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Multi-valued and fuzzy logics provide mathematical and computational tools for handling imperfect information and decision-making with rational collective reasoning and irrational individual judgements.
The suggested implementation of multi-valued logics is based on the uninorm and absorbing norm with generating functions defined by probability distributions. Natural extensions of these logics result in non-commutative and non-distributive logics. In addition to Boolean truth values, these logics handle subjective truth and false values and model irrational decisions. Dynamics of decision-making are specified by the subjective Markov process and learning - by neural network with extended Tsetlin neurons. Application of the suggested methods is illustrated by modelling of irrational economic decisions and biased reasoning in the wisdom-of-the-crowd method, and by control of mobile robots and navigation of their groups.
Topics and features:
- Bridges the gap between fuzzy and probability methods
- Includes examples in the field of machine-learning and robots' control
- Defines formal models of subjective judgements and decision-making
- Presents practical techniques for solving non-probabilistic decision-making problems
- Initiates further research in non-commutative and non-distributive logics
The book forms a basis for theoretical studies and practice of decision-making under uncertainty and will be useful for computer scientists and mathematicians interested in multi-valued and fuzzy logic, as well as for engineers working in the field of data mining and data analysis.
List of contents
1. Introduction.- 2. Background.- 3. Probability-generated multi-valued logic.- 4. Muli-valued logic algebra of subjective trusts.- 5. Algebra with non-commutative norms.- 6. Implementation of subjective trusts in control.
About the author
Dr. Evgeny Kagan is with the Faculty of Engineering, Ariel University, Israel.
Dr. Alexander Rybalov is with the LAMBDA Laboratory, Tel-Aviv University, Israel.
Prof. Ronald Yager is with the Machine Learning Institute, Yona College, New York, USA.
