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The purpose of this work is to establish a priori C 2 ' a estimates for mesh function solutions of nonlinear positive difference equations in fully nonlinear form on a uniform mesh, where the fully nonlinear finite-difference operator Th, is concave in the second-order variables. The estimate is an analogue of the corresponding estimate for solutions of concave fully nonlinear elliptic partial differential equations. We deal here with the special case that the operator does not depend explicitly upon the independent variables. We do this by discretizing the approach of Evans for fully nonlinear elliptic partial differential equations using the discrete linear theory of Kuo and Trudinger. The result in this special case forms the basis for a more general result in part II. We also derive the discrete interpolation inequalities needed to obtain estimates for the interior C 2 ' a semi-norm in terms of the C° norm.

The purpose of this work is to establish a priori C 2,α estimates for mesh function solutions of nonlinear difference equations of positive type in fully nonlinear form on a uniform mesh, where the fully nonlinear finite difference operator F h is concave in the second-order variables. The estimate is an analogue of the corresponding estimate for solutions of concave fully nonlinear elliptic partial differential equations. We use the results for the special case that the operator does not depend explicitly upon the independent variables (the so-called frozen case) established in part I to approach the general case of explicit dependence upon the independent variables. We make our approach for the diagonal case via a discretization of the approach of Safonov for fully nonlinear elliptic partial differential equations using the discrete linear theory of Kuo and Trudinger and an especially agreeable mesh function interpolant provided by Kunkle. We generalize to non-diagonal operators using an idea which, to the author's knowledge, is novel. In this paper we establish the desired Hölder estimate in the large, that is, on the entire mesh n-plane. In a subsequent paper a truly interior estimate will be established in a mesh n-box.

The objective of the paper is to propose a measurement model for trustworthiness of a document to ensure information security. The definition of trustworthiness in this context refers to the reliability value of the information in the document. The document here refers to an article or a web document. The proposed model relates to an approach for assessing trust of data for use of the information consumer. The model helps to capture multiple factors couple with risk profiles in the determination of the trustworthiness of content. It allows consideration of level of confidence and aggregation of attitude towards risk for normalization of a trust index. We use a fuzzy representation to allow the information consumer to decide their confidence level towards the importance of each criterion. The model enables an automated computation method for a straight forward computation for a unique and personalized trustworthiness. The paper also presents an implementation example for practicality of the proposed model.Keywords-Multicriteria decision support, fuzy set theory, fuzzy preference modeling, fuzzy information modelling and identification.

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