## Lectures on Soft Computing and Fuzzy LogicAntonio Di Nola, Giangiacomo Gerla The present volume collects selected papers arising from lectures delivered by the authors at the School on Fuzzy Logic and Soft Computing held during the years 1996/97/98/99 and sponsored by the Salerno University. The authors contributing to this volume agreed with editors to write down, to enlarge and, in many cases, to rethink their original lectures, in order to offer to readership, a more compact presentation of the proposed topics. The aim of the volume is to offer a picture, as a job in progress, of the effort that is coming in founding and developing soft computing's techniques. The volume contains papers aimed to report on recent results containing genuinely logical aspects of fuzzy logic. The topics treated in this area cover algebraic aspects of Lukasiewicz Logic, Fuzzy Logic as the logic of continuous t-norms, Intuitionistic Fuzzy Logic. Aspects of fuzzy logic based on similar ity relation are presented in connection with the problem of flexible querying in deductive database. Departing from fuzzy logic, some papers present re sults in Probability Logic treating computational aspects, results based on indishernability relation and a non commutative version of generalized effect algebras. Several strict applications of soft computing are presented in the book. Indeed we find applications ranging among pattern recognition, image and signal processing, evolutionary agents, fuzzy cellular networks, classi fication in fuzzy environments. The volume is then intended to serve as a reference work for foundational logico-algebraic aspect of Soft Computing and for concrete applications of soft computing technologies. |

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### Contents

I | 1 |

III | 4 |

IV | 7 |

V | 18 |

VI | 19 |

VIII | 20 |

IX | 27 |

X | 31 |

LXIX | 163 |

LXX | 171 |

LXXI | 173 |

LXXIII | 174 |

LXXIV | 175 |

LXXV | 178 |

LXXVI | 181 |

LXXVII | 186 |

XI | 33 |

XIII | 34 |

XIV | 35 |

XV | 41 |

XVII | 43 |

XX | 44 |

XXI | 46 |

XXII | 48 |

XXIII | 55 |

XXV | 57 |

XXVII | 63 |

XXVIII | 64 |

XXIX | 66 |

XXXI | 68 |

XXXII | 69 |

XXXIII | 71 |

XXXV | 73 |

XXXVI | 76 |

XXXVII | 78 |

XXXVIII | 82 |

XXXIX | 87 |

XL | 89 |

XLII | 90 |

XLIII | 94 |

XLIV | 97 |

XLV | 105 |

XLVI | 108 |

XLVII | 111 |

XLVIII | 113 |

XLIX | 114 |

L | 116 |

LI | 119 |

LII | 121 |

LIII | 124 |

LIV | 127 |

LV | 129 |

LVII | 130 |

LVIII | 136 |

LIX | 138 |

LX | 140 |

LXI | 147 |

LXII | 152 |

LXIII | 156 |

LXV | 159 |

LXVII | 160 |

LXVIII | 161 |

LXXVIII | 187 |

LXXIX | 189 |

LXXX | 191 |

LXXXI | 192 |

LXXXII | 202 |

LXXXIII | 212 |

LXXXIV | 225 |

LXXXV | 236 |

LXXXVI | 237 |

LXXXVII | 239 |

LXXXIX | 240 |

XC | 243 |

XCI | 244 |

XCII | 245 |

XCIII | 250 |

XCIV | 251 |

XCV | 252 |

XCVI | 255 |

XCVIII | 257 |

C | 258 |

CI | 261 |

CII | 264 |

CIII | 267 |

CIV | 270 |

CV | 273 |

CVI | 274 |

CVII | 275 |

CVIII | 277 |

CX | 278 |

CXI | 280 |

CXII | 282 |

CXIII | 285 |

CXIV | 292 |

CXV | 296 |

CXVI | 297 |

CXVII | 301 |

CXIX | 304 |

CXX | 306 |

CXXI | 310 |

CXXII | 313 |

CXXIV | 314 |

CXXV | 316 |

CXXVI | 324 |

CXXVII | 336 |

### Other editions - View all

Lectures on Soft Computing and Fuzzy Logic Antonio Di Nola,Giangiacomo Gerla No preview available - 2012 |

### Common terms and phrases

abstract Actor Agents algorithm application approximation attribute axioms BL algebra Boolean algebra Boolean space calculus cell characterized classical complete components condition consider corresponding data mining Deductive Database defined Definition defuzzification denote derivation distributive lattice dual duality elements equivalence example exists finite formula fuzzy logic fuzzy relation fuzzy rules fuzzy sets fuzzy similarity fuzzy theory given GPE-algebra Heyting algebra homomorphism hyperderivation hypersequent information granules input integer intuitionistic intuitionistic logic isomorphic language Lemma linear linearly ordered linguistic Logic Programming Lukasiewicz membership functions minimal ideal Moreover morphism MV-algebra Neural Networks neurons NN's normal form objects obtained operation ordinal sum output po-group poset predicate prime ideals problem Proof properties Proposition pseudo-effect algebra residuated lattice respect satisfies semantics sequent calculus Soft Computing space SpecA string structure subalgebra subset Suppose symbols t-norm Theorem topological truth values valuation variables Wajsberg