Do you have any criticisms of the decision-making method that we used in Example? Are you...

Do you have any criticisms of the decision-making method that we used in Example? Are you comfortable with the way in which decisions are made by this method? Can you suggest any changes? If so, try to implement these changes and then reconsider the examples and exercises of this section to see whether your method results in different decisions being made.

Making Decisions Using Fuzzy Logic

Assume that your car has broken down and you are trying to decide whether to repair it, buy a newer used car, or buy a brand-new car. In Table we list the characteristics of a car that are important to you and assign a number between 0 and 1 to indicate how important each characteristic is to you. Table lists the degree to which each option satisfies these characteristics.

In Tables, the assignment of values between 0 and 1 is somewhat arbitrary. Another person might assign these values differently.

Fuzzy truth values describe how important each characteristic is to you.

Fuzzy truth values describe how well each option sat­isfies the characteristics that are important to you.

The ideal option for you is the one that scores the highest in the characteristics that are important to you. In other words, we want to consider fuzzy statements of the following type:

“If cost is important to you, then repairing your car satisfies this condition.”

“If reliability is important to you, then buying a new car satisfies this condition.”

We thus want truth values for fuzzy statements of the form i → c, where i is a statement that a characteristic is important to you and c is a statement that an option possesses that characteristic. Recall that i → c has the same truth value as (~i) ⋁ c. Let us look at the truth value for the statement

“If cost is important to you, then repairing your car satisfies this condition.”

Here i is the statement “Cost is important to you,” which from Table has a truth value of 0.70. The statement c is “Repairing your car satisfies this condition (cost),” which from Table has a truth value of 0.80. The truth value of (~i) ⋁ c is thus (~0.70) ⋁ 0.80 = 0.30 ⋁ 0.80 = 0.80.

We will now construct a truth table for all the statements (~i) ⋁ c for each option: repair, buy a used car, and buy a new car.

For an option to be satisfactory, you want to have all the conditions satisfied as well as possi­ble. Therefore, you are interested in cost AND reliability AND size AND gas mileage AND safety. Thus, to finish making your decision, you calculate the conjunction of all the expres­sions (~i) ⋁ c for each option. The conjunction of all the expressions (~i) ⋁ c for repairing your car is the minimum of the truth values in this column, which is 0.40 (highlighted). Similarly we obtain a value of 0.60 (highlighted) for buying a newer used car and 0.30 (highlighted) for buying a new car. Because buying a newer used car has the highest final rating, the best choice for you according to this rating method is to buy a newer used car.