Is this limited to fuzzy logic?

No. Intermediate truth values also occur in other many-valued logics; this entry focuses on the fuzzy interpretation.

Can two people assign different degrees?

Yes, if they use different definitions or contexts. Those differences should be made explicit.

Can uncertainty and graded truth coexist?

Yes. A measurement can be uncertain while the concept applied to it is graded; the two issues still need distinct treatment.

AI Glossary / Graphs and symbolic AI / Advanced

Degree of truth

Definition

A degree of truth expresses how fully a proposition is true within a logic that permits intermediate truth values. In the fuzzy-logic setting used here, values commonly range from 0 to 1. For a statement such as “this delivery is fast,” the value describes satisfaction of a defined, graded concept rather than the probability that a sharply defined event occurred.

What it means

Everyday descriptions often have gradual boundaries. A delivery taking 29 minutes is not necessarily meaningfully different from one taking 30 minutes, although a strict threshold can classify them differently. Graded truth offers a way to represent that gradual change explicitly.
The number needs an interpretation. Saying that “fast” has truth degree 0.7 is incomplete unless the relevant delivery context and definition are known. It does not mean that the package has a 70% chance of arriving, nor that the delivery record is 70% accurate. A measured duration can be known exactly while its membership in a vague category remains partial.

How it works

Define a domain, such as delivery durations, and a membership function for a concept. The function maps each input to a value between 0 and 1. For the corresponding fuzzy proposition, that membership value supplies its degree of truth.
Compound statements require specified operators. One common choice uses the minimum for AND, maximum for OR, and one minus the value for NOT. Other fuzzy logics use different operators, so the calculation must follow the chosen system.
A rule engine can use these values when combining rules and producing an output. The truth degree of a condition is not automatically the final action, recommendation, or physical control setting.

Three practical examples

Delivery planning: A service describes journeys as “short” using a gradual function of travel time. Two nearby durations then receive nearby values instead of falling abruptly on opposite sides of a cutoff. A contractual deadline can still require a separate crisp test.
Equipment operation: A controller represents vibration as “high” to varying degrees and combines that assessment with temperature conditions. Its operating rules need validation against equipment behavior; a graded label alone does not establish safety.
Document search: A retrieval system can represent how strongly an item satisfies a graded requirement such as “recent.” The chosen date function makes that criterion inspectable. Other relevance criteria and any mandatory date restrictions remain separate design decisions.

Think of it this way

Imagine shading a map to show how strongly places fit the description “near the station.” The shading represents a defined notion of nearness. It does not express uncertainty about where the station is. Changing the walking context can justify changing the shading rule, even when every distance measurement stays the same.

Worked example

Consider an invented delivery service. Define “fast” as fully satisfied for durations up to 20 minutes, declining linearly to zero at 40 minutes, and zero thereafter. Between those endpoints, the degree is (40 minus duration) divided by 20.
A 26-minute delivery therefore has degree (40 − 26)/20 = 0.7. Separately, suppose a defined package-condition assessment gives “undamaged” degree 0.9. For this demonstration, choose minimum for AND and maximum for OR.
“Fast AND undamaged” has degree min(0.7, 0.9) = 0.7. “Fast OR undamaged” has degree max(0.7, 0.9) = 0.9. Using the specified complement, “NOT fast” has degree 1 − 0.7 = 0.3.
If the designer instead selects product conjunction, the AND result becomes 0.7 × 0.9 = 0.63. That difference follows from the operator choice. It does not imply that the delivery and package condition were independent random events. Neither result says how often customers will complain. These hypothetical definitions would need justification before operational use.

Illustrative case study

Fictional Cedar Dispatch adds a “fast delivery” indicator to its internal dashboard. Staff initially read 0.7 as a 70% probability that a delivery met its promised deadline. That interpretation causes inconsistent reporting because the indicator actually measures gradual satisfaction of a duration-based definition.
The team separates two questions. A crisp field records whether the contractual deadline was met. A second field displays the graded fast-delivery assessment with its definition. Reviewers test examples near the endpoints and examine whether the function suits different service types.
This separation makes the dashboard easier to interpret, but it does not prove that the membership function captures customer satisfaction. Cedar would need relevant evidence for that additional claim. The case illustrates a design distinction, not measured results from a real organization.

Common misconceptions and mistakes

“0.7 true means 70% likely.” Graded satisfaction and probability have different meanings.
“Any confidence score is a truth degree.” A score needs an explicit interpretation and supporting method.
“Fuzzy logic has no precise rules.” Once functions and operators are specified, calculations can be precise.
“AND always means minimum.” That is one operator choice, not the only one.
“Category memberships must sum to one.” Separate fuzzy categories need not form a probability distribution.

Business use

Use graded concepts when gradual distinctions support the actual decision. Record the units, context, membership functions, operators, and treatment of missing measurements. Review examples around boundaries and check how changes affect downstream actions.
Keep contractual, eligibility, or other mandatory conditions explicit. Do not replace a required yes-or-no decision with an unexplained fractional label. When showing degrees to users, explain what the scale represents and avoid probability wording unless the quantity really is probabilistic.

Check your understanding

What is the fast-delivery degree at 30 minutes?

Answer: It is 0.5 under the invented function.

Does degree 0.7 mean a 70% on-time rate?

Answer: No.

Why do minimum and product give different conjunctions?

Answer: They implement different specified operators.

Related terms

Fuzzy logic
Membership function (mathematics)
Degree of belief
Probability
fuzzy set
membership function
many-valued logic
Boolean logic
fuzzy inference

Learn next

Define a graded concept with units and endpoints. Calculate three memberships, then compare minimum and product conjunctions. Explain the interpretation before using the results in a decision.

Sources

Zadeh, Fuzzy Sets, original research paper: https://home.iitk.ac.in/~avrs/ManyValuedLogic/Zadeh-1965.pdf MathWorks, Foundations of Fuzzy Logic: https://www.mathworks.com/help/fuzzy/foundations-of-fuzzy-logic.html

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