Harmonic Aggregation Operator with Trapezoidal Picture Fuzzy Numbers and Its Application in a Multiple-Attribute Decision-Making Problem

Picture fuzzy sets (PFSs) can be used to handle real-life problems with uncertainty and vagueness more effectively than intuitionistic fuzzy sets (IFSs). In the process of information aggregation, many aggregation operators under PFSs are used by different authors in different fields. In this article, a multi-attribute decision-making (MADM) problem is introduced utilizing harmonic mean aggregation operators with trapezoidal fuzzy number (TrFN) under picture fuzzy information. Three harmonic mean operators are developed namely trapezoidal picture fuzzy weighted harmonic mean (TrPFWHM) operator, trapezoidal picture fuzzy order weighted harmonic mean (TrPFOWHM) operator and trapezoidal picture fuzzy hybrid harmonic mean (TrPFHHM) operator. The related properties about these operators are also studied. At last, an MADM problem is considered to interrelate among these operators. Furthermore, a numerical instance is considered to explain the productivity of the proposed operators.

Comparative Study of AMMI- and BLUP-Based Simultaneous Selection for Grain Yield and Stability of Finger Millet [Eleusine coracana (L.) Gaertn.] Genotypes

Finger millet, an orphan crop, possesses immense potential in mitigating climate change and could offer threefold security in terms of food, fodder, and nutrition. It is mostly cultivated as a subsistence crop in the marginal areas of plains and hills. Considering the changes in climate inclusive of recurrent weather vagaries witnessed every year, it is crucial to select stable, high-yielding, area-specific, finger millet cultivars. Sixty finger millet varieties released across the country were evaluated over six consecutive rainy seasons from 2011 to 2016 at the Agricultural Research Station, Vizianagaram. The genotype × environment interaction (GEI) was found to be significant in the combined ANOVA. Furthermore, the Additive Main effects and Multiplicative Interaction (AMMI) analysis asserted that genotypes and the GEI effects accounted for approximately 89% of the total variation. Strong positive associations were observed in an estimated set of eleven stability parameters which were chosen to identify stable genotypes. Furthermore, Non-parametric and Parametric Simultaneous Selection indices (NP-SSI and P-SSI) were calculated utilizing AMMI-based stability parameter (ASTAB), modified AMMI stability value (MASV), and Modified AMMI Stability Index (MASI) to identify stable high yielders. Both methods had inherent difficulties in ranking genotypes for SSI. To overcome this, the initial culling [i.e., SSI with culling strategy (C-SSI)] of genotypes was introduced for stability. In the C-SSI method, the top ten genotypes were above-average yielders, while those with below-average yield were observed in NP-SSI and P-SSI methods. Similarly, the estimation of best linear unbiased prediction (BLUP)-based simultaneous selections, such as harmonic mean of genotypic values (HMGV), relative performance of genotypic values (RPGV), and harmonic mean of relative performance of genotypic values (HMRPGV), revealed that none of the top ten entries had below-average yield. The study has proven that C-SSI and BLUP-based methods were equally worthy in the selection of high-yielding genotypes with stable performance. However, the C-SSI approach could be the best method to ensure that genotypes with a considerable amount of stability are selected. The multi-year trial SSI revealed that entries Indaf-9, Sri Chaitanya, PR-202, and A-404; and VL324 and VL146 were ascertained to be the most stable high-yielding genotypes among medium-to-late and early maturity groups, respectively.

Penerapan Algoritme Nearest Centroid Neighbor Classifier Based on K Local Means Using Harmonic Mean Distance (LMKHNCN) Untuk Klasifikasi Hasil Kinerja Pegawai Negeri Sipil

