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[30912] Artykuł: On stability of formal fuzziness systemsCzasopismo: Information Sciences (Elsevier North Holland, Inc.) Tom: 22, Zeszyt: 1, Strony: 51-68ISSN: 0020-0255 Wydawca: ELSEVIER SCIENCE INC, 655 AVENUE OF THE AMERICAS, NEW YORK, NY 10010 Opublikowano: 1980 Autorzy / Redaktorzy / Twórcy Grupa MNiSW: Publikacja w czasopismach wymienionych w wykazie ministra MNiSzW (część A) Punkty MNiSW: 0 Klasyfikacja Web of Science: Article DOI Web of Science |
The structure of formal fuzziness systems as some abstraction on real fuzziness systems is debated. Then the global definition of α-stability is given. First some necessary and sufficient conditions for α-stability are given for the case of R = A ⇒ B (Sec. 2) and later for the case of R defined by an implication chain of any finite length (Sec. 4). In Secs. 5 and 6 notions of α-stability and α-β strong decision stability are introduced, and some theorems on necessary or sufficient (or both) conditions for these kinds of stability, imposed on the structure of an implication chain, are proved. In Sec. 3 the good-mapping property of a fuzzy relation matrix is analyzed, and because of its heuristic importance it is assumed in further sections. In many cases examples are given to illustrate definitions and theorems or conclusions.