Sanghyuk Lee¹, Eunmi Lee^2,*

CMC-Computers, Materials & Continua, Vol.86, No.2, pp. 1-17, 2026, DOI:10.32604/cmc.2025.070504 - 09 December 2025

Abstract Hesitation analysis plays a crucial role in decision-making processes by capturing the intermediary position between supportive and opposing information. This study introduces a refined approach to addressing uncertainty in decision-making, employing existing measures used in decision problems. Building on information theory, the Kullback–Leibler (KL) divergence is extended to incorporate additional insights, specifically by applying temporal data, as illustrated by time series data from two datasets (e.g., affirmative and dissent information). Cumulative hesitation provides quantifiable insights into the decision-making process. Accordingly, a modified KL divergence, which incorporates historical trends, is proposed, enabling dynamic updates using conditional More >

Zhe Liu^1,2,3,*, Sijia Zhu⁴, Yulong Huang^1,*, Tapan Senapati^5,6,7, Xiangyu Li⁸, Wulfran Fendzi Mbasso⁹, Himanshu Dhumras¹⁰, Mehdi Hosseinzadeh^11,12,*

CMES-Computer Modeling in Engineering & Sciences, Vol.145, No.2, pp. 2157-2188, 2025, DOI:10.32604/cmes.2025.072352 - 26 November 2025

Abstract Uncertainty and ambiguity are pervasive in real-world intelligent systems, necessitating advanced mathematical frameworks for effective modeling and analysis. Fermatean fuzzy sets (FFSs), as a recent extension of classical fuzzy theory, provide enhanced flexibility for representing complex uncertainty. In this paper, we propose a unified parametric divergence operator for FFSs, which comprehensively captures the interplay among membership, non-membership, and hesitation degrees. The proposed operator is rigorously analyzed with respect to key mathematical properties, including non-negativity, non-degeneracy, and symmetry. Notably, several well-known divergence operators, such as Jensen-Shannon divergence, Hellinger distance, and χ²-divergence, are shown to be special cases More >

Sijia Zhu¹, Yuhan Li², Prasanalakshmi Balaji^3,*, Akila Thiyagarajan³, Rajanikanth Aluvalu⁴, Zhe Liu^5,6,7,*

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.2, pp. 2099-2121, 2025, DOI:10.32604/cmes.2025.068734 - 31 August 2025

Abstract While interval-valued picture fuzzy sets (IvPFSs) provide a powerful tool for modeling uncertainty and ambiguity in various fields, existing divergence measures for IvPFSs remain limited and often produce counterintuitive results. To address these shortcomings, this paper introduces two novel divergence measures for IvPFSs, inspired by the Jensen-Shannon divergence. The fundamental properties of the proposed measures—non-degeneracy, symmetry, triangular inequality, and boundedness—are rigorously proven. Comparative analyses with existing measures are conducted through specific cases and numerical examples, clearly demonstrating the advantages of our approach. Furthermore, we apply the new divergence measures to develop an enhanced interval-valued picture More >

Shah Zeb Khan¹, Muhammad Rahim², Adel M. Widyan^3,*, A. Almutairi³, Njood Shaher Ethaar Almutire³, Hamiden Abd El-Wahed Khalifa³

CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.2, pp. 2185-2211, 2025, DOI:10.32604/cmes.2025.063929 - 30 May 2025

Abstract This study introduces a novel distance measure (DM) for spherical fuzzy sets (SFSs) to improve decision-making in complex and uncertain environments. Many existing distance measures either fail to satisfy essential axiomatic properties or produce unintuitive outcomes. To address these limitations, we propose a new three-dimensional divergence-based DM that ensures mathematical consistency, enhances the discrimination of information, and adheres to the axiomatic framework of distance theory. Building on this foundation, we construct a multi-criteria decision-making (MCDM) model that utilizes the proposed DM to evaluate and rank alternatives effectively. The applicability and robustness of the model are More >

Kuo Li^1,*, Aimin Wang¹, Limin Wang¹, Yuetan Zhao¹, Xinyu Zhu²

CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.1, pp. 617-637, 2025, DOI:10.32604/cmes.2025.061242 - 11 April 2025

Abstract A Bayesian network reconstruction method based on norm minimization is proposed to address the sparsity and iterative divergence issues in network reconstruction caused by noise and missing values. This method achieves precise adjustment of the network structure by constructing a preliminary random network model and introducing small-world network characteristics and combines L1 norm minimization regularization techniques to control model complexity and optimize the inference process of variable dependencies. In the experiment of game network reconstruction, when the success rate of the L1 norm minimization model’s existence connection reconstruction reaches 100%, the minimum data required is… More >

