6. Uncertainty, Probabilistic Reasoning, and Decision Theory

Introduction: Intelligence When Knowledge Is Incomplete

Artificial intelligence rarely operates in conditions of complete certainty. A medical diagnosis may be based on incomplete symptoms, a fraud detector may receive ambiguous transaction evidence, and an autonomous vehicle may have only a noisy estimate of another vehicle’s position. Sensors fail, data may be missing, observations may conflict, and several explanations may remain plausible at the same time. An intelligent system must therefore do more than represent facts: it must represent degrees of belief, revise those beliefs as evidence arrives, and choose actions whose consequences may be uncertain.

This chapter examines the principal frameworks used for reasoning and decision-making under uncertainty. Probability provides a formal language for uncertain events and supports Bayesian inference. Bayesian networks organize probabilistic dependencies among variables, while Markov models represent how uncertain states evolve over time. Fuzzy logic addresses graded concepts such as “high temperature” or “moderate risk,” which differ fundamentally from random events. Certainty factors and Dempster–Shafer theory provide alternative approaches for systems in which evidence may be incomplete or supplied by multiple sources. Decision theory adds utilities, preferences, and action consequences to the analysis. Influence diagrams combine these elements into compact models of decision problems.

The distinction between belief and action is central. A system may believe that a patient has a disease with probability 0.4, yet whether it should recommend a test or treatment depends not only on that probability but also on costs, risks, benefits, and ethical constraints. Sound intelligent behavior requires both appropriate inference and appropriate decision analysis.

Learning Objectives

After studying this chapter, the learner should be able to:

1. Explain uncertainty, conditional probability, Bayes’ theorem, independence, and expected utility.

2. Construct and interpret Bayesian networks for diagnostic and predictive reasoning.

3. Describe hidden Markov models and their roles in temporal inference.

4. Distinguish probability from fuzzy membership and explain the uses of fuzzy logic.

5. Compare certainty factors and Dempster–Shafer theory with probabilistic reasoning.

6. Formulate decisions using utilities, risks, value of information, and influence diagrams.

7. Analyze practical, organizational, ethical, and technical challenges in uncertain AI systems.

8. Select an appropriate uncertainty model for a given application.

Why Uncertainty Requires Formal Reasoning

Uncertainty has several sources. A proposition may be uncertain because the world itself is variable, because an observation is noisy, because the system lacks relevant information, or because the model is imperfect. These sources should not automatically be treated as identical. For example, the probability that a sensor reports a vehicle correctly concerns measurement reliability, whereas the probability that a vehicle changes lanes concerns the behavior of the external world.

A proposition is often represented as a Boolean variable, such as Disease or Fraud. In more detailed models, variables may be discrete or continuous. Probability assigns values between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. For events A and B, the conditional probability of A given B is:

P(A|B) = P(A and B) / P(B), provided P(B) is greater than zero.

Bayes’ theorem follows directly:

P(A|B) = P(B|A)P(A) / P(B).

Here, P(A) is the prior belief, P(B|A) is the likelihood of observing B if A is true, P(B) is the evidence probability, and P(A|B) is the posterior belief after considering B. The theorem is important because it permits reasoning from effects to possible causes. A positive test result does not by itself establish disease; the prior prevalence and the test’s false-positive behavior also matter.

For multiple mutually exclusive hypotheses H1, H2, ..., Hn, the evidence probability can be computed using the law of total probability:

P(E) = Σi P(E|Hi)P(Hi).

Conditional independence is a major simplifying assumption. Variables X and Y are conditionally independent given Z when P(X,Y|Z) = P(X|Z)P(Y|Z). Such assumptions allow large reasoning problems to be decomposed into manageable local relationships. However, an incorrect independence assumption can produce confident but erroneous conclusions.

Bayesian Networks: From Causal Structure to Inference

A Bayesian network is a directed acyclic graph whose nodes represent random variables and whose directed edges represent direct probabilistic dependencies. Each node has a conditional probability table, or an equivalent parameterized distribution, given its parents. The network represents a joint distribution through factorization:

P(X1, X2, ..., Xn) = Πi P(Xi | Parents(Xi)).

Consider a simple network containing Rain, Sprinkler, WetGrass, and Traffic. Rain may influence both the sprinkler’s operation and the wetness of grass; wet grass may influence observed traffic conditions. The graph does not merely store correlations. When justified by domain knowledge, it can express a causal interpretation and clarify which variables should be conditioned on.

