Fuzzy Partial Differential Equations and Relational Equations
[Book]
Reservoir Characterization and Modeling /
edited by Masoud Nikravesh, Lotfi A. Zadeh, Victor Korotkikh.
Berlin, Heidelberg :
Imprint: Springer,
2004.
Studies in Fuzziness and Soft Computing,
142
1434-9922 ;
Foreword -- Preface -- Soft Computing for Reservoir Characterization -- An Approach to the Mathematical Theory of Perception-Based Information -- Fuzzy Neural Networks Based on Fuzzy Logic Algebras Valued Relations -- Simulating Continuous Dynamical Systems under Conditions of Uncertainty -- Resolution of Min-Max Fuzzy Relational Equations -- Fuzzy Relation Equations with Words -- A Normative View on Possibility Distributions -- FREs: the ODEs and PDEs of the Fuzzy Modeling Paradigm -- Equations and Inequalitites with BK-Products of Relations -- Decompostition of Fuzzy Relations and Functional Relations -- Introduction to Modeling of Hydrogeologic Systems Using Fuzzy Differential Equations -- Construction of Granular Derivatives and Solution of Granular Initial Value Problem -- Numerical Solutions of Fuzzy Partial Differential Equation and its Application in Computational Mechanics.
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This monograph presents the latest advances of fuzzy logic and soft computing in reservoir characterization and modeling. It proposes for the first time that future develoments require perception-based information processing. The book presents important steps in this direction by introducing fuzzy partial differential equations and relational equations. It provides a unique opportunity for soft computing researchers and oil industry practitioners to understand the significance of the changes in the fields by presenting recent accomplishments and new directions.