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Inverses of fuzzy relations. Application to possibility distributions and medical diagnosis. (English) Zbl 0399.03040


MSC:

03E72 Theory of fuzzy sets, etc.
03E20 Other classical set theory (including functions, relations, and set algebra)
03B52 Fuzzy logic; logic of vagueness
68T50 Natural language processing
92C50 Medical applications (general)
60A99 Foundations of probability theory
Full Text: DOI

References:

[1] Bellman, R. E.; Zadeh, L. A., Local and fuzzy logics, (Memo. No. ERL M584 (1976), University of California: University of California Berkeley, CA) · Zbl 0382.03017
[2] Berge, C., Topological Spaces, Including a Treatment of Multi-valued Mappings (1963), The MacMillan Company: The MacMillan Company New York · Zbl 0114.38602
[3] Dempster, A., Upper and lower probabilities induced by multi-valued mappings, Ann. Math. Statist., 38, 325-339 (1967) · Zbl 0168.17501
[4] Kaufmann, A., (Introduction à la theorie des sous-ensembles flous, Tome IV (1977), Ed. Masson: Ed. Masson Paris) · Zbl 0346.94002
[5] Sanchez, E., Equations de relations floues, Thèse d’Etat de Biologie Humaine (1974), Marseille
[6] Sanchez, E., Resolution of composite fuzzy relation equations, Information and Control, 30, 38-48 (1976) · Zbl 0326.02048
[7] Sanchez, E., Solutions in composite fuzzy relation equations. Application to medical diagnosis in Brouwerian logic, (Fuzzy Automata and Decision Processes (1977), North-Holland: North-Holland New York)
[8] Sanchez, E., On possibility—Qualification in natural languages, (Memo. No. UCB/ERL M77/28 (1977), University of California: University of California Berkeley, CA) · Zbl 0437.03011
[9] Sanchez, E.; Sambuc, R., Relations floues. Fonction Φ-floues. Application à l’aide au diagnostic en pathologie thyroidienne, (Medical Data Processing Symposium (1976), IRIA: IRIA Toulouse)
[10] Shafer, G., A Mathematical Theory of Evidence (1976), Princeton University Press: Princeton University Press Princeton, NJ · Zbl 0359.62002
[11] Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning, Information Sciences, 9, 43-80 (1975), Part III · Zbl 0404.68075
[12] Zadeh, L. A., Theory of fuzzy sets, (Memo. No. UCB/ERL M77/1 (1977), University of California: University of California Berkeley, CA) · Zbl 0377.04002
[13] Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, (Memo. No. UCB/ERL M77/12 (1977), University of California: University of California Berkeley, CA) · Zbl 0377.04002
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