By Professor Rafik Aziz Aliev, Professor Bijan Fazlollahi, Professor Rashad Rafik Aliev (auth.)

This monograph offers a self-contained exposition of the rules of soppy computing, and provides an unlimited compendium of its purposes to company, finance, choice research and economics.

It is the 1st publication on functions of sentimental computing - dependent hybrid tools combining fuzzy common sense, neuro-computing, evolutionary computing, probabilistic computing and chaotic computing in useful components of industrial and economics. The purposes variety from transportation and healthiness case platforms to clever inventory industry prediction, hazard administration structures, and e-commerce.

This booklet is a invaluable relief to an individual contemplating the appliance of sentimental Computing concept and know-how to actual difficulties of commercial and economics and will be used as a uncomplicated textual content for introducing company managers, scientists, academics and scholars to tender Computing expertise, permitting them to start up tasks and make purposes.

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**Sample text**

Xi k is the projeetion offuzzy relation R on, if R p is defined by the following membership funetion OCR (Xil,Xi2,,,,,Xik)= P max xiteXjl ..... Xj(n-k)eXj(n-k) OCR(xj, ... ) where {Xjh ... ,Xj(n-k)} is the eomplement of {Xih""Xik} with respeet to {Xh""Xn} In partieular if R is a fuzzy binary relation on X· Y , then the projection of R on X , denoted Rl , is a fuzzy set in X defined by OCR, (x) = maxOCR (x,y) yeY Definition. Cylindrical extension 01 relation The eylindrieal extension of Rp to Xl' X 2 • Xl' X 2 • ....

Fuzzy relation R is fuzzy transitive. If fuzzy partial order is given on set X then we will say that set X is fuzzy partially ordered. Next we eonsider projections and cylindrieal extension. Let R be n-dimensional fuzzy relation on Cartesian produet X = XI' X 2 · .... X n ofnonempty sets X\,X 2 ,,,,,X n and (iJ>i 2 , ... ,i k ) be a subsequenee of (1,2, ... ,n). Definition. Projection ollUZZY relation It is said, that fuzzy relation R p on Xii' X i2 ..... Xi k is the projeetion offuzzy relation R on, if R p is defined by the following membership funetion OCR (Xil,Xi2,,,,,Xik)= P max xiteXjl .....

50) A where the integral is taken over the region with oc A (x, y) > o. 53) Definition. Adjacency Let A and B be two piecewise constant fuzzy sets of X. k Definition. 55) This index for fuzzy region represents the fraction of the maximum area (covered by the length and breadth of the region) actually covered by the region. Fuzzyarithmetic Fuzzy arithmetic is an important constituent of numerical analysis and main tool for dealing with uncertainly in a computationally effective way. The main concept and kernel offuzzy arithmetic is fuzzy number [51].