In this study a new type of Takagi-Sugeno-Kang (TSK) type fuzzy SYSTEM with dimension reduction section at the input stage called Semi-POLYNOMIAL data Mapping Fuzzy Inference SYSTEM (SPMFIS) is proposed. In the proposed method a semi-POLYNOMIAL feature map is used to transform the input variables to new extracted features with low dimensions. At the next step, these new features are used as the input vector of ANFIS structure. Also gradient descent algorithm is chosen for training parameters of ANFIS and SPM parts of the proposed method. In order to evaluate the capability of the proposed method, its applications in classification of some different benchmark data sets, SYSTEM identification, and time series prediction have been studied. The results show that the proposed method performs better than the conventional models in classification, identification and time series prediction.

In this paper, estimation of second order POLYNOMIAL SYSTEMs’ domain of attraction (DA) via rational Lyapunov function is investigated. One of the methods for estimating DA is to find the greatest level set. In this study, in order to obtain the greatest level set, cost function based on increasing the region enclosed to the level set has been offered instead of using shape factor.Estimating DA has been converted into solving bilinear matrix inequality optimization problem.Capacity of this method compared to other methods in recent studies has been shown through some examples.

In this paper, we present some efficient numerical algorithms for solving SYSTEM of dual fuzzy POLYNOMIAL equations based on Newton’s method. The modified Adomian decom-position method is applied to construct the numerical algorithms. Some numerical illus-trations are given to show the efficiency of algorithms.

Suppose G is a graph, A(G) its adjacency matrix and Ψ (G, λ ) = λ n + a1λ n− 1 + … +an is the characteristic POLYNOMIAL of G. The matching POLYNOMIAL of G is defined as M(G, x) = m(G, 0)xn – m(G, 1)xn− 2 – m(G, 2)xn− 4 + … , where m(G, k) is the number of k− matchings in G. In this paper, the relationship between 2k-th coefficient of the characteristic POLYNOMIAL, a2k, and k-th coefficient of the matching POLYNOMIAL, (− 1)km(G, k), k=0, 1, 2, … , in a regular graph is determined. In addition, these relations for finding 5, 6-matchings of fullerene graphs are applied.

Suppose G is an n-vertex and m-edge simple graph with edge set E(G). An integer-valued function f: E(G)→Z is called a flow. Tutte was introduced the flow POLYNOMIAL F(G, l) as a POLYNOMIAL in an indeterminate l with integer coefficients by F(G, l) = (−1)|E(G)| S SÌE(G)(-1)|S|ln-m+c(G:S), where c(G:S) is the number of connected components of G and (G:S) denotes the spanning subgraph of G with edge set S. In this paper the Flow POLYNOMIAL of some dendrimers are computed.