Inference may be diagnostic, predictive, intercausal, or explanatory. Diagnostic inference reasons from an effect to a cause, such as estimating the probability of an engine fault after observing abnormal vibration. Predictive inference reasons from a cause to an effect, such as estimating failure risk given high temperature. Intercausal reasoning explains how evidence about one possible cause changes belief in another cause when both explain the same observation. If two faults can each explain a warning signal, confirmation of one fault may reduce belief in the other; this phenomenon is sometimes called explaining away.

Exact inference methods include enumeration, variable elimination, and belief propagation in suitable network structures. Inference in general Bayesian networks can be computationally expensive because the number of combinations may grow rapidly. Approximate methods, including Monte Carlo sampling, likelihood weighting, particle filtering, and variational techniques, are therefore important in large or continuous systems.

The quality of a Bayesian network depends on more than its mathematical form. Variables must be selected carefully, probability tables must be estimated or elicited reliably, and the model must be validated against operational data. Expert judgment is useful when data are scarce, but experts may disagree or express probabilities inconsistently. Data-driven learning can estimate structure and parameters, yet learned relationships may reflect bias, confounding, or historical practices rather than genuine causal mechanisms.

Reasoning Through Time: Markov Models

Many intelligent systems must infer changing states. Speech recognition, predictive maintenance, financial monitoring, and robot navigation all involve temporal sequences. A Markov model represents a system in which the next state depends, in a specified manner, on the current state. The first-order Markov property is:

P(St | S1, ..., St−1) = P(St | St−1).

A Markov chain contains observable states and transition probabilities P(St|St−1). For example, a machine may be in Normal, Degraded, or Failed condition. A transition matrix describes the likelihood of moving from each state to another during one time interval. Repeated matrix multiplication can estimate longer-term state distributions.

In a hidden Markov model (HMM), the underlying state is not directly observed. Instead, the system produces observations according to an emission distribution P(Ot|St). Speech phonemes are hidden states and acoustic signals are observations; machine health may be hidden while vibration and temperature are observable. An HMM is commonly specified by initial-state probabilities, transition probabilities, and emission probabilities.

Three classical tasks are associated with HMMs. The evaluation problem computes the likelihood of an observation sequence using the forward algorithm. The decoding problem finds the most likely hidden-state sequence using the Viterbi algorithm. The learning problem estimates model parameters, often using the Baum–Welch expectation–maximization procedure when state labels are unavailable.

A dynamic Bayesian network generalizes these ideas by allowing several interacting variables at each time step and dependencies across time. Such models are more expressive than simple HMMs but may require approximate inference. A practical model must also account for nonstationarity: transition behavior may change with season, workload, user behavior, or equipment age.

Fuzzy Logic: Uncertainty or Vagueness?

Probability and fuzzy logic address different problems. Probability expresses uncertainty about whether a proposition is true. Fuzzy logic expresses the degree to which an object belongs to a vague concept. If the temperature is 28 degrees, the proposition “the temperature is high” may have a fuzzy membership of 0.7. This does not mean that there is a 70 percent chance that the temperature is high. The temperature may be known exactly while the boundary of “high” remains gradual and linguistically defined.

A fuzzy set A is characterized by a membership function μA(x) ranging from 0 to 1. Common membership functions include triangular, trapezoidal, Gaussian, and sigmoidal forms. Linguistic variables such as speed may have terms including slow, moderate, and fast. A fuzzy rule might be:

IF temperature is high AND pressure is low THEN cooling intensity is strong.

A fuzzy inference system typically performs fuzzification, rule evaluation, aggregation, and defuzzification. Fuzzification maps numerical inputs to membership values. Rule evaluation uses operators such as minimum or product for conjunction. Aggregation combines the outputs of applicable rules. Defuzzification converts the resulting fuzzy set into a numerical action, often through the centroid method.

Mamdani systems represent outputs as fuzzy sets and are readily interpretable. Sugeno systems use functions or constants in the consequent and are often computationally efficient and suitable for optimization. Neuro-fuzzy systems learn membership functions or rules from data while retaining some interpretability.

Fuzzy logic is effective when expert knowledge is expressed through gradual categories and precise physical models are unavailable. It does not automatically provide a principled account of random variation, sampling uncertainty, or statistical evidence. In many applications, fuzzy and probabilistic methods can be combined, but their meanings must remain explicit.

