## What Is “The” Fuzzy Logic

Citations: | 1 - 0 self |

### BibTeX

@MISC{Novák_whatis,

author = {Vilém Novák},

title = {What Is “The” Fuzzy Logic },

year = {}

}

### OpenURL

### Abstract

### Citations

791 | The concept of a linguistic variable and its applications to approximate reasoning - Zadeh |

382 | Metamathematics of Fuzzy Logic - Hájek - 1998 |

236 | Triangular Norms - Klement, Mesiar, et al. - 2000 |

78 | A First Course - Nguyen, Walker - 2006 |

75 | Monoidal t-norm based logic: towards a logic for left-continuous t-norms, Fuzzy Sets and Systems - Esteva, Godo - 2001 |

60 |
Algebraic analysis of many valued logics
- Chang
- 1958
(Show Context)
Citation Context ...lds true. A Π-algebra is a BL-algebra fulfilling a ⊗ (a → b) = a ∧ b, a, b ∈ L (4) ¬¬a ≤ (a → a ⊗ b) → b ⊗ ¬¬b, a, b ∈ L.s84 V. NOV ÁK The richest structure is MV-algebra introduced by C. C. Chang in =-=[2]-=- and further intensively studied (cf. [13]). This is a nontrivial generalization of a boolean algebra. L = 〈L, ⊕, ⊗, ¬, 0, 1〉 (5) satisfying the following axioms: (i) (a ⊕ b) ⊕ c = a ⊕ (b ⊕ c), (ii) a... |

53 | A Treatise on Many-Valued Logics - Gottwald - 2001 |

50 | On fuzzy logic I - Pavelka |

33 |
English as a formal language. In Linguaggi nella societá e nella tecnica
- Montague
- 1970
(Show Context)
Citation Context ...antics), we need higher order fuzzy logic — a fuzzy type theory (see [17]). Among others, it enables us direct generalization of various consideration from classical linguistic (e.g. Montague grammar =-=[12]-=-). An important possibility is also elaboration of fuzzy IF-THEN rules as conditional linguistic statements (see [20]) that heads towards developing sophisticated inference schemes of human reasoning.... |

28 | Fuzzy logic and its application to approximate reasoning - Zadeh - 1974 |

27 | Fuzzy Sets and their Applications - Novak - 1986 |

27 | Mathematics behind fuzzy logic - Turunen - 1999 |

23 | The liar paradox and fuzzy logic - Hajek, Paris, et al. - 2000 |

15 | On the Hierarchy of t-norm Based Residuated Fuzzy Logics - Esteva, Godo, et al. - 2003 |

15 |
On fuzzy type theory
- Novák
(Show Context)
Citation Context ...gueness. We conclude that, since a significant role in the agenda of fuzzy logic is played by natural language (and mainly, its semantics), we need higher order fuzzy logic — a fuzzy type theory (see =-=[17]-=-). Among others, it enables us direct generalization of various consideration from classical linguistic (e.g. Montague grammar [12]). An important possibility is also elaboration of fuzzy IF-THEN rule... |

10 | Perfilieva (Eds.), Discovering the World With Fuzzy Logic - Novák, I - 2000 |

9 |
Fuzzy class theory, Fuzzy Sets and Systems
- Běhounek, Cintula
- 2005
(Show Context)
Citation Context ...ding the two-valued one for classical logic 〈{0, 1}, ∨, ∧, ¬, 0, 1〉 where ⊗ = ∧ and a → b = ¬a ∨ b. Otherwise, typical (standard) examples of the above introduced algebras should have the support L = =-=[0, 1]-=- so that the residuated lattice is complete and has the general form L = 〈[0, 1], ∨, ∧, ⊗, →, 0, 1〉 (7) where ⊗ is a left-continuous t-norm. The obtained algebra is MTL-algebra. Example of IMTL-algebr... |

