Fuzzy set and logic theory suggest that all natural language linguistic expressions are imprecise and must be assessed as a matter of degree. But in general membership degree is an imprecise notion which requires that Type 2 membership degrees be considered in most applications related to human decision making schemas. Even if the membership functions are restricted to be Type1, their combinations generate an interval - valued Type 2 membership. This is part of the general result that Classical equivalences breakdown in Fuzzy theory. Thus all classical formulas must be reassessed with an upper and lower expression that are generated by the breakdown of classical formulas.

Key features:

- Ontological grounding
- Epistemological justification
- Measurement of Membership
- Breakdown of equivalences
- FDCF is not equivalent to FCCF
- Fuzzy Beliefs
- Meta-Linguistic axioms
- Ontological grounding
- Epistemological justification
- Measurement of Membership
- Breakdown of equivalences
- FDCF is not equivalent to FCCF
- Fuzzy Beliefs
- Meta-Linguistic axioms

Soft computing is a consortium of computing methodologies that provide a foundation for the conception, design, and deployment of intelligent systems and aims to formalize the human ability to make rational decisions in an environment of uncertainty and imprecision. This book is based on a NATO Advanced Study Institute held in 1996 on soft computing and its applications. The distinguished contributors consider the principal constituents of soft computing, namely fuzzy logic, neurocomputing, genetic computing, and probabilistic reasoning, the relations between them, and their fusion in industrial applications. Two areas emphasized in the book are how to achieve a synergistic combination of the main constituents of soft computing and how the combination can be used to achieve a high Machine Intelligence Quotient.

The world we live in is pervaded with uncertainty and imprecision. Is it likely to rain this afternoon? Should I take an umbrella with me? Will I be able to find parking near the campus? Should I go by bus? Such simple questions are a c- mon occurrence in our daily lives. Less simple examples: What is the probability that the price of oil will rise sharply in the near future? Should I buy Chevron stock? What are the chances that a bailout of GM, Ford and Chrysler will not s- ceed? What will be the consequences? Note that the examples in question involve both uncertainty and imprecision. In the real world, this is the norm rather than exception. There is a deep-seated tradition in science of employing probability theory, and only probability theory, to deal with uncertainty and imprecision. The mon- oly of probability theory came to an end when fuzzy logic made its debut. H- ever, this is by no means a widely accepted view. The belief persists, especially within the probability community, that probability theory is all that is needed to deal with uncertainty. To quote a prominent Bayesian, Professor Dennis Lindley, "The only satisfactory description of uncertainty is probability.

Soft computing is a consortium of computing methodologies that provide a foundation for the conception, design, and deployment of intelligent systems and aims to formalize the human ability to make rational decisions in an environment of uncertainty and imprecision. This book is based on a NATO Advanced Study Institute held in 1996 on soft computing and its applications. The distinguished contributors consider the principal constituents of soft computing, namely fuzzy logic, neurocomputing, genetic computing, and probabilistic reasoning, the relations between them, and their fusion in industrial applications. Two areas emphasized in the book are how to achieve a synergistic combination of the main constituents of soft computing and how the combination can be used to achieve a high Machine Intelligence Quotient.

The Current state of expectations is that Computer Integrated Manufacturing (CIM) will ulti mately determine the industrial growth of world nations within the next few decades. Computer Aided Design (CAD), Computer Aided Manufacturing (CAM), Flexible Manufacturing Systems (FMS), Robotics together with Knowledge and Information Based Systems (KIBS) and Com munication Networks are expected to develop to a mature state to respond effectively to the managerial requirements of the factories of the future that are becoming highly integrated and complex. CIM represents a new production approach which will allow the factories to deliver a high variety of products at a low cost and with short production cycles. The new technologies for CIM are needed to develop manufacturing environments that are smarter, faster, close-cou pled, integrated, optimized, and flexible. Sophistication and a high degree of specialization in materials science, artificial intelligence, communications technology and knowledge-information science techniques are needed among others for the development of realizable and workable CIM systems that are capable of adjusting to volatile markets. CIM factories are to allow the production of a wide variety of similar products in small batches through standard but multi mission oriented designs that accommodate flexibility with specialized software."

The world we live in is pervaded with uncertainty and imprecision. Is it likely to rain this afternoon? Should I take an umbrella with me? Will I be able to find parking near the campus? Should I go by bus? Such simple questions are a c- mon occurrence in our daily lives. Less simple examples: What is the probability that the price of oil will rise sharply in the near future? Should I buy Chevron stock? What are the chances that a bailout of GM, Ford and Chrysler will not s- ceed? What will be the consequences? Note that the examples in question involve both uncertainty and imprecision. In the real world, this is the norm rather than exception. There is a deep-seated tradition in science of employing probability theory, and only probability theory, to deal with uncertainty and imprecision. The mon- oly of probability theory came to an end when fuzzy logic made its debut. H- ever, this is by no means a widely accepted view. The belief persists, especially within the probability community, that probability theory is all that is needed to deal with uncertainty. To quote a prominent Bayesian, Professor Dennis Lindley, "The only satisfactory description of uncertainty is probability.