something adequately. A concept can be very precise, but not - or insufficiently - applicable or relevant in the situation to which it refers. A fuzzy concept may indeed provide more security, because it provides a meaning for something when an exact concept is unavailable - which is better than not being able to denote it at all. A concept such as God, although not easily definable, for instance can provide security to the believer.

Fuzzy concepts and language
Ordinary language, which uses symbolic conventions and associations which are often not logical, inherently contains many fuzzy concepts - "knowing what you mean" in this case depends on knowing the context or being familiar with the way in which a term is normally used, or what it is associated with. This can be easily verified for instance by consulting a dictionary, a thesaurus or an encyclopedia which show the multiple meanings of words, or by observing the behaviours involved in ordinary relationships which rely on mutually understood meanings.

To communicate, receive or convey a message, an individual somehow has to bridge his own intended meaning and the meanings which are understood by others, i.e. the message has to be conveyed in a way that it will be socially understood, preferably in the intended manner. Thus, people might state: "you have to say it in a way that I understand".

This may be done instinctively, habitually or unconsciously, but it usually involves a choice of terms, assumptions or symbols whose meanings may often not be completely fixed, but which depend among other things on how the receiver of the message responds to it, or the context. In this sense, meaning is often "negotiated" (or, more cynically, manipulated). This gives rise to many fuzzy concepts.

But even using ordinary set theory and binary logic to reason something out, logicians have discovered that it is possible to generate statements which are logically speaking not completely true or imply a paradox, even although in other respects they conform to logical rules.

Origin of fuzzy concepts
The origin of fuzzy concepts is partly de to the fact that the human brain does not operate like a computer. While computers use strict binary logic gates, the brain does not; i.e., it is capable of making all kinds of neural associations according to all kinds of ordering principles (or fairly chaotically) in associative patterns which are not logical but nevertheless meaningful. Something can be meaningful although we cannot name it, or we might only be able to name it and nothing else. The human brain can also interpret the same phenomenon in several different but interacting frames of reference, at the same time, or in quick succession.

In part, fuzzy concepts arise also because learning or the growth of understanding involves a transition from a vague awareness, which cannot orient behaviour greatly, to clearer insight, which can orient behaviour.

Some 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. As a certain level of generality, it 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 disappears at another distance.

In psychophysics it has been discovered that the perceptual distinctions we draw in the mind are often more sharply defined than they are in the real world. Thus, the brain actually tends to "sharpen up" our perceptions of differences in the external world. Between black and white, we are able to detect only a limited number of shades of gray, or colour gradations. If there are more gradations and transitions in reality than our conceptual distinctions can capture, then it could be argued that how those distinctions will actually apply must necessarily become vaguer at some point. If, for example, one wants to count and quantify distinct objects using numbers, one needs to be able to distinguish between those separate objects, but if this is difficult or impossible, then, although this may not invalidate a quantitative procedure as such, quantification is not really possible in practice; at best, we may be able to assume or infer indirectly a certain distribution of quantities.

Finally, 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.

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, 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.

Use of fuzzy concepts
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. 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.


 * In politics, it can be highly important and problematic how exactly a conceptual distinction is drawn, or indeed whether a distinction is drawn at all; distinctions used in administration may be deliberately sharpened, or kept fuzzy, due to some political motive or power relationship. A politician may be deliberately vague about some things, and very clear and explicit about others. The "fuzzy area" can also refer simply to a residual number of cases which cannot be allocated to a known and identifiable group, class or set.


 * In translation work, fuzzy concepts are analyzed for the purpose of good translation. A concept in one language may not have quite the same meaning or significance in another language, or it may not be feasible to translate it literally, or at all. Some languages have concepts which do not exist in another language, raising the problem of how one would most easily render their meaning.


 * In information services fuzzy concepts are frequently encountered because a customer or client asks a question about something which could be interpreted in many different ways, or, a document is transmitted of a type or meaning which cannot be easily allocated to a known type or category, or to a known procedure. It might take considerable inquiry to "place" the information, or establish in what framework it should be understood.


