mathematics

Ordinal priority approach

Ordinal priority approach is a mathematics 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 Ordinal priority approach rather than just read about it. In short: Ordinal priority approach (OPA) is a multiple-criteria decision analysis method that aids in solving the group decision-making problems based on preference relations. Description Various methods have been proposed to solve multi-criteria decision-making problems.

Key takeaways

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

Reference excerpt

Ordinal priority approach (OPA) is a multiple-criteria decision analysis method that aids in solving the group decision-making problems based on preference relations.

Description Various methods have been proposed to solve multi-criteria decision-making problems. The basis of methods such as analytic hierarchy process and analytic network process is pairwise comparison matrix. The advantages and disadvantages of the pairwise comparison matrix were discussed by Munier and Hontoria in their book. In recent years, the OPA method was proposed to solve the multi-criteria decision-making problems based on the ordinal data instead of using the pairwise comparison matrix. The OPA method is a major part of Dr. Amin Mahmoudi's PhD thesis from the Southeast University of China.

This method uses linear programming approach to compute the weights of experts, criteria, and alternatives simultaneously. The main reason for using ordinal data in the OPA method is the accessibility and accuracy of the ordinal data compared with exact ratios used in group decision-making problems involved with humans. In real-world situations, the experts might not have enough knowledge regarding one alternative or criterion. In this case, the input data of the problem is incomplete, which needs to be incorporated into the linear programming of the OPA. To handle the incomplete input data in the OPA method, the constraints related to the criteria or alternatives should be removed from the OPA linear-programming model. Various types of data normalization methods have been employed in multi-criteria decision-making methods in recent years. Palczewski and Sałabun showed that using various data normalization methods can change the final ranks of the multi-criteria decision-making methods. Javed and colleagues showed that a multiple-criteria decision-making problem can be solved by avoiding the data normalization. There is no need to normalize the preference relations and thus, the OPA method does not require data normalization.

The OPA method The OPA model is a linear programming model, which can be solved using a simplex algorithm. The steps of this method are as follows: Step 1: Identifying the experts and determining the preference of experts based on their working experience, educational qualification, etc. Step 2: identifying the criteria and determining the preference of the criteria by each expert. Step 3: identifying the alternatives and determining the preference of the alternatives in each criterion by each expert. Step 4: Constructing the following linear programming model and solving it by an appropriate optimization software such as LINGO, GAMS, MATLAB, etc.

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Ordinal priority approach

Start with the simplest possible case. Write down what Ordinal priority approach claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, 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 Ordinal priority approach 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 Ordinal priority approach 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 Ordinal priority approach

In research: Ordinal priority approach appears in mathematics 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 Ordinal priority approach 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: Ordinal priority approach is common in secondary-school and first-year university syllabi. It links to neighbouring topics Decision analysis, Management systems, Mathematical optimization, so understanding it makes those chapters shorter.
In everyday life: Look for Ordinal priority approach 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 Ordinal priority approach in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Ordinal priority approach 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 Ordinal priority approach out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Ordinal priority approach in simple terms?

Ordinal priority approach (OPA) is a multiple-criteria decision analysis method that aids in solving the group decision-making problems based on preference relations. Description Various methods have been proposed to solve multi-criteria decision-making problems.

Why does Ordinal priority approach matter?

Because it connects several mathematics 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 Ordinal priority approach?

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 Ordinal priority approach.