An Study on NP-completeness in Fuzzy Context

The original (0 or 1) set theory models the world as black or white and makes no provision for sets of grey. Life is not always black and white. This two valued logic has proved effective and successful in solving well defined problems. However, a class of problems exists which are typically complex in nature, and are often left to human beings to deal with. It is known that no polynomial algorithm could be found for the problems in NP or NP-hard problems like travelling salesman Problem, the Hamiltonian Cycle Problem. While a method for computing the solutions to NP-complete problems using a reasonable amount of time remains undiscovered, computer scientists and programmers still frequently encounter NP-complete problems. NP-complete problems are often addressed by using algorithms. The objective of this paper is to introduce and study more about NP-Completeness in the fuzzy context.