پاورپوینت کامل Fuzzy Logic 18 اسلاید در PowerPoint

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پاورپوینت کامل Fuzzy Logic 18 اسلاید در PowerPoint

اسلاید ۴: ۴Mamdani Fuzzy InferenceWe examine a simple two-input one-output problem that includes three rules:Rule: 1IF x is A3 ORy is B1 THENz is C1 Rule: 2IF x is A2 AND y is B2 THENz is C2 Rule: 3IF x is A1 THENz is C3 Real-life example for these kinds of rules:Rule: 1IF project_funding is adequate OR project_staffing is small THEN risk is low Rule: 2IF project_funding is marginal AND project_staffing is large THEN risk is normal Rule: 3IF project_funding is inadequate THEN risk is high

اسلاید ۵: ۵Step 1: FuzzificationThe first step is to take the crisp inputs, x1 and y1 (project funding and project staffing), and determine the degree to which these inputs belong to each of the appropriate fuzzy sets.

اسلاید ۶: ۶Step 2: Rule EvaluationThe second step is to take the fuzzified inputs, (x=A1) = 0.5, (x=A2) = 0.2, (y=B1) = 0.1 and (y=B2) = 0.7,and apply them to the antecedents of the fuzzy rules.If a given fuzzy rule has multiple antecedents, the fuzzy operator (AND or OR) is used to obtain a single number that represents the result of the antecedent evaluation.RECALL: To evaluate the disjunction of the rule antecedents, we use the OR fuzzy operation. Typically, fuzzy expert systems make use of the classical fuzzy operation union:AB(x) = max [A(x), B(x)]Similarly, in order to evaluate the conjunction of the rule antecedents, we apply the AND fuzzy operation intersection:AB(x) = min [A(x), B(x)]

اسلاید ۷: ۷Step 2: Rule Evaluation

اسلاید ۸: ۸Step 2: Rule EvaluationNow the result of the antecedent evaluation can be applied to the membership function of the consequent.The most common method is to cut the consequent membership function at the level of the antecedent truth. This method is called clipping (alpha-cut).Since the top of the membership function is sliced, the clipped fuzzy set loses some information.However, clipping is still often preferred because it involves less complex and faster mathematics, and generates an aggregated output surface that is easier to defuzzify.While clipping is a frequently used method, scaling offers a better approach for preserving the original shape of the fuzzy set.The original membership function of the rule consequent is adjusted by multiplying all its membership degrees by the truth value of the rule antecedent.This method, which generally loses less information, can be very useful in fuzzy expert systems.clippingDegree ofMembership1.00.00.2ZC2scalingDegree ofMembershipZ1.00.00.2C2

اسلاید ۹: ۹Step 3: Aggregation of the Rule OutputsAggregation is the process of unification of the outputs of all rules.We take the membership functions of all rule consequents previously clipped or scaled and combine them into a single fuzzy set. The input of the aggregation process is the list of clipped or scaled consequent membership functions, and the output is one fuzzy set for each output variable.

اسلاید ۱۰: ۱۰Step 4: DefuzzificationThe last step in the fuzzy inference process is defuzzification.Fuzziness helps us to evaluate the rules, but the fina