Decision matrix

A decision matrix is a list of values in rows and columns that allows an analyst to systematically identify, analyze, and rate the performance of relationships between sets of values and information. Elements of a decision matrix show decisions based on certain decision criteria. The matrix is useful for looking at large masses of decision factors and assessing each factor's relative significance by weighting them by importance.^[1]

Multiple-criteria decision analysis

The term decision matrix is used to describe a multiple-criteria decision analysis (MCDA) problem. An MCDA problem, where there are M alternative options and each needs to be assessed on N criteria, can be described by the decision matrix which has N rows and M columns, or M × N elements, as shown in the following table. Each element, such as X_ij, is either a single numerical value or a single grade, representing the performance of alternative i on criterion j. For example, if alternative i is "car i", criterion j is "engine quality" assessed by five grades {Exceptional, Good, Average, Below Average, Poor}, and "Car i" is assessed to be "Good" on "engine quality", then X_ij = "Good". These assessments may be replaced by scores, from 1 to 5. Sums of scores may then be compared and ranked, to show the winning proposal.^[2]

Example of Comparison
	Alternative 1	Alternative 2	...	Alternative M
Criterion 1	x₁₁	x₁₂	...	x_1M
Criterion 2	x₂₁	x₂₂	...	x_2M
...	...	...	X_ij = Good	...
Criterion N	x_N1	x_N2	...	x_NM

Sum
Rank
Status		No		No

Belief decision matrix

Similar to a decision matrix, a belief decision matrix is used to describe a multiple criteria decision analysis (MCDA) problem in the Evidential Reasoning Approach. Instead of being a single numerical value or a single grade as in a decision matrix, each element in a belief decision matrix is a belief distribution.

For example, suppose Alternative i is "Car i", Criterion j is "Engine Quality" assessed by five grades {Excellent, Good, Average, Below Average, Poor}, and "Car i" is assessed to be “Excellent” on "Engine Quality" with a high degree of belief (e.g. 0.6) due to its low fuel consumption, low vibration and high responsiveness. At the same time, the quality is also assessed to be only “Good” with a lower degree of belief (e.g. 0.4 or less) because its quietness and starting can still be improved. If this is the case, then we have X_ij={ (Excellent, 0.6), (Good, 0.4)}, or X_ij={ (Excellent, 0.6), (Good, 0.4), (Average, 0), (Below Average, 0), (Poor, 0)}.

A conventional decision matrix is a special case of belief decision matrix when only one belief degree in a belief structure is 1 and the others are 0.

	Criterion 1	Criterion 2	...	Criterion N
Alternative 1	x₁₁	x₁₂	...	x_1N
Alternative 2	x₂₁	x₂₂	...	x_2N
...	...	...	X_ij={ (Excellent, 0.6), (Good, 0.4)}	...
Alternative M	x_M1	x_M2	...	x_MN

References

^ "When to use a weighted decision matrix". Weighted Decision. 15 October 2013. Retrieved 25 May 2022.
^ Enz, Cathy A.; Thompson, Gary (June 2013). "The Options Matrix Tool (OMT): A Strategic Decision-making Tool to Evaluate Decision Alternatives". ecommons.cornell.edu. Retrieved 20 December 2022.

Sources

Shafer, G.A. (1976). Mathematical Theory of Evidence. Princeton University Press. ISBN 0-691-08175-1.
Yang J.B., Singh M.G. (1994). "An evidential reasoning approach for multiple attribute decision making with uncertainty". IEEE Transactions on Systems, Man, and Cybernetics. 24: 1–18. doi:10.1109/21.259681.
Yang J.B., Xu D.L. (2002). "On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty". IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans. 32 (3): 289–304. doi:10.1109/TSMCA.2002.802746.

[1] "When to use a weighted decision matrix". Weighted Decision. 15 October 2013. Retrieved 25 May 2022.

[2] Enz, Cathy A.; Thompson, Gary (June 2013). "The Options Matrix Tool (OMT): A Strategic Decision-making Tool to Evaluate Decision Alternatives". ecommons.cornell.edu. Retrieved 20 December 2022.

[1]

[2]

v t e Decision theory
Core concepts	Ambiguity aversion Bounded rationality Choice architecture Expected utility Expected value Hyperbolic discounting Leximin Loss aversion Multi-attribute utility Path dependence Principle of indifference Prospect theory Rational choice theory Risk aversion Risk-seeking Satisficing Strategic dominance Subjective expected utility Sure-thing Utility theorem
Decision models	Anscombe-Aumann framework Causal decision Decision field theory Emotional choice Evidential decision Fuzzy-trace theory Intertemporal choice Naturalistic decision Normative model Quantum cognition Recognition-primed decision Rubicon model Savage's subjective expected utility model
Decision analysis tools	Analytic hierarchy process Analytic network process Cost–benefit analysis Cost-effectiveness analysis Cost–utility analysis Decision conferencing Decision curve analysis Decision rule Decision support system Decision table Decision tree Decision matrix Decisional balance sheet Gittins index Influence diagram Minimax MCDA Scoring rule Value of information perfect sample uncertainty
Paradoxes and biases	Allais paradox Certainty effect Cognitive bias Decoy effect Disposition effect Ellsberg paradox Endowment effect Framing effect Heuristics Newcomb's paradox Pseudocertainty effect Reference dependence Regret St. Petersburg paradox Status quo bias Sunk cost
Uncertainty and risk	Deep uncertainty Exploration–exploitation Info-gap Pignistic probability Robust decision-making
Related fields	Behavioral economics Game theory Operations research Social choice theory Utility theory
Key people	David Blackwell Bruno de Finetti Morris H. DeGroot Peter C. Fishburn Gerd Gigerenzer Itzhak Gilboa Daniel Kahneman R. Duncan Luce Oskar Morgenstern Howard Raiffa Leonard J. Savage David Schmeidler Herbert Simon Amos Tversky John von Neumann
Category

Decision matrix

Decision matrix

Decision matrix

Add your contribution

Hub overview

Root Wikipedia Article

Decision matrix

Multiple-criteria decision analysis

Belief decision matrix

See also

References

Sources