Fuzzy processes

The highly esteemed management professor Peter Drucker once said, Success is more likely to result from the systematic pursuit of opportunities than from a flash of genius. I will discuss the systematic pursuit of innovation used at ExxonMobil Chemical Company to increase the yield from basic science to commercialization. Although innovation is thought of as an inherently fuzzy process, my role in the last 5 to 10 years of my 35-year career has been to add a fair amount of structure and discipline to the process of innovation. Some of our best practices will be shared. 

Tsujimura, Y, Park, S., Chang, S., and Gen, M. (1993), An Effective Method for Solving Flow Shop Scheduling Problems with Fuzzy Processing Times, Computers and Industrial Engineering, Vol. 25, pp. 239-242. 

J.F. Pietranski, N.F. Marsolan, and K.-H. King, Expert fuzzy process control of a rotary dryer, American Control Conference, Minneapolis, MN, 1987. 

It is quite common to describe the demand with random variables and fiizzy numbers, but in the complicated market surroundings, it is not accurate enough to describe the demand with a single random variable or fiizzy variable under many circumstances. For example, the future market demand might be good, or moderate, or bad, these three cases have happened in a certain probabihty, that is to say it is stochastic, but the market demand after each possibility is a fuzzy process, for example, when the market is good, the demand might be around 5000 units when the market is moderate, it is around 2600 units. In the bad case, it is only around 900 units. These descriptions are fuzzy, which means the customer demand is a fuzzy random variable. 

One variation of rule-based systems are fuzzy logic systems. These programs use statistical decision-making processes in which they can account for the fact that a specific piece of data has a certain chance of indicating a particular result. All these probabilities are combined in order predict a final answer. 

Video-Enhanced Contrast. This technique is more expensive but much more effective than any other contrast-enhancing technique (15). Since the 1970s, the development of video processing of microscopical images has resulted in electronic control of contrast. As Shinya InouH, author of a classic text in the field, states "We can now see objects that are far too thin to be resolved, and extract clear images from scenes that appeared too fuzzy, too pale, or too dim, or that appeared to be nothing but noise" (16). The depth of the in-focus field can now be expanded or confined, very thin but very sharp optical sections can be produced, and a vertical succession of these images can be accumulated to reconstmct thicker stmctures in three dimensions (16). 

While the single-loop PID controller is satisfactoiy in many process apphcations, it does not perform well for processes with slow dynamics, time delays, frequent disturbances, or multivariable interactions. We discuss several advanced control methods hereafter that can be implemented via computer control, namely feedforward control, cascade control, time-delay compensation, selective and override control, adaptive control, fuzzy logic control, and statistical process control. 

Fuzzy Logic Control The apphcation of fuzzy logic to process control requires the concepts of Fuzzy rules and fuzzy inference. A fuzzy rule, also known as a fuzzy IF-THEN statement, has the form ... 

In addition to single-loop process controllers, products that have benefited from the implementation of fuzzy logic are ... 

Equation (10.23) is referred to as the max-min inference process or max-min fuzzy reasoning. 

Fuzzy inference is therefore the process of mapping membership values from the input windows, through the rulebase, to the output window(s). 

Tong, R.M. (1978) Synthesis of fuzzy models for industrial processes, Int. J. General Systems, 4, pp. 143-162. 

The modern DDC controller has only the control function PID. PLC controllers used in process installations may contain more complex regulation functions, for example, the fuzzy or auto-tuning of PID functions. Most DDC controllers are self-sufficient and independent of the controllers or computer programs that are used for system configuration. 

Traditional control systems are in general based on mathematical models that describe the control system using one or more differential equations that define the system response to its inputs. In many cases, the mathematical model of the control process may not exist or may be too expensive in terms of computer processing power and memory. In these cases a system based on empirical rules may be more effective. In many cases, fuzzy control can be used to improve existing controller systems by adding an extra layer of intelligence to the current control method. 

It may be useful to point out a few topics that go beyond a first course in control. With certain processes, we cannot take data continuously, but rather in certain selected slow intervals (c.f. titration in freshmen chemistry). These are called sampled-data systems. With computers, the analysis evolves into a new area of its own—discrete-time or digital control systems. Here, differential equations and Laplace transform do not work anymore. The mathematical techniques to handle discrete-time systems are difference equations and z-transform. Furthermore, there are multivariable and state space control, which we will encounter a brief introduction. Beyond the introductory level are optimal control, nonlinear control, adaptive control, stochastic control, and fuzzy logic control. Do not lose the perspective that control is an immense field. Classical control appears insignificant, but we have to start some where and onward we crawl. 

Zadeh LA (1975) Fuzzy sets and their applications to cognitive and decision processes. Academic Press, New York... 

Control problems represent a major area of application for fuzzy logic since reliable process control may rely on the long-term expertise of one or a few people, and those people may be able to frame their knowledge of the system only in imprecise terms. A typical example is the control of pH in a crystallization reactor.2 A similar application was described by Puig and co-... 

FIGURE 1-19 A myelinated PNS axon (A) is surrounded by a Schwann cell nucleus (N). Note the fuzzy basal lamina around the cell, the rich cytoplasm, the inner and outer mesaxons (arrows), the close proximity of the cell to its myelin sheath and the 1 1 (celhmyelin internode) relationship. A process of an endoneurial cell is seen (lower left), and unstained collagen (c) lies in the endoneurial space (white dots). X20,000. 

When the washing machines with conventional controls are optimized further, more and more decisions have to be left to the user, even though the consumer is not in the situation to check whether or not these decisions are right. The users are only able to evaluate whether the wash result meets with their demands or not, they cannot prove how the same result could have been reached with a reduced use of raw materials. To avoid such a problem, AEG have moved on to the third phase of the development of washing techniques. With the help of the concepts of FUZZY LOGIC, a washing machine has been invented that adapts its wash processes to the demands of the laundry in order to offer the most in easy operation and ecology. 

In order to understand the application of FUZZY CONTROL in the development of washing processes, a short explanation of conventional washing techniques will be necessary. 

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