Cargo Shipping Rate Fuzzy Control System The shipping industry is a

 Cargo Shipping Rate Fuzzy Control System The shipping industry is a huge, multi-billion dollar business. This industry is the lifeblood of the world’s economy. It accounts for 90% of the world’s trade. Ships can carry goods in quantities that are impossible by any other mode of transport. Assume you have a fuzzy inference system that calculates the shipping rate of your package based on its weight. The system has 1 input variable Weight and 1 output variable Shipping Rate. It is claimed that the package is certainly very light when the weight is below 30 kg. However it is considered to be still somehow light at 35 kg, sometimes packages still its light as the weight goes up to 40 kg but not beyond. On contrary, it is claimed that package is too heavy when the weight reaches above 350 kg, but is not considered too heavy below 300 kg. Based on the cargo regulations; the package has a medium weight between 100 kg and 250 kg being certainly medium at weights between 150 kg and 200 kg. While asking the shipping service team about the ranges of the weight for small and heavy, the team suggested that being small somehow overlaps with light starting from 30 kg and ending at 150 kg while peaking at the middle point between the two. The team also said that it is considered heavy starting from 200 kg up till 350 kg again peaking at the middle. The assigned shipping regulations team should have to design the shipping rate fuzzy control system relating the package weight to the shipping rate applied to the package. The shipping rates are modeled as singletons and considered very low at 5%, low at 25%, average at 50%, high at 75% and very high at 100%.

Answer the following questions: a. [20 marks] Describe mathematically the membership functions for the variable weight. In addition, draw the fuzzy sets of the variable weight using a clear and to-scale plot. b. [20 marks] Design a simple rule base relating the weight to the shipping rate. c. [30 marks] Find the output of the fuzzy shipping rate system when the package weight is 125 kg. Use the described membership functions, the designed rule base and the Sugeno defuzzification method. Show the four stages of the computations clearly. d. [30 marks] Use the MATLAB fuzzy toolbox to model and implement the Cargo Shipping Rate Fuzzy Control System and verify the final answer of your analytical