Fuzzy Concept

Life does not always fit neatly in boxes

A fuzzy concept is a concept of which the boundaries of application can vary considerably according to context or conditions, instead of being fixed once and for all. This means the concept is vague in some way, lacking a fixed, precise meaning, without however being unclear or meaningless altogether. It has a definite meaning, which can be made more precise only through further elaboration and specification - including a closer definition of the context in which the concept is used. The study of the characteristics of fuzzy concepts and fuzzy language is called fuzzy semantics. The inverse of a "fuzzy concept" is a "crisp concept" (i.e. a precise concept).

especially boxes that humans defined

In Philosophy

In philosophical logic and linguistics, fuzzy concepts are often regarded as vague concepts which in their application, or formally speaking, are neither completely true nor completely false, or which are partly true and partly false; they are ideas which require further elaboration, specification or qualification to understand their applicability (the conditions under which they truly make sense). 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 if strict criteria are used.


In mathematics and computer science, the gradations of applicable meaning of a fuzzy concept are described in terms of quantitative relationships defined by logical operators. Such an approach is sometimes called "degree-theoretic semantics" by logicians and philosophers, but the more usual term is fuzzy logic or many-valued logic. The novelty of fuzzy logic is, that it "breaks with the traditional principle that formalisation should correct and avoid, but not compromise with, vagueness". The basic idea of fuzzy logic is that a real number is assigned to each statement written in a language, within a range from 0 to 1, where 1 means that the statement is completely true, and 0 means that the statement is completely false, while values less than 1 but greater than 0 represent that the statements are "partly true", to a given, quantifiable extent. Susan Haack comments: "Whereas in classical set theory an object either is or is not a member of a given set, in fuzzy set theory membership is a matter of degree; the degree of membership of an object in a fuzzy set is represented by some real number between 0 and 1, with 0 denoting no membership and 1 full membership." "Truth" in this mathematical context usually means simply that "something is the case", or that "something is applicable". This makes it possible to analyze a distribution of statements for their truth-content, identify data patterns, make inferences and predictions, and model how processes operate. Petr Hájek claimed that "fuzzy logic is not just some "applied logic", but may bring "new light to classical logical problems", and therefore might be well classified as a distinct branch of "philosophical logic" similar to e.g. modal logics.

Fuzzy logic offers computationally-oriented systems of concepts and methods, to formalize types of reasoning which are ordinarily approximate only, and not exact. In principle, this allows us to give a definite, precise answer to the question, "To what extent is something the case?", or, "To what extent is something applicable?". Via a series of switches, this kind of reasoning can be built into electronic devices. That was already happening before fuzzy logic was invented, but using fuzzy logic in modelling has become an important aid in design, which creates many new technical possibilities. Fuzzy reasoning (i.e., reasoning with graded concepts) turns out to have many practical uses.[51] It is nowadays widely used in: The programming of vehicle and transport electronics, household appliances, video games, language filters, robotics, and driverless vehicles. Fuzzy logic washing machines are gaining popularity. All kinds of control systems that regulate access, traffic, movement, balance, conditions, temperature, pressure, routers etc. Electronic equipment used for pattern recognition, surveying and monitoring (including radars, satellites, alarm systems and surveillance systems). Cybernetics research, artificial intelligence, virtual intelligence, machine learning, database design and soft computing research. "Fuzzy risk scores" are used by project managers and portfolio managers to express financial risk assessments.[55] Fuzzy logic has been applied to the problem of predicting cement strength. It looks like fuzzy logic will eventually be applied in almost every aspect of life, even if people are not aware of it, and in that sense fuzzy logic is an astonishingly successful invention. The scientific and engineering literature on the subject is constantly increasing.

In mathematics and statistics, a fuzzy variable (such as "the temperature", "hot" or "cold") is a value which could lie in a probable range defined by some quantitative limits or parameters, and which can be usefully described with imprecise categories (such as "high", "medium" or "low") using some kind of scale or conceptual hierarchy.


Sandwich Example
Food item Contains bread Bread is separately baked Bread contains the other ingredients during eating Two separate bread layers "Sandwich" is in the name (U.S.) Made with slices from English sandwich bread loaf Unweighted score Classified as
Peanut butter and jelly sandwich Yes Yes Yes Yes Yes Yes Yes 7 Sandwich
Bacon, lettuce, and tomato sandwich Yes Yes Yes Yes Yes Yes Yes 7 Sandwich
Toast sandwich Yes Yes Yes Yes Yes (despite inner 3rd bread slice) Yes Yes 7 Sandwich
Croque-monsieur Yes Yes Yes (but re-cooked) No (due to cheese on outside) Yes No Yes 5 Sandwich
Banh mi Yes Yes Yes Yes Maybe Maybe (sometimes called "banh mi sandwich") No (baguette) 5 Roll (UK/Australia) or sandwich (US)
Panini Yes Yes Yes (but re-toasted) Yes Yes No (only in Italian) No 5 Pressed sandwich (e.g. with the Cuban sandwich)
with bun Yes Yes Yes Yes Yes No No (hamburger bun or bread roll) 5 Burger (UK/Australia), sometimes disputed as a sandwich vs. hamburger (US) due to tradition and the use of bun instead of bread.
Hamburger without bun Yes No No No No No No 1 Burger (patty) with toppings
Hot dog with bun Yes Yes Yes Yes No No No (hot dog bun) 4 Disputed. Some classify as a sausage sandwich. Others classify as a hot dog (a type of non-sandwich sausage dish due to tradition or the vertical orientation of the bread sides.
Submarine sandwich Yes Yes Yes Yes Maybe Yes No (hoagie roll) 5.5 Roll (UK/Australia) or sandwich (US)
Pita pocket Yes Yes Yes Yes No No No 4 Pocket sandwich
Gyro Yes Yes Yes Yes No No No 4 Sandwich
Wraps and burritos Yes Yes Yes Yes No No No 4 Disputed. Legal classification varies by jurisdiction.
Tacos and quesadillas Yes Yes Yes Yes No No No 4 Disputed, with some classifying as non-sandwich tortilla-based dishes, either due to separate culinary tradition (Spain vs. UK) or the vertical nature of bread sides in tacos.
Calzone Yes Yes No Yes No No No 3 Dumpling or folded pizza
Bread dumpling Yes Yes No Yes No No No 3 Dumpling
Egg roll Yes Yes No Yes No No No 3 Dumpling
Cha siu bao Yes Yes No Yes No No No 3 Dumpling
Open-faced sandwich Yes Yes Yes No No Yes Yes 5 Open-faced sandwich
Sandwich cake Yes Maybe (cake is bread-like) No No Yes Maybe ("layer cake" in US, "sandwich" in UK) No 3 Cake (mostly named by analogy due to repeated layering)
Pizza Yes Yes No No No No No 2 Savory pie
Salad with croutons Yes Yes Yes No No No No 2 Salad
Ice cream cone with ice cream Yes No No No No No No 1 Pastry
Ice cream sandwich Yes No No No No Yes No 2 Sandwich cookie (named by analogy to bread sandwiches)
Aluminium foam sandwich No No No No No Yes No 1 (named by analogy to bread sandwiches)