If something is true it cannot be false, and if something is false it cannot be true. The same can be said of black and white. This principle of classical logic is one of the mainstays of the scientific method, but it loses effectiveness in the grey areas between these absolutes.
In other words, classical logic cannot adequately quantify elements that are black but also white, and which can only be differentiated by applying arbitrary distinctions of shades such as light grey, dark grey, or very dark grey. How many grains of sand can a desert lose before we cease to consider it a desert? How many degrees does the temperature in a room have to drop for it to be cold?
Fuzzy logic provides a channel for dealing scientifically with these qualitative concepts. “It is an extension of classical logic used to quantify vagueness”, explains Eduard Alarcón, a lecturer in the Department of Electronic Engineering at the UPC.
The concept of fuzzy logic derives from an article called “Fuzzy sets” published in 1965 by the engineer Lofti A. Zadeh. Eduard Alarcón explains that, “in classical logic, according to Bertrand Russell, from a set of antecedents is derived a set of consequents”. The system is based on a combination of rules taking the form “if” (antecedent), followed by “then” (consequent). “In fuzzy logic, both the antecedents and the consequents are fuzzy sets, which aim to quantify the vagueness of the qualifiers”, says Alarcón.
Joan Domingo, of the Department of Automatic Control, explains how fuzzy sets are used in a lighting control system. The system parameters, he explains, are a set of between three and six adjectives that describe the light intensity as, for example, “very low, low, sufficient, high and very high”. A series of light readings are taken, and a value is assigned to indicate the degree to which each reading corresponds to each of the adjectives. Thus, a very weak light could be assigned a value of 0.6 for “very low”, 0.3 could be “low”, and 0.1 “sufficient”. Each measurement is split between different sets, and the degree to which it corresponds to each one is represented by a function.
The system then applies a series of rules of the type “if ... then ...”, which are defined by an expert or directly integrated into the system. Thus, a rule might be, “if the light is very low, then we need to apply very high lighting”. These rules are applied to the input data using a chip- or algorithm-based inference motor. The output of each inference rule is an area, and the area of intersection of all the outputs is the final result, which is then translated into an action over the physical environment to which the system is applied.
These expert systems are based on rules that apply fuzzy logic, and have been integrated into electrical appliances, cameras, air-conditioning systems, industrial control systems and information technology in the last few decades.
More efficient appliances
Fuzzy systems also have a range of domestic applications, such as a washing machine that uses less detergent and water for lighter loads, or a control system for maintaining a comfortable temperature without switching on or off each time the thermostat registers a certain value, and without creating sudden rises or drops in temperature. This smooth transition between temperatures is achieved thanks to the degrees and zones used by fuzzy sets. Eduard Alarcón explains that fuzzy sets are analytical mathematical sets that provide a graded description referring to a specific zone. Each zone is independent of the others, and is therefore responsible for a single control action. By processing input values as degrees of zones, fuzzy systems can interpolate the results of different zones, thus ensuring that the resulting action is less abrupt.
Joan Domingo emphasizes the decision-making speed of inference motors which, unlike conventional processors, work in millions of fuzzy logic inferences per second (MFLIPS). “Classical control systems are analogue and slow, whereas fuzzy systems are digital and run at incredibly high speeds. Fuzzy systems are very easy to use, relatively quick to install, and produce excellent results”, he explains.
In addition to the development of new systems and devices, theoretical advances are also being made. For example, the Research Group on Functional Mathematical Modeling and Applications is currently studying improved fuzzy classification methods for solving problems caused by linguistic ambiguity in the definition of adjectives and imprecise measurement devices.
Control systems are the key product of fuzzy logic in the field automation and control, but UPC researchers are also incorporating fuzzy logic into the design of systems that will improve the quality of life of users in other areas, such as aeronautics and medical image analysis.
Detecting cancer cells
Can cancer cells be detected in a uterine tissue sample? Until recently, to answer this question a pathologist would have had to spend hours over the microscope examining a cytology sample of uterine tissue provided by a gynecologist. Samples of this size contain millions of cells, and prolonged examination can lead to tiredness and increased probability of error.
To minimize this risk, a joint research team from the UPC and Rovira i Virgili University, directed by Pilar Sobrevilla, of the Department of Applied Mathematics II, and Eduard Montseny, of the Department of Automatic Control, is working with the Hospital de Sant Pau to develop an automatic cytology image analysis system. Pilar Sobrevilla explains that “the system, which is based on fuzzy logic, isolates all of the cells in the image and determines their degree of normality”.
The system examines the image and determines the possible presence of abnormal cells on the basis of color and texture. The result is then displayed in a new image that highlights the areas containing cancerous cells. The process can be performed in real time, as the pathologist simply has to feed the original image into the device to obtain a modified version highlighting the areas that need to be examined more thoroughly.
The system is already used by the Hospital de Sant Pau, and researchers are working on a second phase of the project that, explains Sobrevilla, will enable users to pinpoint potentially affected areas with greater precision and obtain data that can be tailored to the specific information required by the doctor.
The same research group has also designed a system which uses a fuzzy logic algorithm to grade the quality of corneal tissue used in transplants, the first version of which is already used by the Tissue Bank of the Hospital de Sant Pau in Barcelona. The system analyzes images of corneal tissue to determine whether it is of suitable quality for transplantation, and factors in data on the general health of potential donors to determine whether they meet the relevant health requirements.
Fuzzy logic can also be used to model the noise pollution produced by planes at take-off and landing. Xavier Prats, of the Department of Mechanical Engineering, takes the idea a step further in his doctoral thesis, which describes a system for defining the optimal trajectory during these maneuvers to minimize the noise pollution affecting local residents. Joseba Quevedo, the joint director of the thesis with Vincenç Puig, explains that new satellite navigation systems have made it possible for planes to follow curved trajectories during take-off and landing, rather than the straight ascents and descents required previously.
By altering the trajectory, it is also possible to reduce the noise pollution suffered by those living close to airports, the severity of which depends on the tolerance of individuals, and is not an objective parameter such as the level of sound produced. As Quevedo explains, “A patient in a hospital ward does not hear things in the same way as a young person shopping in a market, and the perceived level of a particular sound can vary enormously between day-time and night-time due to changes in the acoustic level of the surroundings”. The system uses fuzzy logic to analyze the level of noise pollution and grade the annoyance caused to people in local facilities (such as hospitals, schools and markets) and residential areas located close to the airport. The analysis also takes into account the time of day and the distance at which the plane passes the area.
Fuzzy logic and soft computing
In 1991, Lofti A. Zadeh, a professor at the University of Berkeley and the founder of fuzzy logic, coined the term ‘soft computing’. This branch of artificial intelligence deals with the design of expert systems capable of managing inexact, uncertain and/or incomplete information. Fuzzy logic is one of the principal techniques in this field, together with evolutionary algorithms and neural networks. More than 2000 experts in soft computing from around the world will meet in Barcelona in July 2010 for the lEEE World Congress on Computational Intelligence, organized by the UPC researcher Pilar Sobrevilla.
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