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

This monograph presents a self-contained exposition of the principles of soppy computing, and provides an unlimited compendium of its functions to enterprise, finance, selection research and economics.

It is the 1st e-book on functions of sentimental computing - established hybrid tools combining fuzzy good judgment, neuro-computing, evolutionary computing, probabilistic computing and chaotic computing in practical parts of industrial and economics. The functions diversity from transportation and overall healthiness case platforms to clever inventory industry prediction, hazard administration platforms, and e-commerce.

This e-book is a necessary reduction to an individual contemplating the appliance of soppy Computing idea and know-how 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 delicate Computing know-how, allowing them to begin initiatives and make purposes.

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Sample text

But commutativity, associativity, idempotency, distributivity, and De Morgan laws are held for standard fuzzy operations. For fuzzy union, intersection and complement operations there exist a broad class of functions. Function that qualify as fuzzy intersections and fuzzy unions are defined as t-norms and t-conorms. Definition. e. 17) then t(ocA(x), cxn (x» ~ t(<

20. Notice, that fuzzy relation can be defined in another way. Namely, by two ordered fuzzy sets. 1 Elements of Fuzzy Sets Theory 45 Fuzzy R Fig. 20. Membership function ofR Assurne, two fuzzy sets ocA(x) and oca(y) are given on crisp sets X and Y, respectively. ,y for all pairs (x,y), where x E X and YE Y . As above, fuzzy relation R AB is defined on Cartesian product. For example, let X ={1,2,3} and Y = {Q,L,M} . 1 (3, M)} . The frequently used way of representing finite fuzzy relations is matrices.

87) exists, {'(to) is called the derivative of [(tl at t o . Here d p defines a metric in the Banach space Lp[O,I). Fuzzy maximum 0/a fozzifying fonction Let [(x) be a fuzzifying function from [a, b]~ R to R. 88) with x and a as parameters are assumed to have exactly two solutions in the case a :;t:l and y=f(x). (x) (see Fig. 19. a -level curves of f(x) Integration offozzy fonction At first we consider the integral of a fuzzifying function over a crisp interval [a,b]. 93) LR a It is necessary to mention that br1.

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