Approximate Reasoning with Fuzzy Rules
Approximate reasoning is a powerful feature of fuzzy logic that allows you to draw conclusions even when input information is incomplete, vague, or not strictly true or false. In everyday life, you often make decisions based on imprecise data — such as judging if someone is tall or if the temperature is warm. Fuzzy rules capture this human-like reasoning by expressing knowledge in the form of if–then statements that use linguistic variables and fuzzy sets. For instance, a fuzzy rule might state: If temperature is high and humidity is low, then fan speed should be fast. Here, high, low, and fast are not precise numbers but fuzzy concepts with gradual boundaries.
When you evaluate fuzzy rules, you use the degrees of membership of your inputs to determine how strongly each rule fires. This process involves combining the fuzzy inputs using operators such as the minimum (for AND) or maximum (for OR), and then assigning an output degree that reflects the strength of the rule's conclusion. This way, fuzzy logic enables approximate reasoning by connecting vague inputs to equally flexible outputs, making it ideal for real-world control systems and decision-making where crisp logic would fail.
12345678910111213import numpy as np # Fuzzy membership degrees for input variables # Suppose: temperature is "high" with degree 0.7, humidity is "low" with degree 0.4 temperature_high = 0.7 humidity_low = 0.4 # Fuzzy rule: IF temperature is high AND humidity is low THEN fan speed is fast # Use minimum for fuzzy AND (t-norm) rule_strength = np.minimum(temperature_high, humidity_low) print("Rule strength (degree to which rule fires):", rule_strength) # This output degree (0.4) can be used to shape the fuzzy set for "fan speed is fast"
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Approximate reasoning is a powerful feature of fuzzy logic that allows you to draw conclusions even when input information is incomplete, vague, or not strictly true or false. In everyday life, you often make decisions based on imprecise data — such as judging if someone is tall or if the temperature is warm. Fuzzy rules capture this human-like reasoning by expressing knowledge in the form of if–then statements that use linguistic variables and fuzzy sets. For instance, a fuzzy rule might state: If temperature is high and humidity is low, then fan speed should be fast. Here, high, low, and fast are not precise numbers but fuzzy concepts with gradual boundaries.
When you evaluate fuzzy rules, you use the degrees of membership of your inputs to determine how strongly each rule fires. This process involves combining the fuzzy inputs using operators such as the minimum (for AND) or maximum (for OR), and then assigning an output degree that reflects the strength of the rule's conclusion. This way, fuzzy logic enables approximate reasoning by connecting vague inputs to equally flexible outputs, making it ideal for real-world control systems and decision-making where crisp logic would fail.
12345678910111213import numpy as np # Fuzzy membership degrees for input variables # Suppose: temperature is "high" with degree 0.7, humidity is "low" with degree 0.4 temperature_high = 0.7 humidity_low = 0.4 # Fuzzy rule: IF temperature is high AND humidity is low THEN fan speed is fast # Use minimum for fuzzy AND (t-norm) rule_strength = np.minimum(temperature_high, humidity_low) print("Rule strength (degree to which rule fires):", rule_strength) # This output degree (0.4) can be used to shape the fuzzy set for "fan speed is fast"
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