By Professor Rafik Aziz Aliev, Professor Bijan Fazlollahi, Professor Rashad Rafik Aliev (auth.)
This monograph offers a self-contained exposition of the rules of sentimental computing, and provides an unlimited compendium of its purposes to enterprise, finance, determination research and economics.
It is the 1st booklet on functions of soppy computing - established hybrid equipment combining fuzzy common sense, neuro-computing, evolutionary computing, probabilistic computing and chaotic computing in useful parts of commercial and economics. The purposes diversity from transportation and overall healthiness case platforms to clever inventory marketplace prediction, possibility administration structures, and e-commerce.
This booklet is a beneficial reduction to an individual contemplating the applying of sentimental Computing concept and expertise to actual difficulties of industrial and economics and will be used as a easy textual content for introducing enterprise managers, scientists, lecturers and scholars to smooth Computing expertise, allowing them to begin tasks and make functions.
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Extra resources for Soft Computing and its Applications in Business and Economics
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1 max(A,B)(z) = sup Elements ofFuzzy Sets Theory min[A(x),B(y)]. 70) By using a-cuts we define Va E [0,1] mTn(A a ,Ba) = [min(af ,bf),min(a~ ,b~)], max(A a ,Ba) = [max(af ,bf),max(a~ ,b~)]. 72) Definition. Absolute value offozzy number Absolute value of fuzzy number is defined as: abs(A)= { max(A,-A), for R + (I, for R" LR - representation offozzy numbers LR - representation of fuzzy numbers suggested by Dubois and Prade [35,36] allows considerably simplifying operations of fuzzy arithmetic and gaining computation speed.
Fuzzy n - cube representation All fuzzy sets on uni verse X with n elements can be represented by points in the ndimensional unit cube - n-cube. Assume that universe X contains n elements X = {x .. x 2 , •••,xnl . Each element Xi, i = I,n can be viewed as a coordinate in the n dimensional Euclidean space. A subset of this space for which values of each coordinate are restricted in [0, I] is 20 2 Constituent Methodologies ofSoft Computing called n-cube. e. ,Q) represent crisp sets. The points inside the cube define fuzzy subsets.
Note, that in case ofthe linguistic variable "age" a numerical variable "age" , for example, taking the values of 17, 24, 31, 38, ... , 94, is so-called basis variable of the linguistic variable of age. In tbis case such a linguistic value as "old" can be interpreted as a name for some fuzzy restriction on the values ofthe ba:;is variable. This restriction essentially is the sense ofthe linguistic value "old". The fuzzy restriction on the values of the basis variable is characterized by a compatibility function which maps each value of the basis variable into some number from the interval [0,1], characterizing the relation of this value with the fuzzy restriction.
