A novel intuitionistic fuzzy Yager aggregation framework for decision making in green supply chains

Why smarter green choices matter

Companies are under growing pressure to clean up their supply chains, from sourcing raw materials to delivering finished products. Yet choosing which suppliers are truly eco-friendly is not straightforward: expert opinions are uncertain, data are incomplete, and criteria such as carbon footprint, cost, and reliability often conflict. This paper introduces a new mathematical decision tool that helps organizations sift through this fuzzy information to identify the most sustainable partners in their green supply chains.

Messy reality behind everyday decisions

In real life, decisions rarely rest on clear yes-or-no facts. Managers may be partly confident that a supplier is “green enough,” partly doubtful, and sometimes simply unsure. Traditional methods force these shades of grey into crisp numbers and can miss the hesitation that people naturally feel when information is limited. Earlier fuzzy set techniques improved matters by allowing partial membership (something can be “somewhat green”), but they still struggled to capture how much experts actively reject an option and how uncertain they are about their own judgment.

A richer way to capture doubt

The paper builds on a framework called intuitionistic fuzzy sets, which separately track three ingredients for each assessment: the degree of support, the degree of opposition, and the remaining hesitation. Instead of collapsing these into a single score too early, the method preserves all three throughout the calculation. On top of this, the authors use a family of mathematical building blocks known as Yager operators. These allow the aggregation process to be tuned between more “optimistic” and more “cautious” behavior, so that the decision model can reflect different attitudes toward risk and uncertainty without losing logical consistency.

From scattered opinions to a clear ranking

To turn many expert judgments into a final choice, the authors design a suite of averaging and geometric operators that combine intuitionistic fuzzy evaluations across multiple criteria. They first construct a decision table where each potential supplier is rated on twelve green supply chain dimensions, covering strategy (such as eco-design and green purchasing), daily operations (like manufacturing and logistics), supporting systems (including technology, data, and staff training), and overall sustainability performance. An entropy-based step then measures how informative each criterion is: if experts strongly agree and the data show clear differences, that criterion receives a higher weight; if opinions are vague or conflicting, its influence is reduced.

Putting the method to the test

The researchers apply their framework to a real-world case involving four companies that claim to practice green supply chain management. Expert assessments, expressed in ordinary terms like “very good” or “moderate,” are converted into intuitionistic fuzzy values and passed through the new Yager-based operators. The system consistently identifies one company as the best green supplier, regardless of whether an averaging-style or geometric-style operator is used, and even when the importance of different criteria is systematically varied. Compared with an earlier technique based on Dombi operators, the new approach produces more stable rankings and reacts less erratically to small changes in the input data.

What this means for greener industry

For a non-specialist, the core message is simple: this framework offers a more honest way to deal with doubt when judging how green companies really are. By keeping track of support, opposition, and hesitation separately, and by flexibly combining them through tunable operators, the method gives decision-makers a transparent and robust ranking of suppliers. The case study shows that it can highlight genuinely sustainable partners in complex industrial networks, supporting greener purchasing choices, more responsible manufacturing, and clearer sustainability strategies.

Citation: Kumar, Y., Ramalingam, S. & Zegeye, G.B. A novel intuitionistic fuzzy Yager aggregation framework for decision making in green supply chains. Sci Rep 16, 8779 (2026). https://doi.org/10.1038/s41598-026-37890-4

Keywords: green supply chain, sustainable supplier selection, fuzzy decision making, intuitionistic fuzzy sets, multi-criteria analysis