Linganisha mbinu

	Njia Bora Mbaya Isiyo-Laini	Njia ya Ubora wa Kinyama	Upangaji wa Hisabati Usio na Mstari
Nyanja	Ufanyaji Maamuzi	Ufanyaji Maamuzi	Uboreshaji
Familia	MCDM	MCDM	Process / pipeline
Mwaka wa asili	2016	2015 crisp; 2017 variant applicator	2006
Mwanzilishi	Extended development of Rezaei's BWM framework	Guo, S., Zhao, H.	Jorge Nocedal & Stephen Wright
Aina	Non-linear optimization for flexible weight derivation	Triangular-fuzzy Best-to-Others and Others-to-Worst pairwise comparison with nonlinearly-constrained programming	Continuous mathematical optimization
Chanzo asilia	Rezaei, J. (2015). Best-worst multi-criteria decision-making method: Some properties and a linear model. Journal of Cleaner Production, 229, 976-985.	Guo, S., Zhao, H. (2017). Fuzzy best-worst multi-criteria decision-making method and its applications. Knowledge-Based Systems	Nocedal, J., & Wright, S. J. (2006). Numerical Optimization (2nd ed.). Springer. ISBN: 978-0-387-30303-1
Majina mbadala	Non-linear BWM, Nonlinear BWM	—	NLP optimization, Constrained nonlinear optimization, Smooth optimization, Doğrusal olmayan programlama
Zinazohusiana	3	8	3
Muhtasari	Non-linear BWM is a variant of the Best Worst Method that replaces the linear programming formulation with non-linear optimization. Instead of minimizing the maximum deviation (Chebyshev distance), it minimizes the sum of squared deviations (L2 norm). This provides more flexible weight derivation and better accommodates uncertain or fuzzy preferences.	FUZZY-BWM (Fuzzy BWM — Triangular Fuzzy Best-Worst Method) is a weight subjective multi-criteria decision-making (MCDM) method introduced by Guo, S., Zhao, H. in 2015 crisp; 2017 variant applicator. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.	Nonlinear programming (NLP) is a branch of mathematical optimization concerned with problems in which the objective function or at least one constraint is nonlinear. Formalized comprehensively by Jorge Nocedal and Stephen Wright in their seminal 2006 text, NLP encompasses gradient-based algorithms — including sequential quadratic programming (SQP), interior-point methods, and quasi-Newton approaches — for finding locally or globally optimal solutions to continuous decision problems arising across engineering, economics, and the physical sciences.