Certainty Factors and Dempster–Shafer Theory

Early expert systems often represented belief using certainty factors. A certainty factor is a numerical measure of the strength with which evidence supports or opposes a hypothesis. In rule-based medical systems, a rule might state that a symptom increases confidence in a diagnosis by a specified amount. Certainty-factor systems are attractive because experts can often provide qualitative strengths more easily than precise probabilities.

However, certainty factors are not generally probabilities. Their combination rules depend on the chosen formalism, and they may lack the coherence properties of probability theory. They remain useful in legacy systems and in situations where approximate rule confidence is operationally adequate, but their interpretation must be documented carefully.

Dempster–Shafer theory represents belief using a mass function over sets of hypotheses rather than only individual hypotheses. Let Θ be the frame of discernment. A basic probability assignment m assigns mass to subsets A of Θ, with the total mass equal to one. Mass assigned to a set can represent support for the set without committing to any particular member. For a proposition A, belief is:

Bel(A) = ΣB⊆A m(B),

while plausibility is:

Pl(A) = ΣB∩A≠∅ m(B).

The interval [Bel(A), Pl(A)] represents the range between committed support and the maximum support not contradicted by evidence. This allows explicit representation of ignorance. If two independent sources provide evidence, Dempster’s rule of combination can combine their mass functions, while a conflict term measures disagreement. High conflict can make normalized combination unstable or counterintuitive, so source dependence and conflict management require attention.

Probability, certainty factors, and evidence theory should not be selected merely because their numerical outputs look convenient. The appropriate framework depends on whether the problem involves random variation, vague language, incomplete commitment, or heuristic expert rules.

From Belief to Action: Utility and Decision Theory

Inference identifies what may be true; decision theory determines what should be done. A decision problem contains states of the world, available actions, outcomes, and preferences. Utility is a numerical representation of the desirability of outcomes. If action a can lead to states s1, s2, ..., then its expected utility is:

EU(a) = Σs P(s|e)U(a,s),

where e denotes currently available evidence. A rational decision rule chooses an action with maximum expected utility, subject to constraints and organizational policies.

Expected utility is not the same as the most probable outcome. An unlikely event with catastrophic consequences may dominate a decision. For example, an organization may choose a costly backup system even when failure is unlikely because the utility loss from failure is extremely large.

Decision analysis also considers risk attitudes. A risk-neutral decision-maker evaluates expected monetary value directly. A risk-averse decision-maker may use a concave utility function, making losses more significant than equivalent gains. In safety-critical applications, expected utility should be supplemented by minimum safety standards, precautionary rules, and hard constraints.

The value of information measures whether obtaining additional evidence is worth its cost. The expected value of perfect information is the improvement in expected utility if the true state could be known before acting. The expected value of sample information concerns a particular imperfect test or observation. Information has practical value only when it can change decisions or improve outcomes; collecting data merely because it is available can increase cost, delay, privacy exposure, and complexity.

Influence Diagrams as Decision Models

An influence diagram extends a Bayesian network with three node types: chance nodes, decision nodes, and utility nodes. Chance nodes represent uncertain variables, decision nodes represent choices under the decision-maker’s control, and utility nodes represent preferences or consequences. Arrows indicate probabilistic dependence, information available at decision time, or contribution to utility.

Influence diagrams provide a compact representation of sequential decisions. They help analysts identify which observations are available before an action, which variables are outside the decision-maker’s control, and how consequences should be evaluated. Solving an influence diagram involves evaluating expected utilities and determining an optimal policy—a mapping from available information to actions.

For example, a maintenance decision diagram may include hidden machine condition, sensor readings, inspection decision, repair decision, repair cost, downtime cost, and safety utility. The model can compare immediate repair, inspection followed by conditional repair, or continued operation. The diagram makes explicit the value of inspection and prevents the common error of using information that would not actually be available when the decision is made.

Influence diagrams are particularly useful in enterprise analytics because they connect predictive models with operational choices. A high-risk prediction is not itself a business decision. The organization must specify intervention costs, service-level effects, customer impact, regulatory requirements, and acceptable risk.

