Pham Huy Thong¹, Hoang Thi Canh^2,3,*, Nguyen Tuan Huy⁴, Nguyen Long Giang^1,*, Luong Thi Hong Lan⁴

CMC-Computers, Materials & Continua, Vol.86, No.3, 2026, DOI:10.32604/cmc.2025.071776 - 12 January 2026

Abstract Satellite image segmentation plays a crucial role in remote sensing, supporting applications such as environmental monitoring, land use analysis, and disaster management. However, traditional segmentation methods often rely on large amounts of labeled data, which are costly and time-consuming to obtain, especially in large-scale or dynamic environments. To address this challenge, we propose the Semi-Supervised Multi-View Picture Fuzzy Clustering (SS-MPFC) algorithm, which improves segmentation accuracy and robustness, particularly in complex and uncertain remote sensing scenarios. SS-MPFC unifies three paradigms: semi-supervised learning, multi-view clustering, and picture fuzzy set theory. This integration allows the model to effectively… 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 >

Xingsi Xue¹, Himanshu Dhumras^2,*, Garima Thakur³, Rakesh Kumar Bajaj⁴, Varun Shukla⁵

CMC-Computers, Materials & Continua, Vol.84, No.1, pp. 583-606, 2025, DOI:10.32604/cmc.2025.066310 - 09 June 2025

Abstract Ensuring a sustainable and eco-friendly environment is essential for promoting a healthy and balanced social life. However, decision-making in such contexts often involves handling vague, imprecise, and uncertain information. To address this challenge, this study presents a novel multi-criteria decision-making (MCDM) approach based on picture fuzzy hypersoft sets (PFHSS), integrating the flexibility of Schweizer-Sklar triangular norm-based aggregation operators. The proposed aggregation mechanisms—weighted average and weighted geometric operators—are formulated using newly defined operational laws under the PFHSS framework and are proven to satisfy essential mathematical properties, such as idempotency, monotonicity, and boundedness. The decision-making model systematically… More >

Pham Huy Thong¹, Hoang Thi Canh^2,3,*, Luong Thi Hong Lan⁴, Nguyen Tuan Huy⁴, Nguyen Long Giang^1,*

CMC-Computers, Materials & Continua, Vol.83, No.3, pp. 5461-5485, 2025, DOI:10.32604/cmc.2025.065127 - 19 May 2025

Abstract Multi-view clustering is a critical research area in computer science aimed at effectively extracting meaningful patterns from complex, high-dimensional data that single-view methods cannot capture. Traditional fuzzy clustering techniques, such as Fuzzy C-Means (FCM), face significant challenges in handling uncertainty and the dependencies between different views. To overcome these limitations, we introduce a new multi-view fuzzy clustering approach that integrates picture fuzzy sets with a dual-anchor graph method for multi-view data, aiming to enhance clustering accuracy and robustness, termed Multi-view Picture Fuzzy Clustering (MPFC). In particular, the picture fuzzy set theory extends the capability to… More >

Navaneethakrishnan Suganthi Keerthana Devi¹, Samayan Narayanamoorthy¹, Thirumalai Nallasivan Parthasarathy¹, Chakkarapani Sumathi Thilagasree², Dragan Pamucar^3,4,*, Vladimir Simic^5,6, Hasan Dinçer^7,8, Serhat Yüksel^7,8

CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.3, pp. 2665-2687, 2024, DOI:10.32604/cmes.2024.050954 - 08 July 2024

Abstract Food Waste (FW) is a pressing environmental concern that affects every country globally. About one-third of the food that is produced ends up as waste, contributing to the carbon footprint. Hence, the FW must be properly treated to reduce environmental pollution. This study evaluates a few available Food Waste Treatment (FWT) technologies, such as anaerobic digestion, composting, landfill, and incineration, which are widely used. A Bipolar Picture Fuzzy Set (BPFS) is proposed to deal with the ambiguity and uncertainty that arise when converting a real-world problem to a mathematical model. A novel Criteria Importance Through… More >

Pham Huy Thong^1,2,3, Florentin Smarandache⁴, Phung The Huan⁵, Tran Manh Tuan⁶, Tran Thi Ngan^6,*, Vu Duc Thai⁵, Nguyen Long Giang², Le Hoang Son³

Computer Systems Science and Engineering, Vol.46, No.2, pp. 1981-1997, 2023, DOI:10.32604/csse.2023.035692 - 09 February 2023

Abstract Clustering is a crucial method for deciphering data structure and producing new information. Due to its significance in revealing fundamental connections between the human brain and events, it is essential to utilize clustering for cognitive research. Dealing with noisy data caused by inaccurate synthesis from several sources or misleading data production processes is one of the most intriguing clustering difficulties. Noisy data can lead to incorrect object recognition and inference. This research aims to innovate a novel clustering approach, named Picture-Neutrosophic Trusted Safe Semi-Supervised Fuzzy Clustering (PNTS3FCM), to solve the clustering problem with noisy data… More >

Muhammad Riaz¹, Harish Garg², Hafiz Muhammad Athar Farid¹, Ronnason Chinram^3,4,*

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.2, pp. 771-800, 2021, DOI:10.32604/cmes.2021.014174 - 19 April 2021

Abstract This paper aims to introduce the novel concept of the bipolar picture fuzzy set (BPFS) as a hybrid structure of bipolar fuzzy set (BFS) and picture fuzzy set (PFS). BPFS is a new kind of fuzzy sets to deal with bipolarity (both positive and negative aspects) to each membership degree (belonging-ness), neutral membership (not decided), and non-membership degree (refusal). In this article, some basic properties of bipolar picture fuzzy sets (BPFSs) and their fundamental operations are introduced. The score function, accuracy function and certainty function are suggested to discuss the comparability of bipolar picture fuzzy More >

Muhammad Riaz¹, Masooma Raza Hashmi¹, Dragan Pamucar², Yuming Chu^3,4,*

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.3, pp. 1125-1164, 2021, DOI:10.32604/cmes.2021.013699 - 19 February 2021

Abstract The existing concepts of picture fuzzy sets (PFS), spherical fuzzy sets (SFSs), T-spherical fuzzy sets (T-SFSs) and neutrosophic sets (NSs) have numerous applications in decision-making problems, but they have various strict limitations for their satisfaction, dissatisfaction, abstain or refusal grades. To relax these strict constraints, we introduce the concept of spherical linear Diophantine fuzzy sets (SLDFSs) with the inclusion of reference or control parameters. A SLDFS with parameterizations process is very helpful for modeling uncertainties in the multi-criteria decision making (MCDM) process. SLDFSs can classify a physical system with the help of reference parameters. We… More >