8 |
A development of set theory in fuzzy logic
- Hájek, Haniková
- 2003
(Show Context)
Citation Context ...cessary if we want to prove more non-trivial properties. Another beautiful logic is BL. In a sense, this logic is essential logic for the development of fuzzy set theory (for a successful attempt see =-=[10]-=-) because it covers all continuous t-norms. Unfortunately, the double negation cannot be introduced in BL. When adding it to BL, we obtain ̷Lukasiewicz logic. In this logic, we have almost everything ... |

8 | Are fuzzy sets a reasonable tool for modeling vague phenomena - Novak - 2005 |

8 |
Normal forms in BL-algebra of functions and their contribution to universal approximation of functions. Fuzzy Sets and Systems
- Perfilieva
(Show Context)
Citation Context ...ewhere (later also in [21]). An important operation needed, e.g. for considerations in fuzzy approximation theory (a concept significantly elaborated in the frame of fuzzy logic by I. Perfilieva, cf. =-=[24]-=-) and elsewhere is ordinary product of reals. A logic that uses it as interpretation of strong conjunction is product logic Π. But this logic has some strange properties, it is more special than BL bu... |

7 |
The ̷LΠ and ̷LΠ 1 2 logics: two complete fuzzy systems joining ̷Lukasiewicz and product logics
- Esteva, Godo, et al.
- 2001
(Show Context)
Citation Context ...not preserve double negation.s88 V. NOV ÁK A very nice possibility is to join everything good from all logics into one — the result is ̷LΠ logic. This logic has been established by F. Esteva et al in =-=[5]-=- and further elaborated by P. Cintula [3]. Its only disadvantage is great complexity because of plethora of connectives. But still, this logic seems to be the best to fulfil the agenda of FL, to be ap... |

5 |
Logical structure of fuzzy if-then rules.” Fuzzy Sets and Systems
- Novák, Lehmke
- 2006
(Show Context)
Citation Context ...lization of various consideration from classical linguistic (e.g. Montague grammar [12]). An important possibility is also elaboration of fuzzy IF-THEN rules as conditional linguistic statements (see =-=[20]-=-) that heads towards developing sophisticated inference schemes of human reasoning. We should also mention a recent attempt of L. Běhounek and P. Cintula to develop a sound mathematical basis for fuzz... |

3 |
D’Ottaviano, I.M.L.: Algebraic foundations of many-valued Reasoning
- Mundici, Cignoli
- 2000
(Show Context)
Citation Context ...filling a ⊗ (a → b) = a ∧ b, a, b ∈ L (4) ¬¬a ≤ (a → a ⊗ b) → b ⊗ ¬¬b, a, b ∈ L.s84 V. NOV ÁK The richest structure is MV-algebra introduced by C. C. Chang in [2] and further intensively studied (cf. =-=[13]-=-). This is a nontrivial generalization of a boolean algebra. L = 〈L, ⊕, ⊗, ¬, 0, 1〉 (5) satisfying the following axioms: (i) (a ⊕ b) ⊕ c = a ⊕ (b ⊕ c), (ii) a ⊕ b = b ⊕ a, (iii) a ⊕ 0 = a, (iv) ¬¬a = ... |

3 |
Towards Formalized Integrated Theory of Fuzzy Logic
- Novák
- 1995
(Show Context)
Citation Context ...e agenda of fuzzy logic. It is notable that only Ev̷L is capable at modeling of the concept of intension on the first-order level (this is impossible in traditional syntax) — see the first version in =-=[15]-=- and elsewhere (later also in [21]). An important operation needed, e.g. for considerations in fuzzy approximation theory (a concept significantly elaborated in the frame of fuzzy logic by I. Perfilie... |

2 |
The ̷LΠ and ̷LΠ 1 2 propositional and predicate logics
- Cintula
- 2001
(Show Context)
Citation Context ...K A very nice possibility is to join everything good from all logics into one — the result is ̷LΠ logic. This logic has been established by F. Esteva et al in [5] and further elaborated by P. Cintula =-=[3]-=-. Its only disadvantage is great complexity because of plethora of connectives. But still, this logic seems to be the best to fulfil the agenda of FL, to be applied in fuzzy approximation (see Perfili... |

2 | Fuzzy Logic With Countable Evaluated Syntax - Novák - 2005 |