Applied Case: Probabilistic Maintenance of Industrial Pumps

Background

The following is an illustrative case. A water-treatment facility operates several industrial pumps. Unexpected pump failure causes service interruption and emergency repair costs. The facility has vibration and temperature sensors, but sensor readings are noisy and occasional data are missing.

Situation and Problem

Engineers must choose among three actions: continue operation, schedule preventive maintenance, or conduct an inspection before deciding. The hidden condition of a pump is Normal, Degraded, or Near Failure. A high vibration reading is more likely when the pump is degraded or near failure, but it can also result from temporary imbalance. Maintenance reduces failure risk but causes planned downtime and expenditure.

Analysis

A dynamic Bayesian network is constructed with pump condition at time t, condition at time t+1, vibration, temperature, workload, and maintenance action. Transition probabilities describe deterioration and recovery behavior. Sensor emission probabilities describe the likelihood of each reading under each hidden condition. Historical records provide initial parameter estimates, which are reviewed by maintenance engineers.

The model first performs filtering: it estimates the current condition from all sensor observations to date. If repeated high vibration and temperature readings occur, the posterior probability of Near Failure increases. If vibration is high but temperature and workload are normal, the model assigns some probability to temporary imbalance rather than immediately concluding that the pump is failing.

An influence diagram then adds the decision node Inspection or Maintenance and utility nodes for repair cost, downtime, safety, and service continuity. Inspection has a cost but may reveal useful information. Preventive maintenance has a larger immediate cost but reduces the probability of catastrophic failure. The decision is selected by expected utility rather than by a simple threshold on failure probability.

Approach and Solution

The facility adopts a tiered policy. When estimated failure risk is low, the pump continues operating with routine monitoring. At an intermediate risk level, inspection is recommended if its expected value exceeds its cost. At high risk, planned maintenance is scheduled, subject to safety constraints. The model is recalibrated periodically, and alerts include uncertainty intervals and the main evidence influencing the estimate.

Outcome

The principal benefit is not a claim that the model predicts every failure. Rather, it creates a transparent link between evidence, estimated condition, available actions, and operational consequences. Engineers can challenge implausible probabilities, identify sensor failures, and revise maintenance policies when costs or safety priorities change.

Learning Points

The case illustrates four principles. First, hidden-state inference is appropriate when the condition of interest cannot be observed directly. Second, temporal models are needed because current condition depends on prior condition. Third, prediction and decision are distinct: a risk estimate must be evaluated against action consequences. Fourth, a model should expose assumptions and uncertainty rather than produce an unexplained binary alarm.

Applications Across Professional Domains

In healthcare, Bayesian networks support diagnosis, prognosis, treatment selection, and patient risk stratification. Clinical use requires careful validation, calibration, protection of sensitive data, and human oversight. In finance, probabilistic models estimate credit risk, fraud likelihood, market exposure, and operational loss. A score should not be confused with an automatic denial or approval, especially where anti-discrimination requirements apply.

In cybersecurity, uncertain evidence from logs, endpoints, and network flows can be fused to prioritize incidents. In robotics, probabilistic localization combines motion models with sensor observations, while decision theory selects actions under collision and energy constraints. In natural language processing, probabilistic sequence models support speech recognition, tagging, translation, and uncertainty-aware extraction. In supply chains, uncertain demand, lead times, and disruptions can be modeled to determine inventory and sourcing policies.

Organizationally, uncertainty models should be integrated with governance. Model owners, data owners, domain experts, risk officers, and operational users need clearly defined responsibilities. Monitoring should include calibration, drift, false-positive and false-negative rates, decision outcomes, and subgroup performance where relevant.

Limitations, Failure Modes, and Ethical Issues

A mathematically elegant model can still fail because of poor data. Sampling bias, missing-not-at-random observations, concept drift, measurement error, and unobserved confounding can invalidate conclusions. Probability tables may encode historical discrimination or organizational habits. A model that is well calibrated overall may be poorly calibrated for a vulnerable subgroup.

Common technical mistakes include treating correlation as causation, assuming independence without justification, confusing fuzzy membership with probability, double-counting evidence, and using posterior probabilities without considering utilities. Another error is overconfidence caused by narrow confidence estimates, inadequate model checking, or unrecognized dependence among information sources.

Explainability is especially important when decisions affect health, liberty, employment, credit, or access to essential services. Users should know what evidence was used, how uncertainty was represented, what alternatives were considered, and who can review or override the decision. Human oversight should be meaningful rather than a ceremonial approval step.

