A produce dealer has a warehouse that stores a variety of fruits and vegetables.

When fruit is brought to the warehouse, various types of fruit may be mixed together.

The dealer wants a machine that will sort the fruit according to type. There is a

conveyer belt on which the fruit is loaded. This conveyer passes through a set of

sensors$,$ which measure three properties of the fruit: shape, texture and weight. These

sensors are somewhat primitive. The shape sensor will output a $1$ if the fruit is

approximately round and $a-1$ if it is more elliptical. The texture sensor will output a

$1$ if the surface of the fruit is smooth and $a-1$ if it is rough. The weight sensor will

output a $1$ if the fruit is more than one pound and a if it is less than one pound. The

three sensor outputs will then be input to a neural network. The purpose of the

network is to decide which kind of fruit is on the conveyor, so that the fruit can be

directed to the correct storage bin. To make the problem even simpler, let's assume

that there are only two kinds of fruit on the conveyor: apples and oranges.

As each fruit passes through the sensors it can be represented by a three dimensional

vector. The first element of the vector will represent shape, the second element will

represent texture and the third element will represent weight as below.

$p=\left[\begin{array}{c}\text{s}\text{h}\text{a}\text{p}\text{e}\\ \text{t}\text{e}\text{x}\text{t}\text{u}\text{r}\text{e}\\ \text{w}\text{e}\text{i}\text{g}\text{h}\text{t}\end{array}\right]$

The neural network will receive one three$-$dimensional input vector for each fruit on

the conveyer and must make a decision as to whether the fruit is an orange $(p_1)$ or an

apple $(p_2).$

$($a$)$ Write down the prototype templates for orange $(p_1)$ and apple $(p_2).$

$($b$)$ Design a perceptron to recognize these patterns.

$($c$)$ Design a Hamming network to recognize these patterns.

$($d$)$ Design a Hopfield network to recognize these patterns.

$($e$)$ Test the operation of your networks by applying several different input

patterns. Discuss the advantages and disadvantages of each network.