Diffuse logic | Miquel Lacasta

Casas flotantes de Laurent Chehere, una imagen onírica imposible de reducir a un código binario de argumentos | laurentchehere.com
One of Laurent Chehere’s houseboats, an oneiric image impossible to reduce to a binary code of arguments. Thanks to the photographer Eve Germán for the reference | Source: laurentchehere.com

The essence of the diffuse logic resides in the expression everything is a question of degree, in clear opposition to the logic probabilística pure in that everything is 0 ó 1, really or falsely. In other words the diffuse logic uses expressions that are neither totally true nor completely false, definitively it might be said that the diffuse logic is the logic applied to concepts that can take a value any of veracity inside a set of values that range between two ends, the absolute truth and the total falsehood.

The diffuse logic is directly subsidiary of the concept of multivalency, which opposite is the bivalency, alone where there are two values, two possible ways of solving a question. On the contrary the multivalency admits for definition more than two options. In the bivalency there is needed that certain efforts are realized to adapt a response to both possible values: if or not, 1 ó 0, real or false. He sends directly to a binary logic. While, the multivalency allows answers type: more or less, or, a bit, very much, enough.

The binary, bivalent thought, it is reduccionista and provokes the loss of information on having elaborated a judgment or having given a response, since it rounds the values to come to someone of two opposite answers. On the other hand, the diffuse reasoning allows the use of intermediate values and especially it makes possible that a value belongs to two complementary sets simultaneously.

The diffuse logic definitively allows to be able to handle subjective questions to turn them into degrees, in levels. This characteristic does that it is the ideal tool for the processing of information from an investigation in the social field, for example, where the situations and dynamics cannot be treated like real or false absolute, but they send directly to a question of degree. Also the diffuse logic is very important in the programming software of search, as the very same Google, where searches are realized from approximations, or even from mistakes, grammatical or conceptual, and the program is capable of interpreting the entry of information and of giving an area of answers very near to the looked one. This aptitude to guess for what I am looking is a property that can be parametrized from the programming by diffuse logic.

The diffuse logic was proposed by the Azerbaijani and later nationalized American mathematician, Lotfi Zadeh in 1965 when it was chairman of the Department of Electrical Engineering and Electronics Research Laboratory of the University of California, Berkeley, in a qualified article Fuzzy Sets.Later, in 1968, publishes an extension of the first article in the Journal of Mathematical Analysis and Applications llamado Probability Measures of Fuzzy Events.

In the first article Zadeh it starts by defining the title of the same one as:

“A diffuse set they are a class of objects with a constant degree of belonging. This diffuse set is characterized by a function of belonging that assigns to every object a level of degree of belonging between 0 and 1. The notions of incorporation, an ión, intersection, complementarity, relation, convexity, etc., they are applicable to these sets, and several properties of these notions can be established in the context of the diffuse sets”.

To this diffuse beginning of the article about the diffuse sets, also called blurry sets, clarifier follows in the introduction one more text.

“Habitually the class of objects that we are in the physical royal world, does not have the criterion of belonging defined accurately. For example, the class animal includes clearly to the dogs, the horses, the birds, etc. As members, and also clearly type excludes objects rocks, fluids, plants, etc. Nevertheless, objects as the starfish, a bacterium, etc. They have an ambiguous status with regard to the class of animal that they are. The same type of ambiguity arises in case of a number as 10 in relation to the class of royal numbers that are bigger than 1.

Clearly, the class of all the numbers that are major that 1 or the class of the beautiful women or the class of the high men, they do not constitute a class or a set in the mathematical usual sense of the term. Nevertheless these classes imprecisamente definite play an important paper in the human thought, particularly in the domain of the bosses of recognition, the communication of the information and the abstraction.

The intention of this note is to explore to preliminary level, some of the properties and the implications of a concept that can be used to treat with the concept of class, of the type mentioned previously. The concept in question is such that a diffuse set, it is a class with a constant degree of belonging. It it comes to want to say that an object of this class can belong to several sets simultaneously”.

In the second mentioned article, Zadeh clarifies the nearby area of the theory of the probability to which the diffuse sets it goes affirming that though the notion of event and his probability of event constitutes the most basic concept of the theory of the probability, in the daily experience, one is in the habit of meeting situations where

“The event is rather diffuse, that not slightly perfectly definite”.7

The lack of definition of what it can mean a moderate day, for example, extends the field of application of the theory of the probability if it is applied together with the diffuse logic. That is to say, for some persons the moderate day can to them look like something fresh, and for others the moderate, too warm day. Applying strictly the theory of the probability, the possibility of being with a moderate day is remote well as for the satisfaction of the results refers. If the blurry logic is applied, it is probable that the process is more complex and therefore the most variegated results but it will not leave important parts of the information of side to come to a precise result.

Definitively the diffuse logic assumes that the reality to studying is much more complex than true laborator conditions, that of so abstract, they traverse the risk of being slightly applicable to complex dynamics. To this process Zadeh it is called it diffuse events.

From these two texts, the diffuse logic or the theory of the diffuse sets it developed a great advance at the end of the 70s and beginning of the 80, surely for his aptitude to parametrize linguistic affirmations of a certain vagueness – for example example allowing to establish a range to what a young person means, a person matures and an old person – and for the possibility later of incorporating logical operators like the modifiers linguistic AND, OR and THEN in the language of programming software.

Of the above mentioned thing till now, there is deduced also that the diffuse logic should be the own one of to operate proyectual of the architecture, the urbanism and the contemporary landscape. The projects that operate on the reality do not differ from the reality itself. They are based on the managing of the complexity as the only possible solution, to give pertinent answers. Nothing in the reality is reducible to a binary code, not so even the most basic or simpler operations. It is because of it that it is surprised that great of the current architecture still it is judged and is processed from the binary thing, when it seems to be impossible to close in an alone contraposition, the plot density of a project. Actually it might be said that the diffuse logic is the angular stone of a new modernity.

Miquel Lacasta. PhD architect
Barcelona, november 2013


Ver PEREZ PUEYO, Rossana, Accused and Optimization of Spectra Technical Raman Mediante of Diffuse Logic: Application to the Identification of Pictorial Materials, doctoral thesis of the Department of Teoría del Senyal i Comunicacions, UPC, Universitat Politécnica de Catalunya, Barcelona, 2005.

2 DIEGOLI, Samantha, The behavior of the small groups of work under the perspective of the complexity: descriptive Models and study of cases, doctoral thesis of the Division of Sciences of the Health, Faculty of Psychology of the Department of Social Psychology of the Universitat de Barcelona, 2003.

ZADEH, Lotfi, “Fuzzy Sets”, Information and Control, núm. 8, 1965, pp. 338-353.

ZADEH, Lotfi, “Probability Measures of Fuzzy Events”, Journal of Mathematical Analysis and Aplications, Vol. 23, núm. 2, Agosto 1968, pp. 421-427.

5 Op. Cit., ZADEH, 1965, p. 338.

6 Ibídem, p. 339.

7 Op. Cit., ZADEH, 1968, p. 421.

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