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### Volumes One and Two

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This two-volume set explains the primary tools of soft computing as well as provides an abundance of working examples and detailed design studies. The books start with coverage of fuzzy sets and fuzzy logic and their various approaches to fuzzy reasoning and go on to discuss several advanced features of soft computing and hybrid methodologies. Together they provide a platform for handling different kinds of uncertainties of real-life problems. It introduces the reader to the topic of rough sets.

The volumes:

• Discuss the present state of art of soft computing

• Include the existing application areas of soft computing

• Present original research contributions

• Discuss the future scope of work in soft computing

This set is unique in that it bridges the gap between theory and practice, and it presents several experimental results on synthetic data and real-life data. The books provide a unified platform for applied scientists and engineers in different fields and industries for the application of soft computing tools in many diverse domains of engineering.

The major theme of the volume is to justify the term soft computing, which is essential to handle the vagueness of the real world. The primary tool of soft computing is well discussed with plenty of worked out examples and design studies. The books can be utilized as a standard textbook on soft computing for final-year undergraduate students, postgraduate students, research scholars, professional researchers, and industry R&D groups. The unique feature of the books is that the author clearly presents the state of art with several worked out examples and case studies based on synthetic data and real-life data. The application domains of soft computing are also clearly indicated.

The volumes can be used as a textbook and/or reference book by undergraduate and postgraduate students of many different engineering branches, such as electrical engineering, control engineering, electronics and communication engineering, computer sciences, and information sciences.

**Volume 1: A Unified Engineering Concept**

**Notion of Soft Computing **

Introduction

Scope for future work

**Fuzzy Sets, Fuzzy Operators and Fuzzy Relations **

Introduction

Fuzzy set

Metrics for fuzzy numbers

Difference in fuzzy set

Distance in fuzzy set

Cartesian product of fuzzy set

Operators on fuzzy set

Other operations in fuzzy set

Geometric interpretation of fuzzy sets

T-operators

Aggregation operators

Probability versus Possibility

Fuzzy event

Uncertainty

Measure of fuzziness

Type-2 fuzzy sets

Relation

**Fuzzy Logic**

Introduction

Preliminaries of logic

Lukasiewicz logic

Fuzzy logic

Fuzzy logic as viewed by Zadeh

Algebric structure in fuzzy logic

Critical appreciations on fuzzy logic

Generating logic for fuzzy set

Fuzzifying non-classical logics

Bridging the gap between fuzzy logic and quantum logic

Futuristic ambitions of fuzzy logic

**Fuzzy Implications and Fuzzy If-Then Models**

Introduction

Syntax and semantics of material implication

Fuzzy modifiers (hedges)

