science

Weight-of-conflict conjecture

Weight-of-conflict conjecture is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Weight-of-conflict conjecture rather than just read about it. In short: Weight-of-conflict conjecture was proposed by Glenn Shafer in his book on the Dempster–Shafer theory titled A Mathematical Theory of Evidence. It states that if Q 1 {\displaystyle Q_{1}} and Q 2 {\displaystyle Q_{2}} are commonality functions for two separable support functions S 1 {\displaystyle S_{1}} and S 2 {\displaystyle S_{2}} defined over Θ {\displaystyle \Theta } , and Q 1 ( A ) ≤ Q 2 ( A ) {\displaystyle Q_…

Key takeaways

Weight-of-conflict conjecture belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Weight-of-conflict conjecture to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Weight-of-conflict conjecture from memory before moving on to harder problems.

Reference excerpt

Weight-of-conflict conjecture was proposed by Glenn Shafer in his book on the Dempster–Shafer theory titled A Mathematical Theory of Evidence. It states that if Q 1 {\displaystyle Q_{1}} and Q 2 {\displaystyle Q_{2}} are commonality functions for two separable support functions S 1 {\displaystyle S_{1}} and S 2 {\displaystyle S_{2}} defined over Θ {\displaystyle \Theta } , and Q 1 ( A ) ≤ Q 2 ( A ) {\displaystyle Q_{1}(A)\leq Q_{2}(A)} , then the corresponding weights of conflict satisfy the condition W S 1 ≥ W S 2 {\displaystyle W_{S_{1}}\geq W_{S_{2}}} .

∀ A ⊆ Θ : Q 1 ( A ) ≤ Q 2 ( A ) ⟹ W S 1 ≥ W S 2 {\displaystyle \forall A\subseteq \Theta :Q_{1}(A)\leq Q_{2}(A)\implies W_{S_{1}}\geq W_{S_{2}}}

References

Zhang, Lian-Wen (April 1986). "Weights of Evidence and Internal Conflict for Support Functions". Journal of Information Science. 38 (2).

Further reading Yager, R. R.; Liu, L. (2008). Studies in fuzziness and soft computing. Classic works of the Dempster–Shafer theory of belief functions. Berlin: Springer. ISBN 978-3-540-25381-5.

Worked examples

Example 1 — a first encounter with Weight-of-conflict conjecture

Start with the simplest possible case. Write down what Weight-of-conflict conjecture claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Weight-of-conflict conjecture before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Weight-of-conflict conjecture ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Weight-of-conflict conjecture

In research: Weight-of-conflict conjecture appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Weight-of-conflict conjecture in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Weight-of-conflict conjecture is common in secondary-school and first-year university syllabi. It links to neighbouring topics Dempster–Shafer theory, so understanding it makes those chapters shorter.
In everyday life: Look for Weight-of-conflict conjecture outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Weight-of-conflict conjecture in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Weight-of-conflict conjecture means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Weight-of-conflict conjecture out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Weight-of-conflict conjecture in simple terms?

Why does Weight-of-conflict conjecture matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Weight-of-conflict conjecture?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Weight-of-conflict conjecture.