 * In the legal system, it is essential that rules are interpreted and applied in a standard way, so that the same cases and the same circumstances are treated equally. Otherwise one would be accused of arbitrariness, which would not serve the interests of justice. Consequently, lawmakers aim to devise definitions and categories which are sufficiently precise that they are not open to different interpretations. For this purpose, it is critically important to remove fuzziness, and differences of interpretation are typically resolved through a court ruling based on evidence.


 * In statistical research, it is an aim to measure the magnitudes of phenomena. For this purpose, phenomena have to be grouped and categorized so that distinct and discrete counting units can be defined. It must be possible to allocate all observations to mutually exclusive categories so that they are properly quantifiable. Survey observations do not spontaneously transform themselves into countable data; they have to be identified, categorized and classified in such a way that they are not counted twice or more. Again, for this purpose it is a requirement that the concepts used are exactly defined, and not fuzzy.


 * In theology an attempt is made to define more precisely the meaning of spiritual concepts, which refer to how human beings construct the meaning of human existence, and, often, the relationship people have with a supernatural world. Many spiritual concepts and beliefs are fuzzy, to the extent that, although abstract, they often have a highly personalized meaning, or involve personal interpretation of a type that is not easy to define in a cut-and-dried way.


 * In meteorology, where changes and effects of complex interactions in the atmosphere are studied, the weather reports often use fuzzy expressions indicating a broad trend, likelihood or level. The main reason is that the forecast can rarely be totally exact for any given location.


 * In phenomenology which studies the structure of subjective experience, an important insight is that how someone experiences something can be influenced both by the influence of the thing being experienced itself, but also by how the person responds to it. Thus, the actual experience the person has, is shaped by an "interactive object-subject relationship". To describe this experience, fuzzy categories are often necessary, since it is often impossible to predict or describe with great exactitude what the interaction will be, and how it is experienced.

It could be argued that many concepts used fairly universally in daily life (e.g. "love" or "God" or "health" or "social") are inherently or intrinsically fuzzy concepts, to the extent that their meaning can never be completely and exactly specified with logical operators or objective terms, and can have multiple interpretations, which are in part exclusively subjective. Yet despite this limitation, such concepts are not meaningless. 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.

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 could be a prologue to a more exact formulation of a concept, or a better understanding. It could also simply be a practical method to describe something of which a complete description would be an unmanageably large undertaking, or very time-consuming.

Analysis of fuzzy concepts
In mathematical logic, programming, philosophy and linguistics fuzzy concepts can however be analyzed and defined more accurately or comprehensively, for instance:


 * by specifying a range of conditions to which the concept applies.
 * by classifying or categorizing all or most cases or uses to which the concept applies (taxonomy).
 * by probing the assumptions on which a concept is based, or which are associated with its use (Critical thought).
 * by identifying operational rules for the use of the concept, which cover all or most cases.
 * by allocating different applications of the concept to different but related sets (e.g. using Boolean logic).
 * by examining how probable it is that the concept applies, statistically or intuitively.
 * by examining the distribution or distributional frequency of (possibly different) uses of the concept.
 * by some other kind of measure or scale of the degree to which the concept applies.
 * by specifying a series of logical operators (an inferential system or algorithm) which captures all or most cases to which the concept applies.
 * by mapping or graphing the applications of the concept using some basic parameters.
 * by applying a meta-language which includes fuzzy concepts in a more inclusive categorical system which is not fuzzy.
 * by reducing or restating fuzzy concepts in terms which are simpler or similar, and which are not fuzzy or less fuzzy.
 * by relating the fuzzy concept to other concepts which are not fuzzy or less fuzzy, or simply by replacing the fuzzy concept altogether with another, alternative concept which is not fuzzy yet "works exactly the same way".



In this way, we can obtain a more exact understanding of the 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.

The difficulty that can occur in judging the fuzziness of a concept can be illustrated with the question "Is this one of those?". 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 the nature of the reality being dealt with, the concepts used to interpret it, or the way in which the two are being related by a person.