PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2002 | 12 | 3 | 359-369
Tytuł artykułu

Upper and lower set formulas: restriction and modification of the Dempster-Pawlak formalism

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A modification of Dempster's and Pawlak's constructs forms a new foundation for the identification of upper and lower sets formulas. Also, in this modified Dempster-Pawlak construct we require that subsets of the power set be restricted to the well-known information granules of the power set. An aggregation of upper information granules amongst each other and lower information granules amongst each other determine upper and lower set formulas for both crisp and fuzzy sets. The results are equivalent to the Truth Table derivation of FDCF and FCCF, Fuzzy Disjunctive Canonical Forms and Fuzzy Conjunctive Canonical Forms, respectively. Furthermore, they collapse to , i.e., the equivalence of Disjunctive Normal Forms and Conjunctive Normal Forms, in the combination of concepts once the LEM, LC and absorption, idempotency and distributivity axioms are admitted into the framework. Finally, a proof of the containment is obtained between FDCF and FCCF for the particular class of strict and nilpotent Archimedian -norms and -conorms.
Rocznik
Tom
12
Numer
3
Strony
359-369
Opis fizyczny
Daty
wydano
2002
otrzymano
2002-03-01
poprawiono
2002-06-01
Twórcy
  • Knowledge/Intelligence Systems Laboratory, Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, M5S 3G8, Canada
Bibliografia
  • Bilgic T. (1995): Measumerent-theoretic frameworks for fuzzy set theory with applications to preference modeling. - Ph. D. thesis, University of Toronto.
  • Dempster A.P. (1967): Upper and lower probabilities induced by a multivalued mapping. - Ann. Math. Stat., Vol. 38, pp. 325-339.
  • Pawlak Z. (1991): Rough Sets. - Dordrecht: Kluwer.
  • Resconi G., Türkşen I.B. (2001): Canonical forms of fuzzy truthoods by meta-theory based upon modal logic. - Inf. Sci., Vol. 131, pp. 157-194.
  • Türkşen I.B. (1986): Interval-valued fuzzy sets based on normal forms. - Fuzzy Sets Syst., Vol. 20, pp. 191-210.
  • Türkşen I.B. (1992): Interval-valued fuzzy sets and compensatory AND. - Fuzzy Sets Syst., Vol. 51, pp. 87-100.
  • Türkşen I.B. (1999): Theories of set and logic with crisp or fuzzy information granules. - J. Adv. Comp. Intell., Vol. 3, No. 4, pp. 264-273.
  • Türkşen I.B. (2001): Computing with descriptive and veristic words: Knowledge representation and reasoning, In: Computing With Words (P.P.Wang, Ed.). - New York: Wiley, pp. 297-328.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv12i3p359bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.