Privacy is also relevant. Additional information may improve expected utility but create unacceptable surveillance or confidentiality risks. Data minimization, access controls, secure computation, retention limits, and auditable use policies should accompany uncertainty-aware analytics. In regulated settings, documentation should cover model purpose, training data, assumptions, validation, limitations, thresholds, and change management.

Current Developments and Best Practices

Modern AI systems increasingly combine deep learning with probabilistic modeling. Bayesian deep learning, ensembles, conformal prediction, probabilistic programming, and diffusion-based generative models seek to represent predictive uncertainty or produce calibrated sets of possible outputs. These methods do not eliminate uncertainty; they introduce new questions about whether uncertainty is epistemic—arising from limited knowledge—or aleatoric—arising from inherent variability.

A reliable implementation should follow several practices:

• Define the decision, not merely the prediction target.
• Separate data uncertainty, model uncertainty, and decision uncertainty where possible.
• State assumptions about independence, causality, and missing data.
• Validate calibration as well as accuracy.
• Compare expected benefits with information, operational, privacy, and fairness costs.
• Test models under distribution shift and adverse conditions.
• Use domain experts to assess plausibility, not to conceal weak evidence.
• Record model versions, parameter changes, overrides, and outcomes.
• Communicate uncertainty in forms that users can interpret and act upon.
• Establish escalation rules for high-impact or low-confidence cases.

The most appropriate framework is often hybrid. A Bayesian network may represent causal uncertainty, a fuzzy controller may translate linguistic operating rules into actions, and an influence diagram may evaluate the resulting choices. The essential requirement is conceptual discipline: each numerical quantity must have a clear meaning.

Chapter Summary

Uncertainty is unavoidable in intelligent systems because observations are incomplete, environments are variable, and models are imperfect. Probability and Bayes’ theorem provide a coherent basis for updating beliefs. Bayesian networks factorize joint distributions and support diagnostic, predictive, and explanatory inference. Markov chains, hidden Markov models, and dynamic Bayesian networks extend reasoning to time and hidden states.

Fuzzy logic represents gradual membership in vague concepts rather than randomness. Certainty factors encode heuristic support, while Dempster–Shafer theory represents belief, plausibility, and explicit ignorance. Decision theory connects beliefs with actions through utilities, expected utility, risk preferences, and the value of information. Influence diagrams combine chance, decision, and utility nodes to analyze sequential choices.

Professional systems must address data quality, calibration, bias, dependence, model drift, privacy, explainability, and governance. The central principle is that a probability estimate is not a decision: intelligent action requires an explicit account of consequences, preferences, constraints, and available information.

Key Terms

Probability: A numerical measure of belief or frequency assigned to an event, ranging from 0 to 1.

Conditional probability: The probability of an event given that another event or condition is known.

Bayes’ theorem: A rule for updating prior belief using the likelihood of observed evidence.

Prior probability: Belief assigned to a hypothesis before considering current evidence.

Posterior probability: Updated belief in a hypothesis after evidence has been considered.

Conditional independence: A relationship in which variables become independent after conditioning on another variable or set of variables.

Bayesian network: A directed acyclic graph with probability distributions that represents dependencies among random variables.

Markov property: The assumption that the next state depends on the present state, not the complete past, under a specified model.

Hidden Markov model: A temporal probabilistic model in which states are hidden and observations are generated from those states.

Fuzzy set: A set whose elements have degrees of membership between 0 and 1.

Membership function: A function that assigns the degree to which an input belongs to a fuzzy concept.

Certainty factor: A heuristic numerical measure of support for or against a proposition in a rule-based system.

Dempster–Shafer theory: An evidence framework that represents support over sets of hypotheses and distinguishes belief from plausibility.

Belief function: The total evidence committed wholly to a proposition and its subsets.

Plausibility: The maximum support a proposition could receive without contradicting the available evidence.

Utility: A numerical representation of the desirability of an outcome.

Expected utility: The probability-weighted average utility of an action across possible states.

Value of information: The improvement in decision quality attributable to obtaining additional information.

Influence diagram: A graphical decision model containing chance, decision, and utility nodes.

Calibration: The degree to which predicted probabilities correspond to observed frequencies.

