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

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 using neutral and refusal degrees… 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

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 numbers (BPFNs). Additionally, the concept… 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

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 discuss various real-life applications of… More >