Fuzzy concept

# Fuzzy concept

Discussion

Encyclopedia
A fuzzy concept is a concept
Concept
The word concept is used in ordinary language as well as in almost all academic disciplines. Particularly in philosophy, psychology and cognitive sciences the term is much used and much discussed. WordNet defines concept: "conception, construct ". However, the meaning of the term concept is much...

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
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

, 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
Range
-In mathematics:* Range , the set of all output values produced by a function* Interval , also called a range, a set of real numbers that includes all numbers between any two numbers in the set...

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
Uncertainty
Uncertainty is a term used in subtly different ways in a number of fields, including physics, philosophy, statistics, economics, finance, insurance, psychology, sociology, engineering, and information science...

(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
God
God is the English name given to a singular being in theistic and deistic religions who is either the sole deity in monotheism, or a single deity in polytheism....

, 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
Dictionary
A dictionary is a collection of words in one or more specific languages, often listed alphabetically, with usage information, definitions, etymologies, phonetics, pronunciations, and other information; or a book of words in one language with their equivalents in another, also known as a lexicon...

, a thesaurus
Thesaurus
A thesaurus is a reference work that lists words grouped together according to similarity of meaning , in contrast to a dictionary, which contains definitions and pronunciations...

or an encyclopedia
Encyclopedia
An encyclopedia is a type of reference work, a compendium holding a summary of information from either all branches of knowledge or a particular branch of knowledge....

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
Message
A message in its most general meaning is an object of communication. It is a vessel which provides information. Yet, it can also be this information. Therefore, its meaning is dependent upon the context in which it is used; the term may apply to both the information and its form...

, 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
Context (language use)
Context is a notion used in the language sciences in two different ways, namely as* verbal context* social context- Verbal 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
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...

and binary logic
Binary logic
Binary logic could refer to:* any two-valued logic, especially in social sciences* classical propositional two-valued logic, also called boolean logic in engineering, which is the logical foundation of digital electronics...

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
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...

, 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
Learning
Learning is acquiring new or modifying existing knowledge, behaviors, skills, values, or preferences and may involve synthesizing different types of information. The ability to learn is possessed by humans, animals and some machines. Progress over time tends to follow learning curves.Human learning...

or the growth of understanding
Understanding
Understanding is a psychological process related to an abstract or physical object, such as a person, situation, or message whereby one is able to think about it and use concepts to deal adequately with that object....

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
Analogy
Analogy is a cognitive process of transferring information or meaning from a particular subject to another particular subject , and a linguistic expression corresponding to such a process...

might be that zooming a telescope
Telescope
A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...

, camera
Camera
A camera is a device that records and stores images. These images may be still photographs or moving images such as videos or movies. The term camera comes from the camera obscura , an early mechanism for projecting images...

, or microscope
Microscope
A microscope is an instrument used to see objects that are too small for the naked eye. The science of investigating small objects using such an instrument is called microscopy...

in and out reveals that a pattern which is sharply focused at a certain distance disappears at another distance.

In psychophysics
Psychophysics
Psychophysics quantitatively investigates the relationship between physical stimuli and the sensations and perceptions they effect. Psychophysics has been described as "the scientific study of the relation between stimulus and sensation" or, more completely, as "the analysis of perceptual...

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
Test method
A test method is a definitive procedure that produces a test result.A test can be considered as technical operation that consists of determination of one or more characteristics of a given product, process or service according to a specified procedure. Often a test is part of an experiment.The 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
Flux
In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.* In the study of transport phenomena , flux is defined as flow per unit area, where flow is the movement of some quantity per time...

" 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
Complexity
In general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. The study of these complex linkages is the main goal of complex systems theory. In science there are at this time a number of approaches to characterizing complexity, many of which are...

phenomena, or to describe something which is developing and changing, which might involve shedding some old meanings and acquiring new ones.
• In politics
Politics
Politics is a process by which groups of people make collective decisions. The term is generally applied to the art or science of running governmental or state affairs, including behavior within civil governments, but also applies to institutions, fields, and special interest groups such as the...

