Introduction to Fuzzy Logic. James K. Peckol
The perceptron incorporates capabilities from both fuzzy logic and threshold logic and includes the capability to learn. Starting with a high‐level model, we introduce the vocabulary describing the elementary components and capabilities of the device. From there, we move to the McCulloch–Pitts (MCP) artificial neuron, which we will examine and then implement a basic model. We also illustrate implementing fundamental classic logic devices using the MCP model.
I.12 Testing and Debugging
Once we design and build the hardware and firmware for our system, we move to confirming that it works. To support that process from its beginning, we include two appendices that introduce and present how to write solid Requirements and Design Specifications and to outline the fundamental functionality of your design.
I.13 Summary
We introduced the design and development tools called fuzzy logic, threshold logic, and perceptrons and presented a brief high‐level overview of how fuzzy logic compares with the traditional crisp logic and other possible sources of additional information. The topics discussed are contributing to and pushing the limits of several very interesting technologies.
The full book can provide a powerful tool for the student in the traditional undergraduate electrical engineering, computer engineering, or computing science programs as well as the practicing engineer.
Our goal in introducing the technologies and designing systems based upon those technologies covered in the book is to help people solve today's and tomorrow's interesting and challenging problems. We stress very strongly that the traditional design, test processes, and formal methods (particularly including safety and reliability) do not go away; rather they become more relevant as we move to ever‐increasingly complex systems.
As you work through the book, try to remember a couple of things. People use our products – our designs can affect people's lives. Once again, always do your best to make your designs as safe and as reliable as you can for each application. Remember too that the cost of a product isn't limited to the cost of the parts that make it up. We also have to consider costs of building, selling, supporting, and adding new features to your design.
Remember that good system designers and designs proceed using a minimum of six steps:
✓ Requirements Definition
✓ System Specification
✓ Functional Design
✓ Architectural Design
✓ Prototyping
✓ Testing
Finally, remember that our responsibility for a design doesn't end with design release. Also, we stress that a good, solid, and reliable design always begins with a firm foundation. Without that, everything we add later is fragile. Good luck, have fun, and learn from each design.
Review Questions
Fuzzy Logic
1 I.1 What is fuzzy logic and is it a new technology?
2 I.2 What are the differences between crisp or classic logic and fuzzy logic?
3 I.3 Can you site several applications where fuzzy logic is used?
4 I.4 What are some of the advantages of fuzzy logic?
5 I.5 What is a linguistic hedge and where would it be used?
Threshold Logic
1 I.6 What is threshold logic?
2 I.7 Where might threshold logic be used?
3 I.8 Can you explain what these applications are?
Perceptrons
1 I.9 What are perceptrons?
2 I.10 It is claimed that a perceptron can learn. Can you propose what it should be learning and how that might be done?
Thought Questions
1 I.1 Give two examples of systems that would benefit from fuzzy logic over crisp logic.
2 I.2 What are some of the more difficult problems that a fuzzy system might confront?
3 I.3 What criteria might you use to set values for a threshold in a threshold logic circuit?
4 I.4 Would the same criteria apply for setting a threshold in a perceptron‐based design?
5 I.5 What would be the advantage of a system that could learn?
6 I.6 What would some of your first steps be in starting a fuzzy logic design, a threshold logic design, or a perceptron logic design?
7 I.7 What do you think should be the criteria for specifying tests for a fuzzy logic design, a threshold logic design, or a perceptron logic design?
8 I.8 How would you propose debugging systems developed using such technologies?
9 I.9 What are the major categories of signals that the described systems would interface with in the external world?
10 I.10 What are some of the more difficult problems that designers of the described systems might face? Consider examples such as a very popular consumer product, an intelligent robot system, a mission to Mars, or an automatic loading system on a commercial jet airliner.
11 I.11 What do you think might be some of the more important performance considerations that one should take into account when designing or using any of the systems described?
1 A Brief Introduction and History
THINGS TO LOOK FOR…
Early views on reality, learning, logic, and reasoning.
The early classic laws of thought.
Foundations of fuzzy logic.
A learning and reasoning taxonomy.
The mathematics underlying crisp and fuzzy logic.
Similarities and differences between crisp and fuzzy logic.
Fuzzy logic and approximate reasoning.
Fuzzy sets and membership functions.
1.1 Introduction
We open this text with a challenge and a foundation. Whether crisp or fuzzy, whether involving animals, humans, or machines, philosophers, scientists, and educators have studied, debated, and analyzed terms such as think, ponder, logic, reason, philosophize, or learn for centuries. Yet today, our understanding of these processes still has the opportunity to grow. Given such a history, what do we know?
Let us start with learning. Learning is a process that starts (at least) immediately after birth and continues, often unobtrusively, through the remaining years of life. Recent research, however, has found that learning may actually begin months earlier. Nevertheless, the term itself generally evokes childhood memories of old books, pedagogical teachers, and stuffy classrooms on warm spring afternoons when we would rather be outside playing. If we pause and reflect for a moment, we realize that learning is not limited to that proffered by the pendants of previous days but is a natural part of our daily existence. Each time that we encounter a fresh idea, make a new discovery, or solve one of