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Concepts of soft computing : fuzzy and ANN with programming
Chakraverty S., Sahoo D., Mahato N., Springer International Publishing, New York, NY, 2019. 195 pp. Type: Book
Date Reviewed: Apr 29 2020

Soft computing, a branch of artificial intelligence (AI), deals with computations involving uncertainty in complex real-world problems (as opposed to hard computing, which deals with computations involving certainty only encountered in ideal situations). Soft computing itself has four ingredients: fuzzy systems, evolutionary computation, machine learning (including artificial neural networks), and probabilistic reasoning. The book covers two major topics of soft computing: “Fuzzy Set Theory” (Part 1) and “Artificial Neural Network” (Part 2).

After a brief outline of the four ingredients in the introduction, the authors cover fuzzy set theory in nine chapters. Chapter 1 familiarizes the reader with interval arithmetic and defines basic mathematical operations, namely addition, subtraction, multiplication, and division on intervals. This is followed by interval matrices and corresponding arithmetic operations. Chapter 2, “Fuzzy Sets,” includes sections on membership function; “Support, Height, Core, and Boundary of Fuzzy Set”; and basic set operations like union, intersection, and complement.

Chapter 3, “Fuzzy Numbers,” covers triangular, trapezoidal, and Gaussian fuzzy numbers and the conversion of a fuzzy number to interval form using α-cut and fuzzy arithmetic. Chapters 4 and 5 deal with fuzzy relations and fuzzy functions, respectively, while fuzzy differentiation and integration is covered in chapter 6.

Chapter 7, “Defuzzification,” discusses various methods: aggregation, max-membership method, centroid method, weighted-average method, and mean-max method. The last two chapters in Part I are “Interval System of Linear Equations” (chapter 8) and “Interval Eigenvalue Problems” (chapter 9).

Part 2 begins with a long chapter on various artificial neural network (ANN) terminologies, such as single-layer, multilayer, and competitive-layer neural networks, supervised and unsupervised training, and activation programs, followed by some useful MATLAB programs. The McCulloch-Pitts neural network model is discussed in chapter 11, with accompanying MATLAB programs. This is followed by two chapters on the Hebbian learning rule (chapter 12) and perceptron learning rule (chapter 13); both chapters have supporting MATLAB programs that the reader will find useful. The book concludes with chapter 14, “Delta Learning Rule and Backpropagation Rule for Multilayer Perceptron.”

In addition to the MATLAB code, the book includes useful C code related to the basics of fuzzy sets and interval arithmetic.

The book is easy to read and understand for beginners, with simple examples that explain the concepts and useful references at the end of each chapter for further reading. However, the introduction should have more thoroughly explained the four ingredients of soft computing, rather than merely citing references. Part 2 lacks expository chapters on probabilistic neural networks and hybrid neural networks, and there is no index. Nevertheless, undergraduate students and practitioners of computing science and applied mathematics should find the book useful.

Reviewer:  Soubhik Chakraborty Review #: CR146958 (2011-0254)
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