Linguistic truth value

Group decision making based on linguistic decision process

Linguistic assessments and combination of linguistic values

Linguistic preference relations and linguistic choice process

Fuzzy systems as function approximators

Extracting fuzzy rules from sample data points

Fuzzy basis functions

Extracting fuzzy rules from clustering of training samples

Representation of fuzzy IF-THEN rules by petri net

Transformations among various rule based fuzzy models

Losless rule reduction techniques for fuzzy system

Simplification of fuzzy rule base using similarity measure

Qualitative modeling based on fuzzy logic

**Rough Set**

Introduction

Gateway to roughset concept

Approximation spaces and set approximation

Rough membership function

Information systems

Indiscernibility relation

Some further illustration on set approximation

Dependency of attributes

Approximation and accuracy of classification

Reduction of attributes

Discernibility matrices and functions

Significance of attributes and approximate reducts

Decision rule synthesis

Case study: diagnosis of dengue based on rough set concept

Rough sets, Bayes’ rule & multivalued logic

Rough sets and data mining

Index

Volume 2: Fuzzy Reasoning and Fuzzy Control

**Fuzzy Reasoning**

Introduction

Model of approximate reasoning

Basic approach to Zadeh’s fuzzy reasoning

Extended fuzzy reasoning

Further extension of fuzzy reasoning

Generalized form of fuzzy reasoning

Application of fuzzy reasoning for prediction of radiation fog

Aggregation in fuzzy system modeling

Single Input Rule Modules (SIRMs) connected fuzzy reasoning method

Some properties of compositional rule of inference

Computation of compositional rule of inference under t-norms

Inverse approximate reasoning

Interpolative fuzzy reasoning

On generalized method-of-case inference rule

Generalized disjunctive syllogism

Ray’s bottom-up inferences

Multidimensional fuzzy reasoning based on multidimensional fuzzy implication

**Fuzzy Reasoning Based on Concept of Similarity**

Introduction

Fuzzy reasoning using similarity

Similarity based fuzzy reasoning method

Rule reduction is SBR

Proposed similarity measure

Fuzzy reasoning using similarity measures and computational rule of inference

Applications to different models

Reasoning based on total fuzzy similarity

Similarity-based bidirectional approximate reasoning

Logical approaches to fuzzy similarity-based reasoning

Fuzzy resolution based on similarity-based unification

**Fuzzy Control**

Introduction

Fuzzy controller

Illustration on basic approaches to fuzzy control

Fuzzy associative memory

Fuzzy controller design

Adaptive fuzzy controller design

Self-tuning of fuzzy controller

Single input rule module (SIRM)

Construction of PID controller by simplified fuzzy reasoning method

Fuzzy control as a fuzzy deduction system

**Concluding Remarks**

Review of the applications and future scope

Index

This two-volume set explains the primary tools of soft computing as well as provides an abundance of working examples and detailed design studies. The books start with coverage of fuzzy sets and fuzzy logic and their various approaches to fuzzy reasoning and go on to discuss several advanced features of soft computing and hybrid methodologies. Together they provide a platform for handling different kinds of uncertainties of real-life problems. It introduces the reader to the topic of rough sets.

The volumes:

• Discuss the present state of art of soft computing

• Include the existing application areas of soft computing

• Present original research contributions

• Discuss the future scope of work in soft computing

This set is unique in that it bridges the gap between theory and practice, and it presents several experimental results on synthetic data and real-life data. The books provide a unified platform for applied scientists and engineers in different fields and industries for the application of soft computing tools in many diverse domains of engineering.

The major theme of the volume is to justify the term soft computing, which is essential to handle the vagueness of the real world. The primary tool of soft computing is well discussed with plenty of worked out examples and design studies. The books can be utilized as a standard textbook on soft computing for final-year undergraduate students, postgraduate students, research scholars, professional researchers, and industry R&D groups. The unique feature of the books is that the author clearly presents the state of art with several worked out examples and case studies based on synthetic data and real-life data. The application domains of soft computing are also clearly indicated.

The volumes can be used as a textbook and/or reference book by undergraduate and postgraduate students of many different engineering branches, such as electrical engineering, control engineering, electronics and communication engineering, computer sciences, and information sciences.

**Volume 1: A Unified Engineering Concept**

**Notion of Soft Computing **

Introduction

Scope for future work

**Fuzzy Sets, Fuzzy Operators and Fuzzy Relations **

Introduction

Fuzzy set

Metrics for fuzzy numbers

Difference in fuzzy set

Distance in fuzzy set

Cartesian product of fuzzy set

Operators on fuzzy set

Other operations in fuzzy set

Geometric interpretation of fuzzy sets

T-operators

Aggregation operators

Probability versus Possibility

Fuzzy event

Uncertainty

Measure of fuzziness

Type-2 fuzzy sets

Relation

**Fuzzy Logic**

Introduction

Preliminaries of logic

Lukasiewicz logic

Fuzzy logic

Fuzzy logic as viewed by Zadeh

Algebric structure in fuzzy logic

Critical appreciations on fuzzy logic

Generating logic for fuzzy set

Fuzzifying non-classical logics

Bridging the gap between fuzzy logic and quantum logic

Futuristic ambitions of fuzzy logic

**Fuzzy Implications and Fuzzy If-Then Models**

Introduction

Syntax and semantics of material implication

Fuzzy modifiers (hedges)

