By Jacek Kluska
This publication is concentrated on mathematical research and rigorous layout tools for fuzzy keep watch over structures in line with Takagi-Sugeno fuzzy types, often referred to as Takagi-Sugeno-Kang models.
Read or Download Analytical Methods in Fuzzy Modeling and Control (Studies in Fuzziness and Soft Computing) PDF
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Extra resources for Analytical Methods in Fuzzy Modeling and Control (Studies in Fuzziness and Soft Computing)
M. 53) Every column θj is assigned to a single system output Sj , (j = 1, . . , m). 49). The fundamental matrix Ω of the system is a concatenation of 2n columns which are values of the generator g for the vertices of the hypercuboid Dn , where every vertex corresponds to the appropriate antecedent of the rule. Proof. 4. 30). 7 Equivalence Problem in the Rule-Based Systems The problem of equivalence between the systems of fuzzy “If-then” rules is important especially when one compares the outcomes obtained by various experts or designers, and the number of inputs is greater than two.
Let us consider a MISO TS system with the inputs z1 , . . , zn and the output S (see Fig. 9). This system is deﬁned by 2n rules in the form of implications Fig. 13) n where (i1 , . . ,in ) = “z1 is Ai1 and ... 14) 10 2 MISO Takagi-Sugeno Fuzzy System with Linear Membership Functions and Aik = Nk , for ik = 0 , Pk , for ik = 1 k = 1, . . , n. e. we will consider a zero-order Takagi-Sugeno model . In more general TS systems, the consequents are polynomials of the ﬁrst or higher order or more complicated functions of input variables.
10. Suppose the MIMO P1-TS system with the inputs constituting the vector [z1 , . . , zn ]T = z ∈ Dn and the outputs S1 , . . 50). The row vector of crisp outputs S (z) = [S1 , . . 52) and n Θ = [θ1 , . . 1 ] ∈ R2 , j = 1, . . , m. 53) Every column θj is assigned to a single system output Sj , (j = 1, . . , m). 49). The fundamental matrix Ω of the system is a concatenation of 2n columns which are values of the generator g for the vertices of the hypercuboid Dn , where every vertex corresponds to the appropriate antecedent of the rule.