Fuzzy Reasoning in Decision Making and Optimization

This book starts with the basic concepts of fuzzy arithmetics and progresses through the analysis of sup-t-norm-extended arithmetic operations, possibilistic linear systems and fuzzy reasoning approaches to fuzzy optimization. Four applications of (interdependent) fuzzy optimization and fuzzy reason...

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Main Authors: Carlsson, Christer, Fuller, Robert (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Heidelberg Physica-Verlag HD 2002, 2002
Edition:1st ed. 2002
Series:Studies in Fuzziness and Soft Computing
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1. Fuzzy Sets and Fuzzy Logic
  • 1.1 Fuzzy sets
  • 1.2 Operations on fuzzy sets
  • 1.3 The extension principle
  • 1.4 t-norm-based operations on fuzzy numbers
  • 1.5 Product-sum of triangular fuzzy numbers
  • 1.6 Hamacher-sum of triangular fuzzy numbers
  • 1.7 t-norm-based addition of fuzzy numbers
  • 1.8 A functional relationship between t-norm-based addition and multiplication
  • 1.9 On generalization of Nguyen’s theorems
  • 1.10 Measures of possibility and necessity
  • 1.11 A law of large numbers for fuzzy numbers
  • 1.12 Metrics for fuzzy numbers
  • 1.13 Possibilistic mean value and variance of fuzzy numbers
  • 1.14 Auxiliary lemmas
  • 1.15 Fuzzy implications
  • 1.16 Linguistic variables
  • 2. Fuzzy Multicriteria Decision Making
  • 2.1 Averaging operators
  • 2.2 Obtaining maximal entropy OWA operator weights
  • 2.3 OWA Operators for Ph.D. student selection
  • 2.4 Possibility and necessity in weighted aggregation
  • key features
  • 7.5 Forecasting
  • 7.6 Industry foresight
  • 7.7 The scenario agent
  • 7.8 Interpretation agent
  • 7.9 Coping with imprecision
  • 7.10 Interpretation in a business environment
  • 7.11 Mental models and cognitive maps
  • 7.12 A preliminary description of an interpretation agent
  • 7.13 An interpretation agent: details
  • standard results
  • 6.4.3 Demand signal processing
  • 6.4.4 Order batching
  • 6.4.5 Price variations
  • 6.4.6 A fuzzy approach to demand signal processing
  • 6.4.7 A fuzzy logic controller to demand signal processing
  • 6.4.8 A hybrid soft computing platform for taming the bullwhip effect
  • 7. Future Trends in Fuzzy Reasoning and Decision Making
  • 2.5 Benchmarking in linguistic importance weighted aggregations
  • 3. Fuzzy Reasoning
  • 3.1 The theory of approximate reasoning
  • 3.2 Aggregation in fuzzy system modeling
  • 3.3 Multiple fuzzy reasoning schemes
  • 3.4 Some properties of the compositional rule of inference
  • 3.5 Computation of the compositional rule of inference under t-norms
  • 3.6 On the generalized method-of-case inference rule
  • 4. Fuzzy Optimization
  • 4.1 Possibilistic linear equality systems
  • 4.2 Sensitivity analysis of ãx = b? and ã?x = b??.
  • 4.3 Possibilistic systems with trapezoid fuzzy numbers
  • 4.4 Flexible linear programming
  • 4.5 Fuzzy linear programming with crisp relations
  • 4.6 Possibilistic linear programming
  • 4.7 Possibilistic quadratic programming
  • 4.8 Multiobjective possibilistic linear programming
  • 5. Fuzzy Reasoning for Fuzzy Optimization
  • 5.1 Fuzzy reasoning for FMP
  • 5.2 Optimization with linguistic variables
  • 5.3 Multiobjective optimization with lingusitic variables -