The Fuzz of Fuzzy Logic: An Overview

“Accha lo, bura lo, decision lo.” – Our professor of Operations Management used this line in one of his presentation. The purpose was to make the students understand the importance of decision making. As per him, the students should be firm and definite in their answers and decisions. To quote in his exact words – “It always has to be either YES or NO but never PO”. This statement, however propelled me to ponder on the question – Whether this statement really strikes a chord with the b-school world? (A world wherein each answer and every argument revolves around a two word phrase. We are so fond of this phrase that I am highly certain that most of us would surely start the answer for above question with the same phrase – “It depends”.)

Now coming to the actual question – how is the above discussion related to our today’s topic of JIT? The answer is quite simple, because today we would diving deep into the world of PO which is blurred and FUZZY. Unlike traditional logical systems, fuzzy logic is aimed at providing a model for modes of reasoning which are approximate rather than exact. In this perspective, the importance of fuzzy logic derives from the fact that almost all of human reasoning – and especially common sense reasoning – is approximate in nature.

In bivalent logic, truth is bivalent, implying that every proposition is either true or false, with no degrees of truth allowed. For most part of this era of technology, it was believed that anything and everything innovated in this era followed bivalent logic. This belief was corroborated further by the behaviour of all instruments, gadgets, equipment etc which worked in only two states i.e., either ON (giving maximum throughput) or OFF (giving minimum throughput). However, the problem with bivalent logic is that it is in fundamental conflict with reality – a reality in which almost everything is a matter of degree. To address such problems there is need for a logic for modes of reasoning which are approximate rather than exact. This is what fuzzy logic aims at.

The word fuzzy refers to things which are not clear or are vague. Any event, process, or function that is changing continuously cannot always be defined as either true or false, which means that we need to define such activities in a Fuzzy manner. Fuzzy Logic resembles the human decision-making methodology. It deals with vague and imprecise information. This is gross oversimplification of the real-world problems and based on degrees of truth rather than usual true/false or 1/0 like Boolean logic.

Take a look at the following diagram. It shows that in fuzzy systems, the values are indicated by a number in the range from 0 to 1. Here 1.0 represents absolute truth and 0.0 represents absolute falseness. The number which indicates the value in fuzzy systems is called the truth value.

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In other words, we can say that fuzzy logic is not logic that is fuzzy, but logic that is used to describe fuzziness. There can be numerous other examples like this with the help of which we can understand the concept of fuzzy logic.

Fuzzy logic implies that everything is imprecise, partial and granular and the truth is perception based and a matter of degree. Fuzzy logic has been and still is, though to a lesser degree, an object of controversy. For the most part, the controversies are rooted in perceptions, especially a perception of the relation between fuzzy logic and probability theory. A source of confusion is that the label “fuzzy logic” is used in two different senses – a) narrow sense: fuzzy logic is a logical system b) wide sense: fuzzy logic is coextensive with fuzzy set theory.

Fuzzy logic in control system:

A control system is an arrangement of physical components designed to alter another physical system so that this system exhibits certain desired characteristics. Fuzzy logic is applied with great success in various control application. Almost all the consumer products have fuzzy control. Some of the examples include controlling your room temperature with the help of air-conditioner, anti-braking system used in vehicles, control on traffic lights, washing machines, large economic systems, etc.

Following are some reasons of using Fuzzy Logic in Control Systems −

  • While applying traditional control, one needs to know about the model and the objective function formulated in precise terms. This makes it very difficult to apply in many cases.
  • By applying fuzzy logic for control we can utilize the human expertise and experience for designing a controller.
  • The fuzzy control rules, basically the IF-THEN rules, can be best utilized in designing a controller.

Fuzzy logic control has several advantages like it is cheaper, robust, customizable, reliability, efficiency and emulates human deductive thinking. However, there are certain disadvantages as it requires lots of data, useful in case of moderate historical data, needs high human expertise and regular updating of rules.

