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## The Concept of a Linguistic Variable and its Application to Approximate Reasoning (1975)

Venue: | Journal of Information Science |

Citations: | 1428 - 9 self |

### Citations

6240 | Fuzzy sets - Zadeh - 1965 |

892 |
Outline of a New Approach to the Analysis of Complex Systems and Decision Processes
- Zadeh
- 1973
(Show Context)
Citation Context ... legal systems, educational systems, etc. A single individual and his thought processes may also be viewed as a humanistic system.LINGUISTIC VARIABLE 201 It may be argued, as we have done in [6] and =-=[7]-=- , that the ineffectiveness of computers in dealing with humanistic systems is a manifestation of what might be called the principle of incompatibility-a principle which asserts that high precision is... |

857 | M.J.: An Introduction to Modal Logic - Hughes, Creswell |

680 |
Perceptrons: An introduction to computational geometry
- MINSKY, PAPERT
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(Show Context)
Citation Context ...essed by Thus, we can write [see (3.52)] Al X-XAn= $ u1 x*.-x [I-lA,(‘~)r\“.A~A,(Un)l/(ul,...,U,). v n (3.46) Example3.8. IfU, =U2 =3+5+7, Al =0.5/3-k 1/5+0.6/7andAZ = l/3 t 0.615, then Al X A2 = 0.5/=-=(3,3)-=- + l/(5,3) + 0.6/(7,3) t 0.5/(3,5) + 0.6/(5,5) + 0.6/(7,5). (3.47)228 L. A. ZADEH 7. The operation of fuzzifcatiun has, in general, the effect of transforming a nonfuzzy set into a fuzzy set or incre... |

569 | Semantics of Context-Free Languages, - Knuth - 1968 |

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346 | Formal Languages and Their Relation to Automata - Hopcroft, Ullman - 1969 |

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231 |
Similarity relations and fuzzy orderings,
- Zadeh
- 1971
(Show Context)
Citation Context ...y set A may be decomposed identity’ 3 into its level-sets through the resolution A = $l RYAN 0 (3.28) 13The resolution identity and some of its applications are discussed in greater detail in [6] and =-=[24]-=-.224 L. A. ZADEH or A = c aA,, (3.29) a where oA, is the product of a scalar (Y with the set A, [in the sense of (3.39)] , and j (or Z) is the union of the A,, with cr ranging from 0 to 1. 0 a The re... |

214 | Hedges: A study in meaning criteria and the logic of fuzzy concepts. - Lakoff - 1972 |

212 | Relational completeness of data base sublanguages, Database Systems,
- Codd
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(Show Context)
Citation Context ... Proj S on U,, (3.65) then R n S becomes the join ” of R and S. A basic property of the join of R and S may be stated as “The concept of the join of nonfuzzy relations was introduced by E. F. Codd in =-=[28]-=-.234 L. A. ZADEH PROPOSITION 3.2. If R and S are fuzzy relations in U1 X U, and U2 X U,, respectively, and R CI 3 is the join of R and S, then R = Proj R n S on U1 X U, (3.66) and S=ProjRnS on U, X U... |

208 | Fuzzy groups - Rosenfeld - 1971 |

190 | Probability measures of fuzzy events - Zadeh - 1968 |

150 | A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Set Theory," - Luca, Termini - 1972 |

136 | The Theory - Aho, Ullman - 1973 |

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91 | On fuzzy mapping and control, - Chang, Zadeh - 1972 |

77 |
Computers and Thought.
- Feigenbaum, Feldman
- 1963
(Show Context)
Citation Context ...entation of a linear operator, with K(u) being the counterpart of the impulse response. Example 3.9. Assume that U, A and K(u) are defined by U=lt2+3+4, A = 0.811 + 0.612, K(1) = l/l + 0.4/2, (3.50) K=-=(2)-=- = l/2 + 0.4/l t 0.4/3. F(A;K) = 0.8(1/l + 0.4/2) + 0.6(1/2 •t 0.4/l + 0.4/3) = 0.8/l + 0.612 + 0.2413. (3.5 1) The operation of fuzzification plays an important role in the definition of linguistic b... |

