Foundations of Soft Case-Based Reasoning

By Sankar K. Pal

  • Provides a self-contained description of this significant point of data processing and choice help technology.
  • Presents simple definitions, ideas, purposes, and a close bibliography.
  • Covers a number of real-world examples together with keep an eye on, info mining, and development recognition.

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Four. 1. four Predicting Adjustment via Reasoning and version consider that for a selected case ek ¼ ðxk1 ; xk2 ; . . . ; xkn ; yk Þ; là fuzzy edition ideas were extracted, denoted by way of fri ; i ¼ 1; 2; . . . ; là g. permit the ith fuzzy model rule ri ð1 i lÃ Þ be represented within the following shape: IF ½Atrrð1Þ ¼ Ai1 Š AND ½Atrrð2Þ ¼ Ai2 Š AND Á Á Á AND ½AtrrðnÞ ¼ Ain Š THEN ½Attrðnþ1Þ ¼ Ci Š ð5:9Þ within which Attrð jÞ ð j ¼ 1; 2; . . . ; n þ 1Þ, Aij ð j ¼ 1; 2; . . . ; nÞ, and Ci are as in equation (5. 6). word that a few of the antecedents should be absent as a result of removing approach acknowledged earlier than. enable eq ¼ fxq1 ; xq2 ; . . . ; xqn ; yq Þ be an enter question case, the place the characteristic values xj ð1 j nÞ are recognized, while the motion (solution) yq is unknown and desires to be determined. Assuming that the case ek ¼ ðxk1 ; xk2 ; . . . ; xkn ; yk Þ has been chosen to supply the answer (i. e. , to foretell the worth of unknown yq ) of the question case eq , we compute the discrepancy vector f among situations e and ek , as in equation (5. 1): fqk ¼ eq À ek ¼ ðxq1 À xk1 ; xq2 À xk2 ; . . . ; xqn À xkn ; yq À yk Þ ¼ fyqk;1 ; yqk;2 ; . . . ; yqk;n ; uqk g ð5:10Þ CASE-BASE upkeep utilizing A ROUGH-FUZZY procedure one hundred seventy five the following the feature-difference values yqk; j ð1 j nÞ are identified, whereas the solutiondifference worth uqk is unknown. the worth of uqk will depend on the next approach: Step 1. for every fuzzy variation rule ri ð1 i lÃ Þ linked to ek , compute the club values (i. e. , mij values) of yqk; j 2 Aij ð1 j nÞ of the bushy units such as antecedents ½Attrð jÞ ¼ Aij Š of ri , with Aij 6¼ ; (; is an empty set, 1 j n). Step 2. Compute the general measure of similarity, SMðiÞ , of the feature-difference vector fyqk;j g with admire to the antecedents of the ith rule ri as SMðiÞ ¼ min j ðmij Þ; i ¼ 1; 2; . . . ; là ; j ¼ 1; 2; . . . ; n ð5:11Þ Step three. Compute the final measure of similarity, SMl , of the feature-difference vector fyqk; j g with admire to the antecedents of the entire ideas having an identical consequent fuzzy set Cl ðl ¼ 1; 2; . . . ; fiveþ as SMl ¼ maxi fSMðiÞ jconsequent fuzzy set ¼ Cl g ð5:12Þ the place Cl ðl ¼ 1; 2; . . . ; fiveþ represents the five fuzzy units NB, NS, ZE, playstation , and PB (Fig. five. 3). Step four. Compute the solution-difference uqk [equation (5. 10)] utilizing the defuzzification formulation uqk ¼ 2anþ1 SM1 þ anþ1 SM2 þ bnþ1 SM4 þ 2bnþ1 SM5 SM1 þ SM2 þ Á Á Á þ SM5 ð5:13Þ the place the parameters anþ1 and bnþ1 , reminiscent of the answer characteristic, are defined by way of equation (5. 3). Step five. Compute the predicted resolution ^ yq of case eq as ^ yq ¼ yk þ uqk ð5:14Þ five. four. 1. five opting for consultant instances right here we describe a strategy for choosing consultant circumstances from every one cluster for the aim of keeping the dimensions of a case base utilizing the difference ideas bought within the previous section. the choice procedure relies at the thoughts of e-coverage and e-reliability [39,51]. enable LE be a cluster of m instances the place each one case e is followed by way of a suite of model ideas RðeÞ, enable e be a small optimistic quantity, and enable ep ¼ ðxp1 ; xp2 ; .

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