, 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
Political power
Political power is a type of power held by a group in a society which allows administration of some or all of public resources, including labour, and wealth. There are many ways to obtain possession of such power. At the nation-state level political legitimacy for political power is held by the...

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
Translation
Translation is the communication of the meaning of a source-language text by means of an equivalent target-language text. Whereas interpreting undoubtedly antedates writing, translation began only after the appearance of written literature; there exist partial translations of the Sumerian Epic of...

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
Theology
Theology is the systematic and rational study of religion and its influences and of the nature of religious truths, or the learned profession acquired by completing specialized training in religious studies, usually at a university or school of divinity or seminary.-Definition:Augustine of Hippo...

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
Supernatural
The supernatural or is that which is not subject to the laws of nature, or more figuratively, that which is said to exist above and beyond nature...

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
Meteorology
Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...

, 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
Expletive attributive
Expletive comes from the Latin verb explere, meaning "to fill", via expletivus, "filling out". It was introduced into English in the seventeenth century to refer to various kinds of padding—the padding out of a book with peripheral material, the addition of syllables to a line of poetry for...

term may be uttered arbitrarily.

Fuzzy concepts can be used deliberately to create ambiguity
Ambiguity
Ambiguity of words or phrases is the ability to express more than one interpretation. It is distinct from vagueness, which is a statement about the lack of precision contained or available in the information.Context may play a role in resolving ambiguity...

and vagueness
Vagueness
The term vagueness denotes a property of concepts . A concept is vague:* if the concept's extension is unclear;* if there are objects which one cannot say with certainty whether belong to a group of objects which are identified with this concept or which exhibit characteristics that have this...

, as an evasive tactic, or to bridge what would otherwise be immediately recognized as a contradiction
In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other...

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
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...

, programming, philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...

and linguistics
Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....

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
Taxonomy
Taxonomy is the science of identifying and naming species, and arranging them into a classification. The field of taxonomy, sometimes referred to as "biological taxonomy", revolves around the description and use of taxonomic units, known as taxa...

).
• 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
Boolean logic
Boolean algebra is a logical calculus of truth values, developed by George Boole in the 1840s. It resembles the algebra of real numbers, but with the numeric operations of multiplication xy, addition x + y, and negation −x replaced by the respective logical operations of...

).
• 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
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

) 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.

• Dialectic
Dialectic
Dialectic is a method of argument for resolving disagreement that has been central to Indic and European philosophy since antiquity. The word dialectic originated in Ancient Greece, and was made popular by Plato in the Socratic dialogues...

• Fuzzy logic
Fuzzy logic
Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree between 0 and 1...

• Fuzzy mathematics
Fuzzy mathematics
Fuzzy mathematics forms a branch of mathematics related to fuzzy set theory and fuzzy logic. It started in 1965 after the publication of Lotfi Asker Zadeh's seminal work Fuzzy sets. A fuzzy subset A of a set X is a function A:X→L, where L is the interval [0,1]. This function is also called a...

• Precision
Precision
Concepts* Accuracy and precision, measurement deviation from true value and its scatter* Precision , the number of digits from which a value is expressed* Precision , the percentage of documents returned that are relevant...

• Opaque context
Opaque context
An opaque context is a linguistic context in which it is not always possible to substitute co-referential expressions salva veritate. In other words, substitution of co-referential expressions into an opaque context does not always preserve truth...

• Identity (Philosophy)
Identity (philosophy)
In philosophy, identity, from , is the relation each thing bears just to itself. According to Leibniz's law two things sharing every attribute are not only similar, but are the same thing. The concept of sameness has given rise to the general concept of identity, as in personal identity and...

• Referential transparency (computer science)
• reflexivity (social theory)
Reflexivity (social theory)
Reflexivity refers to circular relationships between cause and effect. A reflexive relationship is bidirectional with both the cause and the effect affecting one another in a situation that does not render both functions causes and effects...

• Phenomenology (science)
Phenomenology (science)
The term phenomenology in science is used to describe a body of knowledge that relates empirical observations of phenomena to each other, in a way that is consistent with fundamental theory, but is not directly derived from theory. For example, we find the following definition in the Concise...