Download Intuitionistic Fuzzy Logics by Krassimir T. Atanassov (auth.) PDF

By Krassimir T. Atanassov (auth.)

The publication bargains a accomplished survey of intuitionistic fuzzy logics. by means of reporting on either the author’s learn and others’ findings, it presents readers with an entire evaluate of the sector and highlights key concerns and open difficulties, therefore suggesting new examine instructions. beginning with an creation to the elemental components of intuitionistic fuzzy propositional calculus, it then presents a advisor to using intuitionistic fuzzy operators and quantifiers, and finally provides cutting-edge functions of intuitionistic fuzzy units. The booklet is a invaluable reference source for graduate scholars and researchers alike.

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9 , →11 , . . , →29 , →46 , . . , →53 , →55 , . . , →57 , →61 , →66 , →71 , →74 , . . , →77 , →79 , →81 , →91 , →94 , →97 , →99 , . . , →102 , →104 , . . , →107 , →109 , . . , →113 , →118 , →119 , →121 , →124 , . . , →128 , →133 , . . , →137 , →151 , →153 , →158 , . . , →161 , →166 , →167 , →169 , . . , →172 , →174 , . . , →177 , →179 , →180 , →182 , →184 , →185 satisfy expression (¬A → ¬B) → ((¬A → B) → ¬¬A) as IFTs. 5 Properties of Intuitionistic Fuzzy Implications and Negations 39 →48 , →52 , →55 , .

2. 1. 2. sg(c− a), f ) ≥ min(max( f, e), 1 − e)) − f ≥ 0; 2. 1. 2. 1. 1. 2. 1. 2. 2. 1. 1. 2. 2. 1. 2. , in this case Axiom VW7 is an IFT. So, we checked the validity of original or modified Conditional Logic Axioms for pair (→4 , →11 ). Open Problem 4. Which pairs of implications (→i , → j ) for 1 ≤ i, j ≤ 185 satisfy these axioms in original or modified forms? , for the case, when the implications ⊃ and → in the seven axioms coincide. If we change the condition for the Axioms to be true with condition for these axioms to be IFTs, then, these pairs with equal components are generated by implications →20 , →23 , →27 , →29 , →74 , →77 , →81 , →101 , →102 , →111 , …, →113 , →118 , →126 , →128 , →167 , →169 .

137 , →151 , →153 , →158 , . . , →161 , →166 , . . , →180 , →182 , . . , →185 satisfy expression (¬A → ¬B) → ((¬A → ¬¬B) → ¬¬A). as IFTs. (b) Implications →2 , →3 , →8 , →11 , →14 , . . , →16 , →19 , →20 , →23 , →31 , →32 , →37 , →40 , . . , →43 , →45 , →47 , →48 , →52 , →55 , . . , →57 , →74 , →77 , →83 , →88 , →97 , →99 , →153 , →171 , . . , →180 satisfy the same expression as tautologies. In [69, 70], the Hauber’s Law is formulated by ((A → B) ∧ (C → D) ∧ (A ∨ C) ∧ ¬(B ∧ D)) → ((B → A) ∧ (D → C)) and it is proved that it is a standard tautology.

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