<p class="Abstrak">Keberhasilan sebuah perusahaan terjadi karena dapat mengelola sumber daya manusianya dengan baik begitu juga sebaliknya. Salah satu instansi yang mengelola sumber daya manusia menggunakan Manajemen Talenta adalah Badan Kepegawaian Daerah (BKD) kota Malang, dengan mengevaluasi pegawainya setiap tahunnya setelah pekerjaan selesai dilakukan. Hal ini menyebabkan hasil pekerjaan yang telah dilakukan tidak optimal, sehingga perlu identifikasi dini pegawai yang memiliki kinerja dibawah rata – rata sehingga dapat dievaluasi dan meminimalisir hasil pekerjaan yang tidak optimal dengan menggunakan teknik klasifikasi. Penelitian ini menggunakan teknik klasifikasi <em>Nearest Centroid Neighbor Classifier Based on K Local Means Using Harmonic Mean Distance</em> (LMKHNCN). Metode ini merupakan metode modifikasi dari metode <em>K-Nearest Neighbor</em> (KNN) dan dibuktikan memiliki performa lebih baik dibandingkan dengan metode aslinya KNN. Dilakukan pengujian <em>F1-Score</em> dan akurasi menggunakan <em>K-Fold Cross Validation</em> untuk mengetahui persebaran akurasi dan juga pengujian mengenai pengaruh normalisasi karena tidak ada informasi normalisasi pada penelitian sebelumnya. Metode pada kasus ini menghasilkan performa klasifikasi yang baik, dibuktikan bahwa hasil akurasi dan <em>F1-Score</em> oleh metode ini berturut – turut ialah mencapai 98,8% dan 98,1%.</p><p class="Abstrak"> </p><p class="Judul2"><strong><em>Abstract</em></strong></p><p><em>The success of company occurs because is manage human resources well and vice versa. One of institute that mange human resource using Talent Management is Malang city Badan Kepegawaian Daerah (BKD), which evaluates its employee annually after the work is completed. This can cause not optimal work result, so it necessary to early identification of employees who have performance below average performance so that can be evaluated and minimize not optimal result. This study is use classification technique Nearest Centroid Neighbor Classifier Based on K Local Means Using Harmonic Mean Distance (LMKHNCN). This method is modified base algorithm of K-Nearest Neighbor (KNN). F1-Score and Accuracy using K-Fold Cross Validation to measure performance of this method and normalization testing due to no any information about that in previous study. This method is proven to have better performance compared to it original algorithm KNN. The method in this study has produced good classification performance. The result of classification accuracy and F1-Score by this method reach </em><em>98,8% dan 98,1%</em>.</p>

Study of a Fractal-Fractional Smoking Models with Relapse and Harmonic Mean Type Incidence Rate

This manuscript investigates fractal-fractional order smoking models with relapse and harmonic mean type incidence rate under the Caputo derivative. We derive the existence and unique results about the solution for the considered model via fixed point theory. For the stability of the considered system, Ulam-Hyers (UH) approach is used. We compute the numerical solution by using fractional Adams-Bashforth method. For the simulation of the model, we consider different values of fractional order δ and fractal dimension θ by using some real values of the parameters. The proposed scheme is used to simulate the available data for some smoking community including potential, light, and quit smokers. Various graphical presentations are given to understand the dynamics of the model at various fractional orders.

A HARMONIC MEAN INEQUALITY CONCERNING THE GENERALIZED EXPONENTIAL INTEGRAL FUNCTION

In this paper, we prove that for $s\in(0,\infty)$, the harmonic mean of $E_k(s)$ and $E_k(1/s)$ is always less than or equal to $\Gamma(1-k,1)$. Where $E_k(s)$ is the generalized exponential integral function, $\Gamma(u,s)$ is the upper incomplete gamma function and $k\in \mathbb{N}$.

Testing for equality of means with equal and unequal variances

In this paper, we are interested in comparing the conventional t –test with the proposed t – test for testing equality of means with unequal and equal variances. Here, we proposed harmonic mean of variances as an alternative to the pooled sample variance when there is heterogeneity of variances. Two sets of secondary data were obtained from Agricultural Development Project (KWADP) and the Ministry of Agriculture in Ilorin, Kwara State to demonstrate the two test statistics used and the results show that the proposed t – test statistic is found to be appropriate than the conventional t – test statistic when we have unequal variances but the conventional t – test perform better when we have equal variances.