67 | Fuzzy logic and the resolution principle", - Lee - 1972 |

38 | Abstraction and pattern classification". - Bellman, Kalaba, et al. - 1996 |

25 |
The metaphorical brain
- Arbib
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(Show Context)
Citation Context ...(X,, . . . , X,) iff R(X,, . . . , X,) is separable, i.e., R(X,, . .,X,J=R(XI)X-XR(X,), (2.16) where,fori= 1,. . . ,n, R(X,.) = Proj R(X,, . . . 9 X,) on Ui =u uk?‘) R(Xi Iu )> (4’) (2.17) A A with u =-=(4)-=- = ui and u = complement of ui in (ur , . . . , un). (4’) Example 2.6. Fig. 9(a) shows two noninteractive variables Xi and X, whose restrictions R(X,) and R(X,) are intervals; in this case, R(X,, X,) ... |

19 |
Fuzzy languages and their relation to human and machine intelligence.
- Zadeh
- 1972
(Show Context)
Citation Context ...systems, legal systems, educational systems, etc. A single individual and his thought processes may also be viewed as a humanistic system.LINGUISTIC VARIABLE 201 It may be argued, as we have done in =-=[6]-=- and [7] , that the ineffectiveness of computers in dealing with humanistic systems is a manifestation of what might be called the principle of incompatibility-a principle which asserts that high prec... |

18 | The Vienna definition language - Wegner - 1972 |

12 | A Note on Fuzzy Set - Brown - 1971 |

11 | The Structure of Probability Theory with Applications - Thomasian - 1969 |

10 | Matrix equations and normal forms for context-free grammars. - Rosenkrantz - 1967 |

7 | Linguistic and natural logic, in Semantics of natural language - Lakoff - 1972 |

7 | Algebraic Properties of Fuzzy Sets - Luca, Termini - 1972 |

4 | On the execution of fuzzy programs using finite state machines - Chang - 1972 |

3 | Rational and Context-Free Power Series in Noncommuting Variables - Shamir, Algebraic - 1968 |

2 | Theory ofFuzzy Sets - Kaufmann - 1972 |

2 | Regular expressions for linear sequential circuits - Brzozowski - 1965 |

2 | et al., Method and notation for the formal definition of programming languages - Lucas - 1968 |

2 | A functional calculus of first order based on strict implication - Barkan - 1946 |

2 | Fuzzy Algorithms,Inf Control - Zadeh - 1968 |

2 | Fuzzy languages and their relation to automata - Lee - 1972 |

1 | Reasoning with loose concepts,Dialogue 2 - Black - 1963 |

1 | Vagueness and the principle of excluded middle - Verma - 1970 |

1 | The Logic of Inexact Concepts, Syntkese - Goguen |

1 | The Logic of “Almost Ah - Adams |

1 | supervaluations and free logic, in The Logical Way of Doing 77rings - Frassen, Presuppositions - 1969 |

1 | General formulation of formal grammars, inf 5 - Mizumoto, Toyoda, et al. - 1972 |

1 |
Decision-making in a fuzzy environment,Munuge
- Bellman, Zadeh
- 1970
(Show Context)
Citation Context ...d; thus AandB=AnB. (3.36) COMMENT 3.1. It should be understood that “(4 Max) and A(4 Min) are not the only operations in terms of which the union and intersection can226 L. A. ZADEH be defined. (See =-=[25]-=- and [26] for discussions of this point.) In this connection, it is important to note that when and is identified with Min, as in (3.36) it represents a “hard” and in the sense that it allows no trade... |

1 |
On the analytic formalism of the theory of fuzzy sets, Inf: Sci
- Bellman, Giertz
- 1973
(Show Context)
Citation Context ...andB=AnB. (3.36) COMMENT 3.1. It should be understood that “(4 Max) and A(4 Min) are not the only operations in terms of which the union and intersection can226 L. A. ZADEH be defined. (See [25] and =-=[26]-=- for discussions of this point.) In this connection, it is important to note that when and is identified with Min, as in (3.36) it represents a “hard” and in the sense that it allows no trade-offs bet... |

1 |
A fuzzy-set-theoretic intrepretation of linguistic hedges
- Zadeh
- 1972
(Show Context)
Citation Context ...ive. However, it is not always possible to express the effect of a fuzzifier in the form (3.48), and slightly is a case in point. A more detailed discussion of this and related issues may be found in =-=[27]-=-.LINGUISTIC VARIABLE 229 Fig. 11. Membership functions of positive and slightly positive. FUZZY RELATIONS If U is the Cartesian product of n universes of discourse U,, . . . , U,,, then an n-ary fuzz... |

1 | Semantics of context-free languages - Zadeth - 1968 |

1 | Quantitative fuzzy semantics, Znf Sci. 3,159-l 76 - Zadeh - 1971 |

1 | Fuzzy algorithms,Inf - Santos - 1970 |