论文信息 - Conditioning on MV-algebras and additive measures - I

Conditioning on MV-algebras and additive measures - I

Abstract We present a lattice-ordered semigroup approach for the foundation of conditional events which covers the special situations where the underlying (unconditional) events are Boolean or fuzzy, respectively. Our proposal is quite different from other, ring theoretical, approaches. The problem of extending additivity of uncertainty measures from unconditional to conditional events will be discussed.

Siegfried Weber

[1] Hung T. Nguyen,et al. Conditional inference and logic for intelligent systems - a theory of measure-free conditioning , 1991 .

[2] G. Schay. An algebra of conditional events , 1968 .

[3] B. O. Koopman. The Axioms and Algebra of Intuitive Probability , 1940 .

[4] Vilém Novák,et al. Topoi and Categories of Fuzzy Sets , 1999 .

[5] C. Chang,et al. Algebraic analysis of many valued logics , 1958 .

[6] U. Höhle. Commutative, residuated 1—monoids , 1995 .

[7] Siegfried Weber,et al. Uncertainty Measures, Realizations and Entropies* , 1997 .

[8] Madan M. Gupta,et al. Conditional Logic in Expert Systems , 1991 .

[9] Hung T. Nguyen,et al. Foundations for an algebraic theory of conditioning , 1991 .

[10] Siegfried Weber,et al. Conditional measures and their applications to fuzzy sets , 1991 .

[11] Ulrich Höhle,et al. Non-classical logics and their applications to fuzzy subsets : a handbook of the mathematical foundations of fuzzy set theory , 1995 .