Currently fuzzy set theory has a wide range to model real life problems with incomplete or vague information which perfectly suits the reality and its application is theatrically increasing. This study explored the basic fuzzy operations with the Gaussian Membership using the α-cut method. As it is known that, the Gaussian membership function has a great role in modelling the fuzzy problems this is what impelled to explore its operation which can further be used in analysis of fuzzy problems. The use of Gaussian Membership function add more realist compartment to investigate each elements behavior and its predication outputs. Graphical analysis has been done for each operation depicting the results of the corresponding operation to the original membership function(s). Primarily the basic operations which has been discussed here are addition, subtraction, multiplication, division, reciprocal, exponential, logarithmic and nth power.
The sightseen operations can further be used in analysis of fuzzy sets with Gaussian Membership and using the alpha-cut method to make things easier for the calculations of all the basic operations. Therefore, we propose this approach to be used when analyzing the fuzzy problem with Gaussian Membership