Some Score Functions on Fermatean Fuzzy Sets and Its Application to Bride Selection Based on TOPSIS Method

The aim of this paper is to propose some score functions for the fruitful ranking of fermatean fuzzy sets (FFSs) and fermatean fuzzy TOPSIS method based on proposed score functions. fermatean fuzzy sets proposed by Senapati and Yager can handle uncertain information more easily in the process of multi-criteria decision making (MCDM). In this paper, the authors have proposed three newly improved score functions for effective ranking of fermatean fuzzy sets. Here, they have applied the proposed score function to calculate the separation measure of each alternative from the positive and negative ideal solutions to determine the relative closeness coefficient. Based on different types of score functions, they have employed the TOPSIS method to solve the multi-criteria decision-making (MCDM) problem in which all preference information provided by the decision makers is expressed in terms of fermatean fuzzy decision matrices. Finally, a numerical example for selecting the bride form matrimonial site has been considered to illustrate the proposed method.

Pemilihan Alternatif Bahan Baku Fly Ash Menggunakan Metode Fuzzy-Topsis di PT. Semen Gresik

PT Semen Gresik Rembang merupakan salah satu perusahaan semen yang ingin memanfaatkan kembali limbah B3 (Bahan Berbahaya dan Beracun). Perusahaan berencana untuk memilih alternatif diantara fly ash kelas F dan C dengan pertimbangan kriteria pozzolan, , dan kuat tekan. Kandungan fly ash kelas F pozzolan 83,95%, 0,49%, 2,21%, kuat tekan 95,53 Mpa dan kandungan fly ash kelas C pozzolan 74%, 2,97%, 2,20%, dan kuat tekan 65,04 Mpa. Penelitian ini bertujuan untuk menentukan alternatif bahan baku fly ash terbaik berdasarkan kriteria yang ditentukan. Penelitian ini menggunakan metode Fuzzy-TOPSIS. Penelitian ini pertama melakukan penentuan membentuk fungsi keanggotaan, menetukan nilai keanggotaan, inferensi sistem terhadap aturan fuzzy, melakukan normalisasi bobot matriks, menentukan solusi ideal positif, menentukan solusi ideal negatif, menentukan separation measure, menentukan kedekatan relatif, dan melakukan perangkingan alternatif yang dapat digunakan sebagai pemilihan alternatif terbaik. Pemilihan alternatif terbaik dilihat berdasarkan kandungan yang dimiliki pada masing-masing kriteria. Kandungan pada masing-masing kriteria dilakukan pengolahan data untuk menentukan hasil terbaik yang akan diterapkan di perusahaan. Diperoleh hasil penelitian fly ash kelas F dan kelas C . Berdasarkan perangkingan alternatif, fly ash kelas C dipilih sebagai bahan baku penunjang produksi semen.

An Iterative Transient Rank Aggregation Technique for Mitigation of Rank Reversal

With the advent of decision science, significant elucidation has been sought in the literature of multi criteria decision making. Often, it is observed that for the same MCDM problem, different methods fetch way-apart ranks and the phenomenon leads to rank reversal. To alleviate this problem, different methodologies like the Borda rule, the Copeland method, the Condorcet method, the statistical Thurstone scaling, and linear programming methods are readily available in the literature. In connection with the same, the authors proposed a novel technique to aggregate the ranks laid by different methods. The algorithm initially assigns equal weights to the methods involved to avoid biasness to a particular method and a simple average rank was obtained. Then, after the separation measures of individual methods with respect to average rank were calculated. Considering the separation measure the higher the weightage, the dynamic weights are ascertained to declare the weighted aggregate rank subjected to the terminal condition which include whether the previous rank equals to the current rank or not. To substantiate the proposed algorithm, a materials selection problem was taken into consideration and solved with the proposed technique. Moreover, the same problem was solved by existing voting techniques like the Borda and the Copeland-Condoract methods. The authors found a correlation of more than 85% between the proposed and existing methodologies.

A Hybrid the Nonsubsampled Contourlet Transform and Homomorphic Filtering for Enhancing Mammograms

Mammogram is important for early breast cancer detection. But due to the low contrast of microcalcifications and noise, it is difficult to detect microcalcification. This paper presents a comparative study in digital mammography image enhancement based on three different algorithms: homomorphic filtering, unsharp masking and our proposed methods. This latter use a hybrid method Combining contourlet and homomorphic filtering. Performance of the given technique has been measured in terms of distribution separation measure (DSM), target-to-background enhancement measure based on standard deviation (TBES) and target-to-background enhancement measure based on entropy (TBEE). The proposed methods were tested with the referents mammography data Base MiniMIAS. Experimental results show that the proposed method improves the visibility of microcalcification.

On the Measures of Separation of a Fuzzy Clustering

This paper tested the measures of separation of a fuzzy clustering. Over the same labeled data, Fuzzy k-Means clustering algorithm generates the first fuzzy clustering, then the proposed revision function in (6) revises it several times to generate various fuzzy partitions with different pattern recognition rates computed by (5), finally the measures of separation measure the separation of each fuzzy clustering. Experimental results on real data show that the measures of separation in literatures fail to measure the separation of a fuzzy clustering in some cases, for they argue that the fuzzy clustering with higher pattern recognition rate is less separate between clusters and worse than that with lower pattern recognition rate.