By Bojadziev G., Bojadziev M.
This can be really an interdisciplinary publication for wisdom employees in enterprise, finance, administration and socio-economic sciences in line with fuzzy common sense. It serves as a consultant to and methods for forecasting, determination making and reviews in an atmosphere related to uncertainty, vagueness, impact and subjectivity. conventional modeling recommendations, opposite to fuzzy good judgment, don't catch the character of advanced platforms specifically while people are concerned. Fuzzy common sense makes use of human adventure and judgement to facilitate believable reasoning with a purpose to achieve a end. Emphasis is on functions provided within the 27 case reports together with Time Forecasting for venture administration, New Product Pricing, and keep watch over of a Parasit-Pest procedure.
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Additional resources for Fuzzy Logic for Business, Finance, and Management
For general studies and also for facilitating fuzzy logic, fuzzy set theory is a very suitable tool. 6. Fuzzy relations were introduced by Zadeh (1971) as a generalization of both classical relations and fuzzy sets. Chapter 2 Fuzzy Logic The chapter gives first a short description of classical and many-valued logics. Classical (two-valued) logic deals with propositions that are either true or false. In many-valued logic, a generalization of the classical logic, the propositions have more than two truth values.
12) where [a1 , a2 ] is the supporting interval and the point (a M , 1) is the peak (see Fig. 17). 12) can be dropped. α (a M ,1) 1 l A 0 a1 A aM r a2 x Fig. 17. Triangular fuzzy number. e. aM = a1 +a 2 . 12) gives A = µA (x) = x−a 1 2 a2 −a1 2 2 ax−a 1 −a2 0 2 for a1 ≤ x ≤ a1 +a 2 , 2 for a1 +a ≤ x ≤ a2 , 2 otherwise. 13) represents a central triangular fuzzy number (see Fig. 18(a)). Similarly to the piecewise-quadratic fuzzy number, it is very suitable to describe the word close (close to a M ).
In Fig. 9 are shown µ A (x) and µB (x), in Fig. 10 the complements µA (x) and µB (x), and in Fig. 11 the union µA∩B (x) and the intersection µA∩B (x). 1 1 µA (x) µB (x) U U Fig. 9. Membership function µA (x), µB (x). 11 shows that A ∩ B ∈ A ∪ B. Law of excluded middle and fuzzy sets The classical sets possess an important property, the law of excluded middle,2 expressed by A ∩ A = φ and A ∪ A = U . It is illustrated in Fig. 12 by the means of Venn diagrams. 18 Chapter 1. Fuzzy Sets The law of excluded middle is not valid for the fuzzy sets since A ∩ A = φ and A ∪ A = U .
Fuzzy Logic for Business, Finance, and Management by Bojadziev G., Bojadziev M.