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8 Canonical forms

• Published: May 1990
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A canonical form is a standard form to which a certain class of matrices can be reduced by a defined set of operations. We have already encountered some simple canonical forms in earlier chapters, and it is useful to recall these: In Section 5.3.3 we noted that any m x n matrix A having rank r can be reduced by elementary row and column operations to the normal form N, where N is the m x n matrix having l’s in positions (1, 1), (2, 2), ... , (r, r) and zeros elsewhere. This is the canonical form of A under an equivalence transformation, as in (5.12).

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Research status and development trend of wire arc additive manufacturing technology for aluminum alloys.

1. Introduction

2. waam digital control system and the parameters monitoring, 2.1. waam digital control system, 2.1.1. cad model processing and slicing algorithm, 2.1.2. path planning, 2.2. processing parameters, 2.2.1. current, 2.2.2. wire feeding speed (wfs), 2.2.3. travel speed (ts), 2.2.4. shielding gas, 2.2.5. auxiliary additive manufacturing, 3. waam process regulation, 3.1. heat input, 3.2. alloy composition, 3.3. heat treatment, 4. mechanical properties of the waam deposition, 5. application, 6. future prospects, author contributions, institutional review board statement, informed consent statement, data availability statement, conflicts of interest.

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Dai, P.; Li, A.; Zhang, J.; Chen, R.; Luo, X.; Wen, L.; Wang, C.; Lv, X. Research Status and Development Trend of Wire Arc Additive Manufacturing Technology for Aluminum Alloys. Coatings 2024 , 14 , 1094. https://doi.org/10.3390/coatings14091094

Dai P, Li A, Zhang J, Chen R, Luo X, Wen L, Wang C, Lv X. Research Status and Development Trend of Wire Arc Additive Manufacturing Technology for Aluminum Alloys. Coatings . 2024; 14(9):1094. https://doi.org/10.3390/coatings14091094

Dai, Pan, Ao Li, Jianxun Zhang, Runjie Chen, Xian Luo, Lei Wen, Chen Wang, and Xianghong Lv. 2024. "Research Status and Development Trend of Wire Arc Additive Manufacturing Technology for Aluminum Alloys" Coatings 14, no. 9: 1094. https://doi.org/10.3390/coatings14091094

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A novel dual-level multi-source information fusion approach for multicriteria decision making applications

• Published: 29 August 2024

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• Iman Mohamad Sharaf 1 ,
• O. S. Albahri 2 , 3 ,
• M. A. Alsalem 4 ,
• A. H. Alamoodi 5 , 6 &
• A. S. Albahri   ORCID: orcid.org/0000-0003-3335-457X 7 , 8  

The objective of this paper is to propose a novel dual-level multisource information fusion approach for handling open multicriteria decision-making (MCDM) issues related to accurately determining the weights of criteria while considering the relative importance of expert opinions, handling heterogeneous information, and selecting an appropriate MCDM ranking method. The proposed approach includes two levels. The first integrates the “analytic hierarchy process (AHP)—full consistency method (FUCOM)”, which comprises two phases. In the first phase, criteria weights are assigned using AHP, and FUCOM is employed to correct inconsistencies. In the second phase, the weights are computed for decision-makers. Triangular fuzzy numbers are employed due to their ability to encapsulate all the utilized heterogeneous data types. At the second level of the approach, three well-known distance-based methods, including “technique for order preference by similarity to ideal solution”, “visekriterijumska optimizacija i kompromisno resenje”, and “multiattributive border approximation area comparison”, are fused to process a homogeneous decision matrix and provide comprehensive and robust rankings for alternatives. To develop our novel approach, a renewable energy source for Pakistan's electricity generation is adopted as a case study. The decision matrix contains four alternatives (i.e., hydropower, biomass energy, solar energy, and wind energy) and six main evaluation criteria (i.e., economic, quality of energy, social, political, environmental, and technical), with several subevaluation criteria under each criterion. The findings of the proposed approach were as follows: A2 was in the first rank with a score of 1.7889 , and A4 was in the last rank with a score of 0.1199 . The rest of the alternatives were distributed between them. The paper’s implications include the advancement of decision-making methods, enhancement of decision-making outcomes, and addressing heterogeneous information to highlight the relative importance of experts.

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Department of Basic Sciences, Higher Technological Institute, Tenth of Ramadan City, Egypt

Iman Mohamad Sharaf

Computer Techniques Engineering Department, Mazaya University College, Nasiriyah, Iraq

O. S. Albahri

Australian Technical and Management College, Melbourne, Australia

Department of Management Information System, College of Administration and Economics, University of Mosul, Mosul, Iraq

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Applied Science Research Center, Applied Science Private University, Amman, Jordan

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MEU Research Unit, Middle East University, Amman, Jordan

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All the authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Iman Mohamad Sharaf and O.S. Albahri. The first draft of the manuscript was written by M. A. Alsalem, A.H. Alamoodi, and A.S. Albahri. All authors commented on previous versions of the manuscript. All the authors have read and approved the final manuscript.

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Sharaf, I.M., Albahri, O.S., Alsalem, M.A. et al. A novel dual-level multi-source information fusion approach for multicriteria decision making applications. Appl Intell (2024). https://doi.org/10.1007/s10489-024-05624-6

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