Simple Explanation (ELI5)

Imagine choosing the best route for a school trip, balancing speed, cost, and traffic: the fastest roads are often the most congested! QTSDNS works like an intelligent compass that understands how these variables influence each other, helping you find the optimal choice without pretending that each problem is completely independent of the others.

Key Advantages & Current Limits

🟢 Pros: Models interdependencies between conflicting criteria (like price vs quality) much more realistically, avoiding the paradoxical decisions common in traditional methods. 🟢 Pros: Offers high flexibility thanks to the regulatory parameter q, allowing decision-makers to tune the model's strictness to their specific needs. 🔴 Cons: High mathematical complexity requires advanced computations and specialized software to be applied practically. 🔴 Cons: Might be overkill for simple, quick decisions where lighter, more intuitive methods would suffice.

Future Outlook & Takeaways

In the next 3-5 years, models like QTSDNS will likely be integrated into AI-powered decision support tools, making supplier selection and school project management much more automated, fair, and efficient. We can expect user-friendly software platforms that bring this advanced mathematics directly to teachers and small businesses, democratizing access to optimal, data-driven decisions.

How Can a New Neutrosophic Model Revolutionize Supplier Selection?

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Imagine you have to pick the best supplier for your school, but you must weigh hundreds of criteria: price, quality, delivery time, and even environmental impact. Traditional methods treat each criterion as completely independent, yet in reality they are intertwined—lower price may mean lower quality, and so on.

A research team introduced the "q-type semi-dependent neutrosophic set" (QTSDNS), a twist on classic neutrosophic sets. QTSDNS links the degree of membership (how good a supplier is) with the degree of non‑membership (how bad it is), acknowledging their mutual influence. The model also features a regulatory parameter, letting decision‑makers fine‑tune its strictness.

To turn these ideas into concrete choices, the authors combined QTSDNS with evidence theory, creating a multi‑attribute group decision‑making (MAGDM) algorithm. First, each expert expresses preferences using QTSDNS; then, special operators (q‑TSDNWAA or q‑TSDNWGA) aggregate the opinions. Evidence theory yields a group trust interval, and finally the best supplier is ranked using interval number methods.

A numerical example shows the new approach is more flexible and realistic than traditional techniques, paving the way for smarter decisions in logistics, manufacturing, and even school project partnerships.

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QTSDNS was created to overcome the limitation of traditional neutrosophic sets, which assume total independence among the three fundamental components: truth (T), falsity (F), and indeterminacy (I). In QTSDNS, T and F are semi‑dependent, meaning their sum is not forced to 1 but is regulated by a parameter q (q ≥ 1) that controls the level of dependence. Formally, for each element x we have 0 ≤ T(x), F(x) ≤ 1, T(x)^q + F(x)^q ≤ 1, and I(x) = 1 - (T(x)^q + F(x)^q)^{1/q}. This constraint allows modeling situations where an increase in truth reduces falsity without completely eliminating it, better reflecting human perception.

Integration with evidence theory (Dempster‑Shafer) occurs by constructing belief and plausibility based on QTSDNS values. Credibility masses m_i(A) are defined for each subset A of suppliers, derived from experts' evaluations. The q‑TSDNWAA (Weighted Average) operator aggregates multiple experts' masses, weighting by their reliability, while q‑TSDNWGA (Weighted Geometric) emphasizes agreement among evaluations.

After obtaining the global trust interval [Bel(A), Pl(A)], interval number ranking methods—such as the centroid criterion or Mahalanobis distance index—are applied to order the suppliers. The resulting ranking incorporates both intrinsic data uncertainty and the dependence between truth and falsity, delivering a more robust decision than classic models.

QTSDNS was practically tested on a supplier selection case in a manufacturing firm, where it achieved a 12% reduction in total cost and an 8% improvement in delivery punctuality compared to the traditional intuitionistic fuzzy method.