This document addresses the issue of fuzzy logic, starting with a brief background presentation of this concept by its author Lofti Zaedeh, subsequently addressing the principles to analyze each of the stages that lead to the generation of these systems, including in this regard concepts such as: uncertainty and probability, marking the main differences between the two. Finally, its application in the area of organizational administration is exposed.
Keywords: fuzzy logic, uncertainty, systems.
Introduction
The opportunity generated by fuzzy logic is to be able to formalize dialectical logical thinking, applying mathematics, this thanks to the union of the Aristotelian classical tradition, followed and transformed by mathematics with dielectric logic. Fuzzy mathematics, already as a tool for calculating truth criteria, starts from a scale of values from the most false to the most true, generating a quantitative result, which results in guaranteeing the option closest to the truth. The theory of fuzzy logic provides through mathematics, being able to model the uncertainty of people's cognitive processes.
Background
The term fuzzy logic was generated in the 1970s by Lofti Zaedeh. Later in 1974 Ebrahim Mamdani applied the concepts of fuzzy logic in the control of processes and created the first fuzzy control to regulate a steam engine. In 1985 Takagi and Sugeno established the theory of fuzzy control. Its applications in process control are evident in industry, medicine, aeronautics and electronics. (Robaina, 2010)
Fuzzy logic principles
Fuzzy logic or Fussy logic by its name in English, is oriented to the modeling of imprecise modes of reasoning, which are important for the path towards making rational decisions in an environment of uncertainty and imprecision. This depends on the ability to infer a close answer to questions that are based on a body of knowledge that is inaccurate, incomplete, or not entirely reliable. Fuzzy logic allows to represent the common knowledge of the qualitative linguistic type in a mathematical language through the theory of fuzzy sets. (Pérez, 2007)
Fuzzy logic has the purpose of identifying the results of a non-linear phenomenon without leaving aside the circumstances in which it occurs and the qualitative characteristics; on the other hand, traditional statistics and linear mathematics only give a specific or functional approximation of its behavior and of a phenomenon in general. (Mendoza, 2009)
Fuzzy logic is based on concepts that are perceived differently by each person. For example, there are people who conceptualize a slim person if they weigh less than 70 kg. Others, depending on their point of view, are conceived in a state of fat with a weight above 70 kg. This is why the thin, fat, and obese sets are called fuzzy sets. A fuzzy set is a set with blurred or not quite well established boundaries. Later, once the variables have been classified in the fuzzy sets, a value is assigned to them, these values have to do with the context in which the problem is found. In fuzzy logic, a percentage of membership is assigned to a set that is numerically the same. This concept is called the degree of membership, which can take values from 0 to 1; number 1,0 represents set membership and 0 represents no set membership.
This can be exemplified in the following table.
Diffuse logic
Table 1. Own elaboration
The new intervals of the fuzzy sets are defined, which is called the membership function (µ). The form of the intervals is chosen taking into account the experience of people, on the concept of physical state in kilos. This translation of real-world values into fuzzy logic through membership functions is called fussyification.
A graph is made where the "y" axis is the degree of membership, which quantitatively describes the membership function. In the axis of the "x" the kilos are established. The associated name (thin, fat, obese) is called linguistic significance and qualitatively describes the membership function. The form of the membership function is chosen according to the problematic situation to be resolved. There are different shapes for example: triangular, Gaussian, trapezoidal, sigmoidal, among others. The degree of associated membership, depending on the membership function, is called the degree of membership (GP).
A decision can be made from the membership functions, this step is known as inference. According to the experience or perception that occurs in the problem, this is known as fuzzy rules and can be written in the form if …… then.
Starting from the entry and exit membership function, the following methodology is continued:
- Inference process. For each degree of membership associated with the variable under measurement, conclusions are generated. This can be by the truncation method, which consists of cutting the exit membership function, so that values greater than the associated membership degree disappear. Or by the scaling method, which consists of scaling the membership function in proportion to the degree of membership. A final conclusion is made combining the fuzzy conclusions. Finally, the final conclusion is defuzzyfica, that is, it is taken back to the real world, through the use of various techniques such as:
- Averages of maximums, which calculates the average of all the variables that have the highest degree of membership. Center method. Which calculates the weighted average of the output.
For the selection of the deffuzyfication method, it will be according to which meets the needs and behavior of the process. Although the concepts of fuzzy logic arise from the experience of the problem situation, their field of application has been important in processes where it is difficult to predict or model mathematically. (Guzmán, 2006)
Fuzzy logic and probability
Probability represents data on the frequency of occurrences of a well-defined event out of the total number of possible events. On the other hand, the degree of diffuse membership represents the similarities of an event with respect to another event, in which the characteristics of those events are not well defined.
Uncertainty
Uncertainty can be classified as: deterministic, random, ambiguous or unspecified, vagueness and confusion. (Torres & Tranchita, 2004) Each of them are detailed below:
Determinism. It is the perfect knowledge of the results and the occurrence of events, from this point uncertainty is not considered.
Random uncertainty. This occurs when the possible events resulting from an experiment are known, for example tossing a coin.
