Virtual-Intelligence Applications in Petroleum Engineering: Part 3—Fuzzy Logic
Authors: Mohaghegh Shahab 
Published: June 2014

Distinguished Author Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized to be experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: to inform the general readership of recent advances in various areas of petroleum engineering.

Summary
Parts 1 and 2 of this series of articles presented a general overview of artificial neural networks and evolutionary computing, respectively, and their applications in the oil and gas industry.1,2 The focus of this article is fuzzy logic. The article provides overview of the subject and its potential application in solving petroleum-engineering-related problems. As the previous articles mentioned, the most successful applications of intelligent systems, especially when solving engineering problems, have been achieved by use of different intelligent tools in concert and as a hybrid system. This article reviews the application of fuzzy logic for restimulation-candidate selection in a tight-gas formation in the Rocky Mountains. We chose this particular application because it uses fuzzy logic in a hybrid manner integrated with neural networks and genetic algorithms.

Background
The science of today is based on Aristotle&apos;s crisp logic formed more than2,000 years ago. Aristotelian logic looks at the world in a bivalent manner, such as black and white, yes and no, and 0 and 1. The set theory developed in the late 19th Century by German mathematician Cantor was based on Aristotle&apos;sbivalent logic and made this logic accessible to modern science. Subsequent superimposition of probability theory made the bivalent logic reasonable and workable. Cantor&apos;s theory defines sets as a collection of definite, distinguishable objects. Fig. 1 is a simple example of Cantor&apos;s set theory and its most common operations, such as complement, intersection, and union.
The first work on vagueness dates back to the first decade 20th Century, when American philosopher Pierce noted that "vagueness is no more to be done away with in the world of logic than friction in mechanics." 3 In the early 1920&apos;s, Polish mathematician and logician Lukasiewicz4developed three-valued logic and talked about many-valued, or multi-valued, logic. In 1937, quantum philosopher Black5 published a paper on vague sets. These scientists built the foundation on which fuzzy logic was later developed.
Zadeh,6 known as the father of fuzzy logic, published his landmark paper "Fuzzy Sets" in 1965. He developed many key concepts, including membership values, and provided a comprehensive framework to apply the theory to engineering and scientific problems. This framework included the classical operations for fuzzy sets, which comprise all the mathematical tools necessary to apply the fuzzy-set theory to real-world problems. Zadeh was the first to use the term "fuzzy," which provoked much opposition. A tireless spokesperson for the field, he was often harshly criticized. At a 1972 conference, Kalman stated that "Fuzzification is a kind of scientific permissiveness; it tends to result in socially appealing slogans unaccompanied by the discipline of hard scientific work." 7 (Note that Kalman is a former student of Zadeh&apos;sand inventor of the famous Kalman filter, a major statistical tool in electrical engineering. The Kalman filter is the technology behind the Patriotmissiles used in the Gulf War. Claims have been made that it has been proved that use of fuzzy logic can significantly increase the accuracy of these missiles.8,9) Despite all its adversaries, fuzzy logic continued to flourish and has become a major force behind many advances in intelligent systems.
The word "fuzzy" carries a negative connotation in Western culture, and" fuzzy logic" seems to misdirect the attention and to celebrate mentalfog.10 On the other hand, Eastern culture embraces the concept of coexistence of contradictions as it appears in the yin/yang symbol (Fig.2). While Aristotelian logic preaches A or Not-A, Buddhism is all about Aand Not-A.
Many believe that the tolerance of Eastern culture for such ideas is the main reason behind the success of fuzzy logic in Japan. While fuzzy logic was being attacked in the U.S., Japanese industries were busy building amultibillion-dollar industry around it. Today, the Japanese hold more than2,000 fuzzy-related patents. They have used fuzzy technology to build intelligent household appliances, such as washing machines and vacuum cleaners(Matsushita and Hitachi), rice cookers (Matsushita and Sanyo), air conditioners(Mitsubishi), and microwave ovens (Sharp, Sanyo, and Toshiba), to name a few. Matsushita used fuzzy technology to develop its digital image stabilizer for camcorders. Adaptive fuzzy systems (a hybrid with neural networks) can be found in many Japanese cars. Nissan patented a fuzzy automatic transmission that is now very popular with many other manufacturers, such as Mitsubishi and Honda.10