Review Questions

Short Answer Questions

1. Distinguish prior probability from posterior probability.

2. What does conditional independence mean in a Bayesian network?

3. Why is fuzzy membership not the same as probability?

4. Identify the three node types in an influence diagram.

5. What is the purpose of the Viterbi algorithm in a hidden Markov model?

Long Answer Questions

1. Explain Bayes’ theorem and illustrate diagnostic reasoning with a suitable example.

2. Describe the structure, inference tasks, and limitations of Bayesian networks.

3. Explain hidden Markov models, including evaluation, decoding, and learning problems.

4. Compare probability, fuzzy logic, certainty factors, and Dempster–Shafer theory.

5. Discuss how expected utility and value of information improve decisions under uncertainty.

Analytical / Application Questions

1. A disease has a prevalence of 2 percent. A test detects the disease with sensitivity 95 percent and produces a false positive for 5 percent of healthy people. Explain how Bayes’ theorem should be used to evaluate a positive result and why prevalence matters.

2. A factory can continue operating a machine, inspect it, or perform preventive maintenance. Design an influence-diagram structure for this problem and identify the chance, decision, and utility variables.

3. A monitoring system receives high vibration readings from two sensors that share the same power supply. Explain why treating the readings as independent may produce overconfidence, and propose a more appropriate modeling approach.

22. Multiple Choice Questions with Answers

Question 1

A medical test is positive for a patient. Which quantity is most directly needed to determine the probability that the patient actually has the disease?

A. The prior disease probability, test sensitivity, and false-positive rate

B. The number of symptoms alone

C. The utility of treatment alone

D. The fuzzy membership of the symptom

Correct Answer: A. The prior disease probability, test sensitivity, and false-positive rate

Question 2

In a Bayesian network, conditional independence is primarily useful because it:

A. Makes every variable deterministic

B. Allows the joint distribution to be factorized into local relationships

C. Removes the need for probability tables

D. Ensures that all causal conclusions are correct

Correct Answer: B. Allows the joint distribution to be factorized into local relationships

Question 3

In a hidden Markov model, the Viterbi algorithm is used to:

A. Estimate the most likely hidden-state sequence

B. Calculate fuzzy membership values

C. Construct a utility function

D. Combine conflicting evidence masses

Correct Answer: A. Estimate the most likely hidden-state sequence

Question 4

A fuzzy membership value of 0.7 for “high temperature” means that:

A. There is a 70 percent probability that the temperature is high

B. The temperature belongs to the vague concept “high” to degree 0.7

C. The sensor is 70 percent accurate

D. The temperature will remain high for 70 percent of the time

Correct Answer: B. The temperature belongs to the vague concept “high” to degree 0.7

Question 5

Which feature most clearly distinguishes Dempster–Shafer theory from ordinary probability assignment to individual hypotheses?

A. It cannot represent uncertainty

B. It can assign support to sets of hypotheses and represent ignorance

C. It requires all hypotheses to be independent

D. It replaces evidence with utility

Correct Answer: B. It can assign support to sets of hypotheses and represent ignorance

Question 6

An action has a small probability of causing a very large loss. Which decision-theoretic concept ensures that this consequence is considered?

A. Expected utility

B. Fuzzification

C. Membership normalization

D. The Markov property

Correct Answer: A. Expected utility

Question 7

Which influence-diagram node represents a choice controlled by the decision-maker?

A. Chance node

B. Utility node

C. Decision node

D. Evidence node

Correct Answer: C. Decision node

Question 8

Two sensor readings are strongly dependent because both are affected by the same hardware fault. Treating them as independent will most likely:

A. Produce overconfident evidence updating

B. Guarantee perfect calibration

C. Convert probability into fuzzy logic

D. Eliminate the need for a transition model

Correct Answer: A. Produce overconfident evidence updating

Question 9

The expected value of information is positive when additional information:

A. Always increases the number of model variables

B. Can improve the decision enough to justify its cost

C. Makes every outcome certain

D. Removes all ethical constraints

Correct Answer: B. Can improve the decision enough to justify its cost

Question 10

Which statement best expresses the difference between prediction and decision?

A. Prediction estimates possible states; decision analysis selects actions using consequences and preferences

B. Prediction always uses fuzzy logic; decision always uses probability

C. Prediction requires utilities; decision never requires probabilities

D. They are identical whenever a model is calibrated

Correct Answer: A. Prediction estimates possible states; decision analysis selects actions using consequences and preferences