### Homanga Bharadwaj

The multiple milestones of Artificial Intelligence have taken the world by storm ever since the advent of techniques that could implement the age old ideas of making machines that mimic humans. Fuzzy logic is the mathematical formulation of approximating reality. It is well known that binary logic has ones and zeroes only i.e. either a statement is completely true or false. Although it is mathematically and computationally convenient to have such a system in place, it does not fit in well with the ways in which humans think and act. For example, when we increase the temperature of the air conditioner, we have a thought process akin to, “It is getting very cold now and so I should increase the temperature of the air conditioner” and not, ”Since the temperature is now 2.3 degrees below 25.6 degree Celsius, I will increase the AC knob by 2.3 degrees”. So, instead of saying that something is true or false, we attach a ‘degree of certainty’ with every statement. Linguistic uncertainty (that arises in human communication) and probabilistic uncertainty are the two major sources of randomness that arise in a control system. Fuzzy logic helps in mathematical modeling of the former while Probability theory deals with the latter

Over the recent years, fuzzy theory has proven to be highly effective in system identification and modeling. It is especially useful in designing rule based expert systems where the linguistic uncertainty is high. Presently, fuzzy methods of inference have been combined with traditional training methods like neural networks to generate more robust systems. Another advantage is that in contrast to classical system modeling, where both the order and the type (i.e. linear or nonlinear) of the model are important, in fuzzy modeling we are mostly concerned about the order of the model, which is actually the number of rules included in the rule base . The design of a fuzzy model is usually carried out via a training procedure which determines the number of rules needed to describe the system and estimates the appropriate system parameters

Membership grades are used to quantify the extent to which an element be- longs to a particular group(set). Conventionally, a membership value runs from 0 to 1. In Type -I fuzzy sets, the membership grades of each data point of the input are ”crisp”, meaning non fuzzy or distinct. The topic of current research is Type-II fuzzy sets, where the membership values are themselves fuzzy intervals. Type -II fuzzy sets are used to model situations where we are unsure of to what extent each data point belongs to a given set. Since, statistical uncertainties are always present in experimental data, this formulation is considered to be more realistic

Fuzzy logic controllers are increasingly being used in modern AI architectures. They have an edge over conventional PID controllers in modeling a non linear system with a high degree of accuracy. The input set is first fuzzified by associating membership values to each data point on some predefined membership functions. Then the input is passed through a ”knowledge base” which contains rules and also a method to determine the degree to which each rule fires. The rules applied on the fuzzified input generate fuzzy outputs which are finally defuzzified using various techniques like centre of sets, centroid defuzzification etc. This results in a traditional ”crisp” output.

Fuzzy inference combined with other machine learning techniques are beginning to define new standards that can be achieved by the current state of the art AI architectures. It is only a matter of time before we build machines that outperform us in almost all walks of life