A STUDY ON FUZZY AND FUZZY LOGIC

Author (s) : V.Jothilakshmi, Dr.B.Venkatachalam & S.Saranya

---

Abstract :
Basically, fuzzy logic is the logic of classes with unsharp boundaries. In human cognition, classes with unsharp boundaries are the norm rather than exception. Everyday examples are the concepts of red, small, near, fast, heavy, similar, etc. A major application area in fuzzy logic is Computing with Words (CW or CWW). Computing with Words is a system of computation which offers an important capability which traditional systems of computation do not have–the capability to compute with information described in natural language. This capability opens the door to a wide-ranging enlargement of the role of natural languages in scientific theories. Let P be a “well defined” property in a set S, i.e., a property such that given any element x in S, either x satisfies P or not. Then, the axiom of separation in classical set theory enables us to assert that the elements of S satisfying P define a subset of S we denote by {x ∈ S : x satisfies P}. As an example, if S is the set of natural numbers and P is the property “odd”, then the set {x ∈ S : x is an odd number} is defined. Now, there are properties that are “vague” and therefore not well defined. This since they can be satisfied with several different degrees. For instance, “short”, “big”, “near”, are vague properties. Then, the question arises whether these properties isolate some type of subset and therefore whether we can give a precise meaning to intuitive notions as “the set of short men”, “the set of big numbers”, “the set of shops near to the station”, and so on.

Keywords : Fuzzy Logic, Closure Operator, Fuzzy Subset

Conference Date : 30/08/2019

Pages : 333

Paper ID : 19324