Fuzzy Partial Differential Equations and Relational Equations

During last decade significant progress has been made in the oil indus try by using soft computing technology. Underlying this evolving technology there have, been ideas transforming the very language we use to describe problems with imprecision, uncertainty and partial truth. These developments offer exciting opportunities, but at the same time it is becoming clearer that further advancements are confronted by funda mental problems. The whole idea of how human process information lies at the core of the challenge. There are already new ways of thinking about the problems within theory of perception-based information. This theory aims to understand and harness the laws of human perceptions to dramatically im prove the processing of information. A matured theory of perception-based information is likely to be proper positioned to contribute to the solution of the problems and provide all the ingredients for a revolution in science, technology and business. In this context, Berkeley Initiative in Soft Computing (BISC), Univer sity of California, Berkeley from one side and Chevron-Texaco from another formed a Technical Committee to organize a Meeting entitled "State of the Art Assessment and New Directions for Research" to understand the signifi cance of the fields accomplishments, new developments and future directions. The Technical Committee selected and invited 15 scientists (and oil indus try experts as technical committee members) from the related disciplines to participate in the Meeting, which took place at the University of California, Berkeley, and March 15-17, 2002.

Proposing new directions for future developments in reservoir characterization and modeling Unique opportunity for soft computing researchers and oil industry practitioners to understand the significance of fuzzy partial differential equations and relational equations for their fields Includes supplementary material: sn.pub/extras

Klappentext

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.

Inhalt
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: the Probability and the Possibility Approaches.- 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 Modelling Paradigm.- Equations and Inequalities with BK-Products of Relations.- Decomposition of Fuzzy Relations and Functional Relations.- 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 Equations and Its Applications in Computational Mechanics.