Fuzzy logic system

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. 

A defuzzifier is the opposite of a fuzzifier it maps the output sets into crisp numbers, which is essential if a fuzzy logic system is to be used to control an... 

Fuzzy logic systems grew out of a desire to quantify rule-based expert systems. Fuzzy set theory had provided us with an effective framework for dealing with fuzzy information and for translating control strategies based on an expert knowledge into an automatic control strategy. 

AI techniques can be roughly divided into two categories symbolic AI and computational intelhgence. The former focuses on development of knowledge-based systems while the latter focuses on development of a set of nature-inspired computational approaches. The latter primarily includes evolutionary computations, artificial nemal networks and fuzzy logic systems. A brief introduction to these techniques begins on the next page. 

A fuzzy logic system maps crisp inputs into crisp outputs using the theory of fuzzy sets. In a fuzzy logic system, an inference engine works with fuzzy rules. 

The engine takes inputs, some of which may be fuzzy, and generates outputs, some of which may be fuzzy. The fuzzy core of the inference engine is bracketed by one step that can convert crisp data into fuzzy data, and another step that does the reverse. Figure 2.10 shows the general procedures involved in a fuzzy logic system as follows. 

AND is used to evaluate the conjunction of rule antecedents. Typically, fuzzy logic systems utilize the classical fuzzy operation intersection to implement this operation. Consider fuzzy rule 1 ... 

Similarly, OR is used to evaluate the disjunction of rule antecedents, which is implemented by the classical fuzzy operation union in fuzzy logic systems. Consider fuzzy rule 2 ... 

The last step in a fiizzy logic system is defuzzification. As the name suggests, defuzzification is the opposite of fuzzification, which produces crisp output f for a fuzzy logic system from the aggregated output of fuzzy set B. A number of defuzzifiers have been developed the most popular is the centroid defuzzifier, which finds a vertical line and divides an aggregated set into two equal portions. Mathematically the center of gravity (COG) can be defined by ... 

Learning of Type-2 Fuzzy Logic Systems by Simulated Annealing with Adaptive Step Size... 

Type-2 fuzzy logic systems are rule-based systems that are similar to type-1 fuzzy logic systems in terms of the structure and components but a type-2 fuzzy logic system has an extra output process component which is called the type-reducer before defuzzification as shown in Fig. 5.3. The type-reducer reduces outputs type-2 fuzzy sets to type-1 fuzzy sets and then the defuzzifier reduces them to crisp outputs. The components of a type-2 Mamdani fuzzy logic system are [26] ... 

Defuzzifier Defuzzifier maps the reduced output type-1 fuzzy sets that have been reduced by type-reducer into crisp values exactly as the case of defuzzification in type-1 fuzzy logic systems. 

Dadone P (2001) Design optimization of fuzzy logic systems. PhD thesis, Virginia Polytechnic... 

Kamik NN, Mendel JM, Liang Q (1999) Type-2 fuzzy logic systems. IEEE Trans Fuzzy Syst 7... 

Mendel JM (2001) Uncertain rule-based fuzzy logic systems introduction and new directions. Prentice Hall, Englewood Cliffs, NJ... 

Fuzzy Logic System Institute, Fukuoka 820-0067, Japan K. Sethanan... 

Fuzzy logic systems have been used extensively in decision-making problems especially supplier selection problems in a supply chain. Shaw et al. (2012) and Lee (2009) applied fuzzy models for supplier selection. 

Fuzzy logic systems are cheap, training data are not required, models or joint/conditional probability distributions are not needed. 

Martinez, J. S., John, R. L, Hissel, D., and Pera, M.-C. (2012). A survey-based type-2 fuzzy logic system for energy management in hybrid electrical vehicles. 

For advanced techniques in modeling, identification, and control, MATLAB has a variety of additional toolboxes that are licensed individually. Relevant toolboxes for process control include control system, fuzzy logic, system identification, model predictive control, neural networks, optimization, partial differential equations, robust control, and statistics. 

The intuitionistic model logieally joins variables that miss in the conventional fuzzy model. In both of the cases, we have to analyze the same number of variables. Because of the dependency (3.16) the intuitionistie model operate with 2/3 from the variables, and the remaining 1/3 are calculated after solving the system. For this reason, the intuitionistic fuzzy logic will be 33.3% faster as computing time in comparison with the conventional fuzzy logic systems. 

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