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Hedge algebras: an algebraic approach to structure of sets of linguistic truth values. (English) Zbl 0704.03007

A fundamental article on hedge algebras, fuzzy reasoning, and fuzzy logic. Axiomatizability is shown, and basic properties are discussed. It seems to be an algebraic approach to linguistic hedges with applications to fuzzy logic. Further development remains to be seen.
Reviewer: He Ming (Ogden)

MSC:

03B52 Fuzzy logic; logic of vagueness
03G25 Other algebras related to logic
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References:

[1] N. Cat Ho, Fuzziness in structure of linguistic truth values: a foundation for development of fuzzy reasoning, Proc. ISMVL’87; N. Cat Ho, Fuzziness in structure of linguistic truth values: a foundation for development of fuzzy reasoning, Proc. ISMVL’87
[2] N. Cat Ho and W. Wechler, Extended hedge algebras and their application to some fuzzy logic, Manuscript.; N. Cat Ho and W. Wechler, Extended hedge algebras and their application to some fuzzy logic, Manuscript. · Zbl 0786.03018
[3] Giles, R., Lukasiewicz logic and fuzzy set theory, Internat. J. Man-Machine Stud., 8, 313-327 (1976) · Zbl 0335.02037
[4] Fukami, S., On fuzzy reasoning, Systems-Computers-Controls, 9, 44-53 (1978)
[5] Lakoff, G., Hedges: a study in meaning criteria and the logic of fuzzy concepts, (paper presented at the 8th Regional Meeting of the Chicago Linguistic Society (1972)) · Zbl 0315.02023
[6] Skala, H. J., On many-valued logics, fuzzy sets, fuzzy logics and their applications, Fuzzy Sets and Systems, 1, 129-149 (1978) · Zbl 0396.03024
[7] Smets, P.; Magrez, P., Implication in fuzzy logic (1987), submitted for publication · Zbl 0643.03018
[8] Tsukamoto, Y., An approach to fuzzy reasoning method, (Gupta, M. M.; Ragade, R. K.; Yager, R. R., Advances in Fuzzy Set Theory and Applications (1979), North-Holland: North-Holland Amsterdam), 137-149
[9] Wechler, W., The Concept of Fuzziness in Automata and Language Theory (1978), Akademie Verlag: Akademie Verlag Berlin · Zbl 0401.94048
[10] Zadeh, L. A., A fuzzy-set-theoretic interpretation of linguistic hedges, J. of Cybernet., 2, 4-34 (1972)
[11] Zadeh, L. A., The concept of linguistic variable and its application to approximate reasoning (II), Inform. Sci., 8, 301-357 (1975) · Zbl 0404.68074
[12] Zadeh, L. A., Fuzzy logic and approximate reasoning, Synthese, 30, 407-428 (1975) · Zbl 0319.02016
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