Related Experiment Video
Updated: Apr 1, 2026

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm
Published on: December 9, 2012
An integrated VIKOR-AHP method for green energy systems based on q-fractional hesitant fuzzy multi-criteria
Hariwan Fadhil M Salih1, Zanyar A Ameen2, Badr Alharbi3
1Department of Mathematics, College of Science, University of Duhok, 42001, Duhok, Iraq.
Abstract:
The q-fractional hesitant fuzzy sets (q-FHFSs) extend the conventional hesitant and intuitionistic fuzzy sets by providing a richer framework for representing uncertainty. This paper proposes an integrated VIKOR-AHP framework based on q-FHFSs to enhance multi-criteria decision-making (MCDM) under uncertain conditions. To address the challenge of comparing fractional and heterogeneous hesitant elements, this study develops an LCM-based generalized distance measure for q-fractional hesitant fuzzy numbers, enabling consistent comparison among hesitant elements with different cardinalities. As criteria weights are inherently subjective, the AHP method is used to systematically derive objective priority weights. The proposed VIKOR-AHP hybrid model improves flexibility in handling fractional hesitancy and conflicting criteria, while preserving mathematical rigor in distance quantification. To demonstrate its applicability, the model is applied to the selection of Green Energy Systems, evaluated under selected subcriteria from Cavallaro and Ciraolo's list of sustainability criteria. A sensitivity analysis is conducted to examine the influence of parameter q. Finally, a comparative evaluation against q-fractional hesitant fuzzy TOPSIS (q-FHF TOPSIS), hesitant q-rung orthopair fuzzy TOPSIS (Hq-ROF TOPSIS), hesitant q-rung orthopair fuzzy VIKOR (Hq-ROF VIKOR) and hesitant fuzzy VIKOR (HF VIKOR) across varying q values confirms the effectiveness and robustness of the proposed decision-making method.
Related Concept Videos
Decision Making: P-value Method
First, a specific claim about the population parameter is proposed. The claim is based on the research question and is stated in a simple form. Further, an opposing statement to the claim is also stated. These statements can act as null and alternative hypotheses: a null hypothesis would be a neutral statement while the alternative hypothesis can...
Decision Making: Traditional Method
First, a specific claim about the population parameter is decided based on the research question and is stated in a simple form. Further, an opposing statement to this claim is also stated. These statements can act as null and alternative hypotheses, out of which a null hypothesis would be a...
Power Factor Correction
Integration of Rational Functions Using Partial Fractions
Fast Decoupled and DC Powerflow
Heuristics
People often rely on heuristics when faced with an overload of information, limited time, low importance of the decision, limited information, or when a heuristic readily comes to mind. For...