Preface

The concept of fuzzy logic systems came to the fore in 1965 when Prof. Lofti Zadeh introduced the idea of Fuzzy Sets, which were defined as a "class of objects with a continuum of grades of membership." In 1973, Prof. Zadeh also introduced the use of linguistic variables and fuzzy algorithms, a technique that provides an approximate but effective way of describing system characteristics that are too complex and difficult to define and analyze using mathematical models. Prof. Zadeh emphasized that this technique played a very important role in the applications of animate rather than inanimate system constituents' behaviors. In those years, the elites in the academic and scientific community did not initially appreciate the concept of linguistic variables. This is largely because the use of words in systems and decision analysis conflicts with the deep-seated tradition presented by Lord Kelvin in 1883 that gave high regard and respect for numbers in controls. Some critics of Prof. Zadeh's theory include Prof. Rudolf Kalman and Prof. William Kahan, a man with a brilliant mind and an esteemed colleague of Prof. Zadeh. These critics of Prof. Zadeh were proven to be wrong in 1975 when E. H. Mamdami successfully presented an experiment on a fuzzy logic controller for a steam engine of an industrial plant. In 1985, the application of a fuzzy logic controller was solidified when Takagi and Sugeno (TS) published their work, "Fuzzy identification of systems and its applications to modeling and control." The TS method uses linear functions of input variables as the consequence.

The early commercial applications of fuzzy logic were successfully implemented in Japan. In 1987, the Sendai Namboku line began using fuzzy logic to control the subway train's motion, including acceleration and stop operation. The Matsushita vacuums use a fuzzy logic algorithm to adjust suction power automatically. The Hitachi washing machines use fuzzy logic controllers based on weight load, a mixture of fabric, and dirt sensors to automatically set the wash cycle for efficient operation. The Canon camera uses fuzzy logic for its autofocus operation to measure the clarity of the image. The Mitsubishi air conditioners use fuzzy logic to control the room temperature more efficiently than conventional units. Giant corporations like General Motors, Chrysler, Allen Bradley, Whirlpool, Eaton, and Boeing use fuzzy logic systems for efficient use of automotive transmissions, low-power refrigerators, and electric motors. The research on fuzzy logic has grown and flourished, particularly for developing applications in intelligent machines and hybrid controllers. To date, numerous concepts and theories have been formulated for in-depth understanding and advancement of fuzzy logic systems.

This book introduces basic and advanced ideas concerning fuzzy logic systems. It is divided into two sections. The first section (Chapters 1–4) deals with the foundations of the theories and concepts of the fuzzy logic system in advancing technology. The second section (Chapters 5–9) deals with the applications and implementations of these advanced technologies for the benefit of humanity.

Chapter 1, "Review of Type-1 and Type-2 Fuzzy Numbers", emphasizes that fuzzy number theory can be reduced to an argument for interval analysis. It proposes a way of perceiving the concept of fuzzy numbers by comparing it with round numbers.

Chapter 2, "Decoupling of Attributes and Aggregation for Fuzzy Number Ranking", discusses how intuition has been used as a guiding principle for fuzzy number ranking. The chapter adopts the multi-attribute decision-making framework to analyze such intuition.

Chapter 3, "Computing the Performance Parameters of the Markovian Queueing System FM/FM/1 In Transient State", the L–R method to calculate the parameters of performance of the fuzzy Markovian queueing system. The calculation used is the arithmetic of L–R fuzzy numbers restricted to secant approximations. The membership function helps represent graphically the curves of fuzzy parameters' performance in the three-dimensional space of a transient regime in a fuzzy environment.

Chapter 4, "Development of *L*-Group Theory", shows a systematic and successful development of L-group theory. It provides a universal construction of a generated L-subgroup by using level subsets of given L-subsets. This construction allows for defining and studying commutator L-subgroups, normalizer of an L-subgroup, nilpotent L-subgroups, solvable L-subgroups, and normal closure of an L-subgroup. The chapter examines all these concepts and their inter-relationships.

Chapter 5, "Fuzzy Photogrammetric Algorithm for City Built Environment Capturing into Urban Augmented Reality Model", describes and uses Fuzzy Cognitive Maps (FCMs) as a computing framework for matching visual features in an augmented urban-built environment modelling process.

Chapter 6, "PID-like Fuzzy Controller Design for Anti-Slip System in Quarter-Car Robot", proposes a new methodology to control the slip of a Quarter-Car robot using an internal loop based on fuzzy logic inference to compute the gains of a Proportional Integral (PI) structure. The slip is calculated, such as the difference between the linear velocity given by an S-curve velocity profile, and the longitudinal speed is calculated according to the rotational speed of the Quarter-Car tire.

Chapter 7, "Methodology for the Implementation of a Fuzzy Controller on Arduino, MATLAB™ and Nexys 4™ Platforms", discusses a methodology to implement a fuzzy controller in different hardware platforms that can be used to control a process and as an approximator to identify non-linearities and unknown uncertainties of a system.

Chapter 8, "Performance Improvement for Fighter Aircraft using Fuzzy Switching LQI Controller", discusses the switching controller designed for the stabilisation of high-performance aircraft, the Aero-Data Model in Research Environment (ADMIRE). The developed fuzzy logic switching controller has been tested and obtained a robust stabilisation control structure compared to a single conventional LQI and the switched LQI controller.

Chapter 9, "Adaptive Neuro-Fuzzy Inference System-Based GPS-IMU Data Correction for Capacitive Resistivity Underground Imaging with Towed Vehicle System", examines how the Capacitive Resistivity (CR) method utilizes GPS to create maps quickly

**V**

and with less equipment and labor compared to traditional surveying. However, data acquisition errors can still occur due to GPS sensor accuracy, digital map quality, and map-matching slipups. Also, environmental factors sometimes cause GPS sensors to fail. Hence, reducing errors in GPS receiver accuracy is crucial for correct underground utility location and map matching. This chapter uses an Adaptive Neuro-Fuzzy Inference System (ANFIS) to correct the latitude and longitude positions of a

Department of Manufacturing Engineering and Management,

**Elmer Dadios**

De La Salle University, Manila, Philippines

towed vehicle for underground imaging.

and with less equipment and labor compared to traditional surveying. However, data acquisition errors can still occur due to GPS sensor accuracy, digital map quality, and map-matching slipups. Also, environmental factors sometimes cause GPS sensors to fail. Hence, reducing errors in GPS receiver accuracy is crucial for correct underground utility location and map matching. This chapter uses an Adaptive Neuro-Fuzzy Inference System (ANFIS) to correct the latitude and longitude positions of a towed vehicle for underground imaging.

> **Elmer Dadios** Department of Manufacturing Engineering and Management, De La Salle University, Manila, Philippines

Section 1

Foundations of the Theories

and Concepts of the Fuzzy

Logic Systems

**1**
