Fuzzy theory

Conventional computers initially were not conceived to handle vague data. Human reasoning, however, uses vague information and uncertainty to come to a decision. In the mid-1960 this discrepancy led to the conception of fuzzy theory [14]. In fuzzy logic the strict scheme of Boolean logic, which has only two statements true and false), is extended to handle information about partial truth, i.e., truth values between "absolutely true" and absolutely false". It thus gives a mathematical representation of uncertainty and vagueness and provides a tool to treat them. 

Chang CL, Lo SL, Yu SL (2005) Applying fuzzy theory and genetic algorithm to interpolate precipitation. J Hydrol 314 92-104... 

Otto M, Bandemer H (1986b) Calibration with imprecise signals and concentrations based on fuzzy theory. Chemom Intell Lab Syst 1 71... 

Calibration with imprecise signals and analytical values (concentrations) based on fuzzy theory has been dealt with by Otto and Bandemer [1986]. 

Fuzzy theory is wrong, wrong, and pernicious. I cannot think of any problem that could not be solved better by ordinary logic.... The danger of fuzzy theory is... 

One can see that the truth values in fuzzy logic strongly resemble the stochastic values from the theory of probabilities. However, methods based on the use of statistics are not considered fuzzy by the orthodox fuzzy theory protagonists. Instead of using probability values, fuzzy theory works with possibility values. It is argued that both values are substantially different and that the latter have to be evaluated by methods other than statistical. Our understanding, however, is that at a very fundamental level, both values have essentially the same nature. 

Methods based on fuzzy theory, neural nets, and evolutionary strategies are denoted as soft computing... 

The theory of fuzzy sets enables representation and processing of vague propositions and uncertain information. In contrast to probability theory, fuzzy theory is a possibilistic approach, that is, it is based on possibility theory. The concept of fuzzy sets was introduced by Lotfi A. Zadeh of the University of California (USA) in 1965. 

Linguistic Variables Verbal fuzzy expressions are described by fuzzy theory by means of linguistic variables for example, the solubility of a substance in water can be characterized by the fuzzy terms high and low. If the linguistic variables are further to be distinguished, the so-called modifiers are applied. 

Fuzzy theory can be used either for data analysis or for dealing with fuzzy logic. Typical applications in analytics are [20] as follows ... 

Table 8.6 comprises some applications of fuzzy theory in analytics. 

Ida, K. and Gen, M. (1997), Improvement of Two-Phase Approach for Solving Fuzzy Multiple Objective Linear Programming, Journal of Japan Society for Fuzzy Theory and System, Vol. 19, pp. 115-121 (in Japanese). 

Shibano, T., Sakawa M., and Obata H. (1996), Interactive Decision Making for Multiobjective 0-1 Programming Problems with Fuzzy Parameters through Genetic Algorithms, Journal cf Japan Society for Fuzzy Theory and System, Vol. 18, pp. 1144-1153 (in Japanese). 

Because neural network requires that input must meet [0, 1] interval, data normalization processing of input unit is necessary by applying fuzzy theory. Processing rules is The unit set is 17 = C/j Uj 17,, the factor sets are 17, = u m, = Iwji... 

Zhong, L. Youchao, S. 2007. Research on Maintainability Evaluation Model Based on Fuzzy Theory. Chinese Journal of Aeronautics 20 402—407 Zio, E. etal. 2003. The analytic hierarchy process as a systematic approach to the identification of important parameters for the reliability assessment of passive systems. Nuclear Engineering and Design 226 311 336... 

Filev DP, Kishimoto M, Sengupta S, Yoshida T, Taguchi H. Application of fuzzy theory to simulation of batch fermentation J Ferment Technol 1985 63 545. 

Kishimoto M, Yoshida T. Application of fuzzy theory on fermentation process. Hakko Kogaku 1991 69 107. 

Uncertainty theory is also referred to as probability theory, credibility theory, or reliability theory and includes fuzzy random theory, random fuzzy theory, double stochastic theory, double fiizzy theory, the dual rough theory, fiizzy rough theory, random rough theory, and rough stochastic theory. This section focuses on the probability theory and fiizzy set theory, including probability spaces, random variables, probability spaces, credibility measurement, fuzzy variable and its expected value operator, and so on. 

Modeling, tests, calculation of the characteristic quantities of the method, and graphical visualization are supported by computer programs (e.g,. [25]), which however usually consider only certain aspects of the calibration. An alternative method of calibration for imperfect response features and concentration quantities is to apply fuzzy theory [26]. 

Fuzzy theory Zadeh (1965) presented mathematical techniques for deriving particular solutions. Chien et al. (2011) developed a comprehensive modular framework to derive various configurations of fuzzy numbers for fuzzy ranking. Also, Kumar (2012) summarized the definitions of the arithmetic operations of fuzzy numbers as follows. 

It is abundantly clear that fuzzy logic is better able to represent human knowledge in a form of rules while ANNs are better able to learn from examples. As a consequence of their complementary properties, then, extensive efforts are being made to combine fuzzy theory and neutral networks to profit from the advantages of each while trying to bypass the disadvantages of the isolated techniques. 

Infrared Spectrum-Structure-Correlations Based on Fuzzy Theory. 

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