Harsh Mankodiya¹, Priyal Palkhiwala¹, Rajesh Gupta^1,*, Nilesh Kumar Jadav¹, Sudeep Tanwar¹, Osama Alfarraj², Amr Tolba², Maria Simona Raboaca^3,4,*, Verdes Marina⁵

CMC-Computers, Materials & Continua, Vol.77, No.1, pp. 1123-1142, 2023, DOI:10.32604/cmc.2023.038556 - 31 October 2023

Abstract The amalgamation of artificial intelligence (AI) with various areas has been in the picture for the past few years. AI has enhanced the functioning of several services, such as accomplishing better budgets, automating multiple tasks, and data-driven decision-making. Conducting hassle-free polling has been one of them. However, at the onset of the coronavirus in 2020, almost all worldly affairs occurred online, and many sectors switched to digital mode. This allows attackers to find security loopholes in digital systems and exploit them for their lucrative business. This paper proposes a three-layered deep learning (DL)-based authentication framework More >

Junzhe Cui¹, Dechun Zhang¹, Peng Li^1,*, Yiren Yang¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.26, No.1, pp. 1-1, 2023, DOI:10.32604/icces.2023.010401

Abstract This study investigates the static instability of a cracked plate in subsonic airflow. The plate model is an inverted cantilever plate, where its leading edge is free and the trailing edge the clamped. A mathematical model of the crack is developed using the Dirac function, while Theodorsen aerodynamic mode is applied for the fluid force. To account for angle discontinuity caused by cracks, Fourier expansion is employed to transform the form corresponding to the angle into a continuous model. The critical divergent dynamic pressure and mode of an inverted cantilever plate with a crack are More >

Ashaduzzaman Sagar¹ , Md. Sabibul Haque¹, Md. Alamgir Hossain¹, Md. Nesar Uddin¹, Jannat E. Tajkia¹, Md. Ashik Mia¹, Toufika Hossain Shabi², Md. Solaiman Ali Fakir¹, Md. Abdul Kader^3,4,5, Walid Soufan⁶, Md. Atikur Rahman⁷, Muhammad Aamir Iqbal⁸, Mohammad Sohidul Islam⁹, Ayman El Sabagh^10,*, A. K. M. Zakir Hossain^1,*

Phyton-International Journal of Experimental Botany, Vol.92, No.8, pp. 2349-2368, 2023, DOI:10.32604/phyton.2023.028974 - 25 June 2023

Abstract Salt stress is one of the major limitations to modern agriculture that negatively influences plant growth and productivity. Salt tolerant cultivar can provide excellent solution to enhance stress tolerance with plant fitness to unfavorable environments. Therefore, this study was aimed to screen salt tolerant sorghum genotypes through evaluating of different morphological, biochemical, and physiological attributes in response to salinity stress. In this study, we have been evaluated total six sorghum genotypes including Hybrid sorgo, Debgiri, BD-703, BD-706, BD-707, and BD-725 under salt stress (12 dS m⁻¹ NaCl). The response variables included length and weight of root… More >

Syed Ali Zafar^1,*, Muhammad Aslam², Haroon Zaman Khan³, Sehrish Sarwar¹, Rao Saad Rehman⁴, Mariam Hassan¹, Ramala Masood Ahmad², Rafaqat A. Gill⁵, Basharat Ali⁶, Ibrahim Al-Ashkar⁷, Abdullah Ibrahim⁷, Md Atikur Rahman⁸, Ayman El Sabagh^9,*

Phyton-International Journal of Experimental Botany, Vol.92, No.6, pp. 1887-1906, 2023, DOI:10.32604/phyton.2023.027679 - 11 April 2023

Abstract The availability of favorable genetic diversity is a thriving vitality for the success of a breeding program. It provides a firm basis of selecting superior breeding lines for the development of high yielding crop genotypes. In this context, present investigation aimed to generate information on genetic divergence and character association in a diversity panel of 123 local and exotic soybean genotypes. Analysis of variance revealed significant response of the evaluated genotypes based on studied attributes. It depicted the probability of selecting desirable soybean genotypes by focusing on character association studies and genetic diversity analysis. Correlation… More >

Mao Yuxin, Wang Honglin^*

CMC-Computers, Materials & Continua, Vol.75, No.1, pp. 863-878, 2023, DOI:10.32604/cmc.2023.034879 - 06 February 2023

Abstract In the financial sector, data are highly confidential and sensitive, and ensuring data privacy is critical. Sample fusion is the basis of horizontal federation learning, but it is suitable only for scenarios where customers have the same format but different targets, namely for scenarios with strong feature overlapping and weak user overlapping. To solve this limitation, this paper proposes a federated learning-based model with local data sharing and differential privacy. The indexing mechanism of differential privacy is used to obtain different degrees of privacy budgets, which are applied to the gradient according to the contribution… More >