Fuzzy logic in decision making:

Fuzzy logic is a logic trying to be as close as possible to human thinking and perception. It is based on the assumption that people are not thinking in the exact variables (yes / no), but distinguish a range of “blurry” values (rather yes, much yes, maybe no, and yes and no). This means that it operates with cloudy concepts and blurred boundaries.

The procedure of fuzzy processing is realized in the following steps: problem identification, fuzzification, fuzzy interference and rule base, deffuzification, interpretation and verification.

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Steps for decision making:

The steps involved in the decision making process −

  • Determining the Set of Alternatives − In this step, the alternatives from which the decision has to be taken must be determined.
  • Evaluating Alternative − Here, the alternatives must be evaluated so that the decision can be taken about one of the alternatives.
  • Comparison between Alternatives − In this step, a comparison between the evaluated alternatives is done.

Fuzzy logic in Neural Network:

Artificial neural network (ANN) is a network of efficient computing systems the central theme of which is borrowed from the analogy of biological neural networks. ANN acquires large collection of units that are interconnected in some pattern to allow communications between units. These units, also referred to as nodes or neurons, are simple processors which operate in parallel.

Following are some reasons to use fuzzy logic in neural networks −

  • Fuzzy logic is largely used to define the weights, from fuzzy sets, in neural networks.
  • When crisp values are not possible to apply, then fuzzy values are used.
  • We have already studied that training and learning help neural networks perform better in unexpected situations. At that time fuzzy values would be more applicable than crisp values.
  • When we use fuzzy logic in neural networks then the values must not be crisp and the processing can be done in parallel.

Neural-trained Fuzzy logic:

The reverse relationship between neural network and fuzzy logic, i.e., neural network used to train fuzzy logic is also a good area of study. Following are two major reasons to build neural trained fuzzy logic −

  • New patterns of data can be learned easily with the help of neural networks hence, it can be used to pre-process data in fuzzy systems.
  • Neural network, because of its capability to learn new relationship with new input data, can be used to refine fuzzy rules to create fuzzy adaptive system.

Examples where Neural-Trained Fuzzy system is applied −

  • The Laboratory for International Fuzzy Engineering Research (LIFE) in Yokohama, Japan has a back-propagation neural network that derives fuzzy rules. This system has been successfully applied to foreign-exchange trade system with approximately 5000 fuzzy rules.
  • Ford Motor Company has developed trainable fuzzy systems for automobile idle-speed control.
  • NeuFuz, software product of National Semiconductor Corporation, supports the generation of fuzzy rules with a neural network for control applications.
  • AEG Corporation of Germany uses neural-trained fuzzy control system for its water – and energy conserving machine. It is having total of 157 fuzzy rules.

Applications of Fuzzy logic:

In aerospace, fuzzy logic is used in the following areas −

  • Altitude control of spacecraft
  • Satellite altitude control
  • Flow and mixture regulation in aircraft vehicles

In automotive, fuzzy logic is used in the following areas −

  • Trainable fuzzy systems for idle speed control
  • Shift scheduling method for automatic transmission
  • Intelligent highway systems

In business, fuzzy logic is used in the following areas −

  • Decision-making support systems
  • Personnel evaluation in a large company

In defense, fuzzy logic is used in the following areas −

  • Underwater target recognition
  • Automatic target recognition of thermal infrared images
  • Naval decision support aids
  • Control of a hypervelocity interceptor

In the finance field, fuzzy logic is used in the following areas −

  • Banknote transfer control
  • Fund management
  • Stock market predictions

In industrial, fuzzy logic is used in following areas −

  • Cement kiln controls heat exchange control
  • Activated sludge wastewater treatment process control
  • Water purification plant control

In securities, fuzzy logic is used in following areas −

  • Decision systems for securities trading
  • Various security appliances

In Pattern Recognition and Classification, fuzzy logic is used in the following areas −

  • Fuzzy logic based speech recognition
  • Fuzzy image search
  • Fuzzy logic based facial characteristic analysis

In Psychology, fuzzy logic is used in following areas −

  • Fuzzy logic based analysis of human behavior
  • Criminal investigation and prevention based on fuzzy logic reasoning

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