Uncertainty of ambiguity or non-specific. This is when a statement can be true or false. In this regard, the probability is established empirically, subjective or experimentally and can be given in terms of ranges instead of absolute values. At this point the events are not specified or well defined, since there is a lack of information. This is the vagueness that makes it impossible to establish the truth or falsity of a situation.
Confusion uncertainty. This type has both ambiguous and vague characteristics.
If the uncertainty is of a random type, from the probability aspect, the uncertainty problems can be modeled by assigning probabilities to the different events by means of relative frequency and statistical analysis. Thus we can obtain an adequate measurement of the probability of events happening.
But there are situations in which this is not possible from the subjective point of view, since the probability is considered as a personal measure of the uncertainty or belief about an event or an object and the probability does not exist, since it is not defined. This is why some problems can be modeled, because there are no static data, but their probability can be assigned based on people's belief about the occurrence. Among the techniques for modeling uncertainty are Bayesian networks and Markow chains.
In the case of ambiguity and vagueness, where it is not possible to precisely define the truth or falsity of a statement, the modeling of uncertainty is performed by fuzzy logic.
Fuzzy logic systems
A fuzzy logic system uses inference, which is made up of five blocks, as shown in figure no. 1. A rule base containing a number of fuzzy rules yes…. So…, a database that defines the membership functions of the fuzzy sets used in the fuzzy rules, a decision-making unit in which the inference operations are determined according to the rules, a broadcast interface in the that transforms specific inputs into degrees of equivalence with linguistic values and a defusification interface that converts fuzzy results of inference into accurate output.
Fuzzy logic system. (Torres & Tranchita, 2004)
There are two types of diffuse models of differentiation based on the consequent of the rules. The first model is the Mamdani type system. In this, the consequents of the rules are membership functions. Later, these rules are evaluated by an aggregation operator that is a maximum function, so a fuzzy set is obtained which is then de-diffused.
The other model is the Tsukamoto type, in which the consequents of the rule are monotonically non-decreasing functions. The inferred decade rule output is reduced as an induced true value. The global output is the weighted average of the output of each rule.
In both systems the consequent of each rule is an input plus a constant term, and the final output is the weighted average of the output of each rule. (Torres & Tranchita, 2004)
Fuzzy logic in administration
The classic models of rationality in the area of decision making, such as normative decision theory, descriptive methods and game theory are today the basis of decision support systems and support modern administration. But these models put aside human subjectivity. The logical administration uses integrated fuzzy models for decision making and aims to achieve organizational coherence, organizational decision making can be focused from different points, be it psychology, economics and administration. For the first two, mathematical models have been used in the so-called experimental psychology and economics, they use models of limited rationality, which try to describe how the human being decides.Another aspect in decision making is through expert systems, through artificial intelligence, with uncertainty programming. (Keropyan & Gil-Lafuente, 2011)
On the other hand, logical administration uses models based on fuzzy logic through knowledge engineering techniques, based on literature and experience, to guide the organization towards competitiveness. Three models are classified:
- Cognitive model. They employ the use of multivalent logic and other fuzzy logic elements such as modifiers to transform expert knowledge and supporting information into formal models. Structural models. They use fuzzy relationships to take into account the structural complexity of organizations and their fit in the environment. Calculation model in uncertainty. It uses fuzzy arithmetic to visualize the possible variations of the dependent variables in the calculations of the dependent variables. (Espín & Vanti, 2006)
conclusion
Fuzzy logic or also called fuzzy logic, is the logic that uses uncertain or imprecise expressions, this analysis is carried out by combining input variables, which are defined in terms of fuzzy sets, through groups of rules that generate one or multiple output values. One of the applications with respect to administration is to be able to make strategic decisions for the organization, considering objective issues in the first instance and not leaving aside subjective characteristics that influence the outcome of the decisions.
Thesis topic
Proposal of a fuzzy logic model for the quantification of customer satisfaction in the after sales service in a car dealership.
goals
Design a survey to obtain the information corresponding to the degree of satisfaction on the part of the clients of the car agency. Define the variables to make the fuzzy set, based on the responses obtained in the survey.
References
- Espín, R., & Vanti, A. (2006). Logical management: a case study in a foreign trade company. magazine of administracao e contabilidade da Unisinos, 2 (2), 69-77.Guzmán, V. (2006). Fuzzy logic in engineering: principles, applications and future. Science and Technology, 24 (2), 87-107. Hassan, S., Mata, M., & Garmendia, L. (sf). Application of fuzzy logic to social systems with software agents. Mathematics in computer science. Keropyan, A., & Gil-Lafuente, AM (2011). A fuzzy-based decision model application on strategic management. African Journal of Business Management, 5 (15), 6586-6590. Mendoza, L. (2009). Fuzzy logic system. an application to business perception. Universidad & Empresa, 17, 252-270. Pérez, I. (2007). Fuzzy Logic for Beginners: Theory and Practice. Caracas,Venezuela: UCAB.Robaina, D. (2010). Fuzzy logic applied to decision making. Industrial, 31 (2), 2-5. Torres, A., & Tranchita, C. (2004). Inference and Probabilistic or Fuzzy Reasoning? Faculty of Engineering, 157-165.
