A Fiedler’s Approach to LINEX Intuitionistic Fuzzy C-means Clustering Induced Spectral Initialization for Data Analysis
M. Nithya,
K. Bhuvaneswari,
S. Senthil
Issue:
Volume 12, Issue 4, August 2023
Pages:
82-91
Received:
19 May 2023
Accepted:
12 June 2023
Published:
21 July 2023
Abstract: Clustering is a common technique for statistical data analysis. The clustering method based on intuitionistic fuzzy set has attracted more and more scholar’s attention nowadays. This paper discusses the intuitionistic fuzzy C-means clustering algorithm. There are a number of clustering techniques developed in the past using different distance/similarity measure. In researchers have used various distance measure like Hamming distance, Euclidean distance etc., to solve the clustering problems. In this paper, we proposed a novel LINEX for intuitionistic fuzzy c means clustering based on minimal spanning tree using Fiedler’s approach initialization method. Our main motives of using the LINEX methods consist inducing a class of robust non-Euclidean distance measures for the original data space to derive new objective functions and thus clustering the integration of datasets, enhancing robustness of the original clustering algorithms to noise and outliers, and still retaining computational simplicity. The proposed Fiedler’s approach LINEX IFCM, which requires the determination of the eigenvector belonging to the second Eigen value of the Laplacian matrix. Finally, evaluation is illustrated by the intuitionistic fuzzy C-means clustering method and the method is compared with the fuzzy C-means clustering method as well.
Abstract: Clustering is a common technique for statistical data analysis. The clustering method based on intuitionistic fuzzy set has attracted more and more scholar’s attention nowadays. This paper discusses the intuitionistic fuzzy C-means clustering algorithm. There are a number of clustering techniques developed in the past using different distance/simil...
Show More
A q-Operational Equation for Carlitz’s q-Operators with Some Applications
Jian Cao,
Cheng Zhang,
Sama Arjika
Issue:
Volume 12, Issue 4, August 2023
Pages:
92-108
Received:
11 June 2023
Accepted:
8 July 2023
Published:
21 July 2023
Abstract: Rogers–Szegö polynomials are the basis in the Scheme of basic hypergeometric orthogonal polynomials. By solving a q-operational equation with formal power series, Liu introduced a new q-exponential operational identity and developed a systematic method to prove the identities involving the Rogers–Szegö polynomials. In this paper, motivated by Carlitz’s q-operators and Liu’s q-operational equation, we construct an q-operational equation for Carlitz’s q-operators and give some applications to some generating functions for Rogers–Szegö polynomials and Hahn polynomials, which generalize the method of exponential operator decomposition introduced by Cao and provide a new proof of results of Carlitz and Saad et al.. We chose Mehler’s formula, q-Nielsen’s formula for Rogers–Szegö polynomials and Mehler’s formula for Hahn polynomials as examples to show that the q-series theory can be applied, which takes us quickly the results. One of the main characteristics of this method is that it provides an effective approach to calculate generating functions for some q-polynomials. This method also brings a new research perspective to problems of the sum and integration of q-polynomials.
Abstract: Rogers–Szegö polynomials are the basis in the Scheme of basic hypergeometric orthogonal polynomials. By solving a q-operational equation with formal power series, Liu introduced a new q-exponential operational identity and developed a systematic method to prove the identities involving the Rogers–Szegö polynomials. In this paper, motivate...
Show More
