Fuzzy Bayesian system reliability assessment based on exponential distribution

The Bayesian system reliability assessment under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed as fuzzy random variables with fuzzy prior distributions. The (conventional) Bayesian estimation method will be used to create the fuzzy Bayes point estimator of system reliability based on Exponential distribution by invoking the well-known theorem called “Resolution Identity” in fuzzy sets theory. On the other hand, we also provide the computational procedures to evaluate the membership degree of any given Bayes point estimate of system reliability. In order to achieve this purpose, we transform the original problem into a nonlinear programming problem. This nonlinear programming problem is then divided into four subproblems for the purpose of simplifying computation. Finally, the subproblems can be solved by using any commercial optimizers, e.g., GAMS or LINGO (LINDO).     

n-Simple theories

The main topic of this paper is the investigation of generalized amalgamation properties for simple theories. That is, we are trying to answer the question of when a simple theory has the property of n-dimensional amalgamation, where two-dimensional amalgamation is the Independence Theorem for simple theories. We develop the notions of strong n-simplicity and n-simplicity for 1≤n≤ω, where both “1-simple” and “strongly 1-simple” are the same as “simple”. For strong n-simplicity, we present examples of simple unstable theories in each subclass and prove a characteristic property of strong n-simplicity in terms of strong n-dividing, a strengthening of the dependence relation called dividing in simple theories. We prove a strong three-dimensional amalgamation property for strongly 2-simple theories, and, under an additional assumption, a strong (n+1)-dimensional amalgamation property for strongly n-simple theories. In the last section of the paper we comment on why strong n-simplicity is called strong.     

Stable theories

We studyK _T(λ)=sup {|S(A)| : |A|≦λ} and extend some results for totally transcendental theroies to the case of stable theories. We then investigate categoricity of elementary and pseudo-elementary classes. This paper is a part of the author’s doctoral dissertation written at the Hebrew University of Jerusalem, under the kind guidance of Profeossr M. Rabin.     

Critical theories

Sverdlovsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 29, No. 1, pp. 23–31, January–February, 1988.     

Supersimple theories

We prove elimination of hyperimaginaries in supersimple theories. This means that if an equivalence relation on the set of realisations of a complete type (in a supersimple theory) is defined by a possibly infinite conjunction of first order formulas, then it is the intersection of definable equivalence relations.

     

Weak theories of concatenation and minimal essentially undecidable theories

We consider weak theories of concatenation, that is, theories for strings or texts. We prove that the theory of concatenation \({\mathsf{WTC}^{-\varepsilon}}\) , which is a weak subtheory of Grzegorczyk’s theory \({\mathsf{TC}^{-\varepsilon}}\) , is a minimal essentially undecidable theory, that is, the theory \({\mathsf{WTC}^{-\varepsilon}}\) is essentially undecidable and if one omits an axiom scheme from \({\mathsf{WTC}^{-\varepsilon}}\) , then the resulting theory is no longer essentially undecidable. Moreover, we give a positive answer to Grzegorczyk and Zdanowski’s conjecture that ‘The theory \({\mathsf{TC}^{-\varepsilon}}\) is a minimal essentially undecidable theory’. For the alternative theories \({\mathsf{WTC}}\) and \({\mathsf{TC}}\) which have the empty string, we also prove that the each theory without the neutrality of \({\varepsilon}\) is to be such a theory too.     

Convexity theories III. Classification of certain real convexity theories

In this paper we classify all real convexity theories that contain the standard convexity theory _c. For this purpose we consider three subcases: finitary; infinitary and (_sc\_c)Ø; infinitary and _sc=_c. In each of these subcases one encounters a phenomenon resembling bifurcation.This research was supported by the Deutsche Forschungsgemeinschaft.     

Bounded and well-placed theories in the lattice of equational theories

In Memory of Evelyn Nelson     

Generalized Green's theories

A generalization is given of the relations and equivalences on a semigroup S associated with J. A. Green by introducing the concepts of Green's pairs and generalized Green's theories first on an arbitrary set X and finally on a semigroup S. Most of the results about the usual Green's relations and equivalences are proved, and it is shown that previous generalizations obtained by Wallace, Anscombre, Marki and Steinfeld, and Pastijn may be obtained as special cases of the theory developed. Dedicated to D. D. Miller in honor of his retirement at the University of Tennessee after 32 years of service.     

Primitive connected theories

We prove the quantifier-elimination theorem for so-called primitive connected theories, exemplified by theories of modules. The theorem generalizes the well-known Baur-Monk-Garavaglia theorem on the elimination of quantifiers in the model theory of modules. The definition of a class of primitive connected theories, as distinct from modules. is not supposed to impose any conditions on a type of axioms that would specify those theories. Dedicated to the 60th birthday of Academician Yu. L. Ershov Supported by RFFR grant No. 99-01-00600. Translated fromAlgebra i Logika, Vol. 39, No. 2, pp. 145–169, March–April, 2000.     

Metrically generated theories

Many examples are known of natural functors describing the transition from categories of generalized metric spaces to the ``metrizable" objects in some given topological construct . If preserves initial morphisms and if is initially dense in , then we say that is -metrically generated. Our main theorem proves that is -metrically generated if and only if can be isomorphically described as a concretely coreflective subconstruct of a model category with objects sets structured by collections of generalized metrics in and natural morphisms. This theorem allows for a unifying treatment of many well-known and varied theories. Moreover, via suitable comparison functors, the various relationships between these theories are studied.