An Innovative Fuzzy-Logic-Based Strategy for an Effective Exploitation of Noisy Inverse Scattering Data
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(65) v=1,.. V m=1,.. M n=1,.. N. ·A¹vº ¾Ë¼Ìo; ÎÐÏaÑ óÇò¸ÒaÓÉÔ_Õ"Öv×?MWJâuwJ J L«d^P^q[eldXI hVz K#K#÷(LX\XeliØPSZ[I#_fq]R[P^q]I#\S ~lÌ. « υn. v. νm v. µ( υ n ) v. µ( ν vm ) INFERENCE. RULES DATABASE. FUZZY. µ(ψ). µ( γ ). FUZZY SYSTEM ARCHITECTURE. DEFUZZIFIER. FUZZIFIER. n. ψv. γ mv. v=1,.. V m=1,.. M n=1,.. N.
(66) µ(). µ() Ant4. Cons4 1.0. activation value. 0.5. 0.5. 0.0 0.0. 1.0. 0.5. úTÿ. ν or υ. 0.0 0.0. Ú}ÙÚ}Ù Ú}ÙÚ}Ù Ú}ÙÚ}Ù Ú}ÙÚ}Ù ÚÙÚÙ ÚÙ}ÚÙ}Ú}ÙÚ}Ù Ú}ÙÚ}Ù Ú}ÙÚ}Ù ÚÙÚÙ ÚÙ}Ú}Ù Ú}ÙÚ}Ù Ú}ÙÚ}Ù Ú}ÙÚ}Ù ÚÙÚÙ Ú}ÙÚÙ}Ú}ÙÚ}Ù Ú}ÙÚ}Ù Ú}ÙÚ}Ù ÚÙÚÙ ÚÙ}Ú}Ù Ú}Ù Ú}Ù ÚÙ 0.5. 1.0. µ() Cons2. Cons3. Cons5. ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÛÝÛ ÛÝÛÜÝÜ ÛÝÜ Û Û Û Û Û Û Û Û Û Û Û ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÛÝÛ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÝÛÜ Û Û Û Û Û Û Û Û Û Û Û Û ÝÛÜ ÝÛÝÛ Û Û Û Û Û Û Û Û Û Û Û Û ÝÛÜ Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý ÛÝÛÜÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÛÝÛ Cons4 Û Û Û Û Û Û Û Û Û Û Û Û ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÝÛÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÛÝÛ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÝÛÜ Û Û Û Û Û Û Û Û Û Û Û Û ÝÛÜ ÝÛÝÛ ÛÝÛÜÝÜ ÛÝÜ Û Û Û Û Û Û Û Û Û Û Û ÝÜ Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÛÝÛ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÝÛÜ Û Û Û Û Û Û Û Û Û Û Û Û ÝÛÜ ÝÛÝÛ Û Û Û Û Û Û Û Û Û Û Û Û ÝÛÜ Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý ÛÝÛÜÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÛÝÛ Û Û Û Û Û Û Û Û Û Û Û Û ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÝÛÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÜ ÝÛÝÛ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÛÝÜ ÝÛÜ Û Û Û Û Û Û Û Û Û Û Û Û ÝÛÜ ÝÛÝÛ ÛÝÛÜÝÜ ÛÝÜ Û Û Û Û Û Û Û Û Û Û Û ÝÜ Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Ü Ý Û ÝÜ Û ÝÜ Û ÝÜ Û ÝÜ Û ÝÜ Û ÝÜ Û ÝÜ Û ÝÜ Û ÝÜ Û ÝÜ Û ÝÜ Û ÝÛ. 1.0 Membership functions. Membership functions. 1.0. 0.5. 0.0 0.0. output value. 0.5. úÇÿ. 1.0. ν or υ. ·A¹vº ¾|¿RÌo; ÎÐÏaÑ óÇò¸ÒaÓÉÔ_Õ"Öv×?MWJâuwJ J L«d^P^q[eldXI hVz K#K#÷(LX\XeliØPSZ[I#_fq]R[P^q]I#\S ~lÌ. Q. γ or ψ.
