Fuzzy Logic- Introduction

L.A Zadeh

Crisp Logic:

Crisp logic is concerned with absolutes-true or false, there is no in-between.

Example:

Rule:

If the temperature is higher than 80F, it is hot; otherwise, it is not hot.

Cases:

Temperature = 100F

Temperature = 80.1F

Temperature = 79.9F

Temperature = 50F

If temperature >= 80F, it is hot (1 or true);

If temperature <>

Drawbacks of crisp logic

The membership function of crisp logic fails to distinguish between members of the same set.

Conception of Fuzzy Logic

Many decision-making and problem-solving tasks are too complex to be defined precisely
however, people succeed by using imprecise knowledge

Fuzzy logic resembles human reasoning in its use of approximate information and uncertainty to generate decisions.

Natural Language

Consider:

Joe is tall -- what is tall?

Joe is very tall -- what does this differ from tall?

Natural language (like most other activities in life and indeed the universe) is not easily translated into the absolute terms of 0 and 1.

Fuzzy Logic

An approach to uncertainty that combines real values [0…1] and logic operations

Fuzzy logic is based on the ideas of fuzzy set theory and fuzzy set membership often found in natural (e.g., spoken) language.

Example: “Young”

Example:

Ann is 28, 0.8 in set “Young”

Bob is 35, 0.1 in set “Young”

Charlie is 23, 1.0 in set “Young”

Unlike statistics and probabilities, the degree is not describing probabilities that the item is in the set, but instead describes to what extent the item is the set.

Benefits of fuzzy logic

You want the value to switch gradually as Young becomes Middle and Middle becomes Old. This is the idea of fuzzy logic.