(67) y. y. x. @BC!ù. Ò«¯ H *'57698:-9±. x. ¥ C¥. úTÿ. @«C(ù. Ò«¯ H *I57698:-± ú0ÿ. y. x. @BC!ù. Ò«¯ H *I57698J-9±. ú]¯«ÿ. ¥ C¥. ·A¹vº ¾|ÀRÌo; ÎÐÏaÑ óÇò¸ÒaÓÉÔ_Õ"Öv×?MWJâuwJ J L«d^P^q[eldXI hVz K#K#÷(LX\XeliØPSZ[I#_fq]R[P^q]I#\S ~lÌ. Ç. ¥ C¥.
(68) 12. Standard Approach (Fuzzy-Logic)-based Approach. ζtot. 9. 6. 3. 0 5. 10. 15. 20. 25. 30. úTÿ. SNR [dB]. 35. Standard Approach (Fuzzy-Logic)-based Approach. 28. ζint. 21. 14. 7. 0 5. 10. 15. 20. 25. 30. úÇÿ. SNR [dB]. ·A¹vº ¾§ÁbÞ ßcàoÌo; ÎÐÏaÑ óÇò¸ÒáÓÔ_Õ"Öv×?MWJâuwJ J`LÇd^P^q[eldSI!hVz K#K#÷(LX\SegiØPSZTI?_fq]R[P^q]I#\S ~lÌ. «.
(69) 10. Standard Approach (Fuzzy-Logic)-based Approach. 8. ζext. 6. 4. 2. 0 5. 10. 15. 20. 25. 30. úk¯Qÿ. SNR [dB]. ·A¹º ¾oÁbÞ ß/ßcà§Ì|;ÎÐÏaÑ óÇòâÒaÓÔzÕ"Öv×t?MWJuwJ J L«d^P^q]e~dXI hVz K?Ksw÷(LX\Xegi²DP^Z[I?_fq[R]P^q[I?\Sël~ . Ç.
(70) y. y. x. Ò«¯ H *I57698:-±. @BC!ù. úTÿ. ¥ C¥. x. Ò«¯ H '* 5768J-9± úÇÿ. @BC(ù. y. ¥ C¥. y. x. @BC!ù. Ò«¯ H *I57698:-±. úk¯Qÿ. ¥ C¥. x. @BC(ù. Ò«¯ H *'5768J-9±. úTVÿ. ·A¹vº ¾|ÃRÌo; ÎÐÏaÑ óÇò¸ÒaÓÉÔ_Õ"Öv×?MWJâuwJ J L«d^P^q[eldXI hVz K#K#÷(LX\XeliØPSZ[I#_fq]R[P^q]I#\S ~lÌ. «. ¥ C¥.
(71) 1. ΦRef Fuzzy. ΦRef Fuzzy. Arbitrary Unit. Φ. Φ Data Term Data Term. 0.1. 0.01 0. 200. 400. 600 800 Iteration Number, k. úTÿ. 1. 1000. 1200. 1400. ΦRef Fuzzy. Arbitrary Unit. Φ Ref Φ Data Term ΦFuzzy Data Term. 0.1. 0.01 0. 500. 1000 Iteration Number, k. úÇÿ. 1500. 2000. ·A¹vº ¾|ÄRÌo; ÎÐÏaÑ óÇò¸ÒaÓÉÔ_Õ"Öv×?MWJâuwJ J L«d^P^q[eldXI hVz K#K#÷(LX\XeliØPSZ[I#_fq]R[P^q]I#\S ~lÌ. «.
(72) 2000. ΦRef Fuzzy. Φ. Iteration Number, k. 1500. 1000. 500. 0 5. 10. 15. 20. 25. 30. SNR. ·A¹vº ¾ÆÂÌo; ÎÐÏaÑ óÇò¸ÒaÓÉÔ_Õ"Öv×?MWJâuwJ J L«d^P^q[eldXI hVz K#K#÷(LX\XeliØPSZ[I#_fq]R[P^q]I#\S ~lÌ. S.
(73) 12. Standard Approach (Fuzzy-Logic)-based Approach. ζtot. 9. 6. 3. 0 5. 10. 15. 20. 25. 30. úTÿ. SNR [dB]. 35. Standard Approach (Fuzzy-Logic)-based Approach. 30 25. ζint. 20 15 10 5 0 5. 10. 15. 20. 25. 30. úÇÿ. SNR [dB]. ·A¹vº ¾|ÇcÞ ßcàoÌo; ÎÐÏaÑ óÇò¸ÒáÓÔ_Õ"Öv×?MWJâuwJ J`LÇd^P^q[eldSI!hVz K#K#÷(LX\SegiØPSZTI?_fq]R[P^q]I#\S ~lÌ. .
(74) 10. Standard Approach (Fuzzy-Logic)-based Approach. 8. ζext. 6. 4. 2. 0 5. 10. 15. 20. 25. 30. úk¯Qÿ. SNR [dB]. ·A¹º ¾ÉÇcÞ ß/ßcà§Ì|;ÎÐÏaÑ óÇòâÒaÓÔzÕ"Öv×t?MWJuwJ J L«d^P^q]e~dXI hVz K?Ksw÷(LX\Xegi²DP^Z[I?_fq[R]P^q[I?\Sël~ . X.
(75) 14. Standard Approach (Fuzzy-Logic)-based Approach. 12 10. ζtot. 8 6 4 2 0 5. 10. 15. 20. 25. 30. úTÿ. SNR [dB]. 35. Standard Approach (Fuzzy-Logic)-based Approach. 28. ζint. 21. 14. 7. 0 5. 10. 15. 20. 25. 30. úÇÿ. SNR [dB]. ·A¹vº ¾|ÈcÞ ßcàoÌo; ÎÐÏaÑ óÇò¸ÒáÓÔ_Õ"Öv×?MWJâuwJ J`LÇd^P^q[eldSI!hVz K#K#÷(LX\SegiØPSZTI?_fq]R[P^q]I#\S ~lÌ. S.
(76) 12. Standard Approach (Fuzzy-Logic)-based Approach. ζext. 9. 6. 3. 0 5. 10. 15. 20. 25. 30. úk¯Qÿ. SNR [dB]. ·A¹º ¾ÉÈcÞ ß/ßcà§Ì|;ÎÐÏaÑ óÇòâÒaÓÔzÕ"Öv×t?MWJuwJ J L«d^P^q]e~dXI hVz K?Ksw÷(LX\Xegi²DP^Z[I?_fq[R]P^q[I?\Sël~ . ^.
(77) y. y. x. Ò«¯ H *I57698:-±. @BC!ù. úTÿ. ¥ C¥. x. Ò«¯ H '* 5768J-9± úÇÿ. @BC(ù. y. ¥ C¥. y. x. @BC!ù. Ò«¯ H *I57698:-±. úk¯Qÿ. ¥ C¥. x. @BC(ù. Ò«¯ H *'5768J-9±. úTVÿ. ·A¹º ¾Ë¼1ÊãÌoÍ
(78) ¾ÎÐÏaÑ óÇò¸ÒáÓÔ_Õ"Öv×?MOJuwJ`J L«dSP0q]eldSI hbz`K?K#w÷LS\Xegi²DPSZTI?_fq[R]P^q[I?\S ~~ . X. ¥ C¥.
(79) 1. ΦRef Fuzzy. ΦRef Fuzzy. Φ. Φ Data Term Data Term. Arbitrary Unit. 0.1. 0.01. 0.001 0. 500. 1000 Iteration Number, k. úTÿ. 1. 1500. 2000. ΦRef Fuzzy. ΦRef Fuzzy. Φ. Φ Data Term Data Term. Arbitrary Unit. 0.1. 0.01. 0.001 0. 500. 1000 Iteration Number, k. 1500. 2000. úÇÿ. ·A¹º ¾Ë¼z¼ÌoÍ
(80) ¾ÎÐÏaÑ óÇò¸ÒáÓÔ_Õ"Öv×?MOJuwJ`J L«dSP0q]eldSI hbz`K?K#w÷LS\Xegi²DPSZTI?_fq[R]P^q[I?\S ~~ . S.
(81)
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In fact, its original title was La confusione which became later The Smile on the Face of the Lion in the English translation and then Il sorriso del leone