Linguistic truth value

Group decision making based on linguistic decision process

Linguistic assessments and combination of linguistic values

Linguistic preference relations and linguistic choice process

Fuzzy systems as function approximators

Extracting fuzzy rules from sample data points

Fuzzy basis functions

Extracting fuzzy rules from clustering of training samples

Representation of fuzzy IF-THEN rules by petri net

Transformations among various rule based fuzzy models

Losless rule reduction techniques for fuzzy system

Simplification of fuzzy rule base using similarity measure

Qualitative modeling based on fuzzy logic

**Rough Set**

Introduction

Gateway to roughset concept

Approximation spaces and set approximation

Rough membership function

Information systems

Indiscernibility relation

Some further illustration on set approximation

Dependency of attributes

Approximation and accuracy of classification

Reduction of attributes

Discernibility matrices and functions

Significance of attributes and approximate reducts

Decision rule synthesis

Case study: diagnosis of dengue based on rough set concept

Rough sets, Bayes’ rule & multivalued logic

Rough sets and data mining

Index

Volume 2: Fuzzy Reasoning and Fuzzy Control

**Fuzzy Reasoning**

Introduction

Model of approximate reasoning

Basic approach to Zadeh’s fuzzy reasoning

Extended fuzzy reasoning

Further extension of fuzzy reasoning

Generalized form of fuzzy reasoning

Application of fuzzy reasoning for prediction of radiation fog

Aggregation in fuzzy system modeling

Single Input Rule Modules (SIRMs) connected fuzzy reasoning method

Some properties of compositional rule of inference

Computation of compositional rule of inference under t-norms

Inverse approximate reasoning

Interpolative fuzzy reasoning

On generalized method-of-case inference rule

Generalized disjunctive syllogism

Ray’s bottom-up inferences

Multidimensional fuzzy reasoning based on multidimensional fuzzy implication

**Fuzzy Reasoning Based on Concept of Similarity**

Introduction

Fuzzy reasoning using similarity

Similarity based fuzzy reasoning method

Rule reduction is SBR

Proposed similarity measure

Fuzzy reasoning using similarity measures and computational rule of inference

Applications to different models

Reasoning based on total fuzzy similarity

Similarity-based bidirectional approximate reasoning

Logical approaches to fuzzy similarity-based reasoning

Fuzzy resolution based on similarity-based unification

**Fuzzy Control**

Introduction

Fuzzy controller

Illustration on basic approaches to fuzzy control

Fuzzy associative memory

Fuzzy controller design

Adaptive fuzzy controller design

Self-tuning of fuzzy controller

Single input rule module (SIRM)

Construction of PID controller by simplified fuzzy reasoning method

Fuzzy control as a fuzzy deduction system

**Concluding Remarks**

Review of the applications and future scope

Index

This two-volume set explains the primary tools of soft computing as well as provides an abundance of working examples and detailed design studies. The books start with coverage of fuzzy sets and fuzzy logic and their various approaches to fuzzy reasoning and go on to discuss several advanced features of soft computing and hybrid methodologies. Together they provide a platform for handling different kinds of uncertainties of real-life problems. It introduces the reader to the topic of rough sets.

The volumes:

• Discuss the present state of art of soft computing

• Include the existing application areas of soft computing

• Present original research contributions

• Discuss the future scope of work in soft computing

This set is unique in that it bridges the gap between theory and practice, and it presents several experimental results on synthetic data and real-life data. The books provide a unified platform for applied scientists and engineers in different fields and industries for the application of soft computing tools in many diverse domains of engineering.

The major theme of the volume is to justify the term soft computing, which is essential to handle the vagueness of the real world. The primary tool of soft computing is well discussed with plenty of worked out examples and design studies. The books can be utilized as a standard textbook on soft computing for final-year undergraduate students, postgraduate students, research scholars, professional researchers, and industry R&D groups. The unique feature of the books is that the author clearly presents the state of art with several worked out examples and case studies based on synthetic data and real-life data. The application domains of soft computing are also clearly indicated.

The volumes can be used as a textbook and/or reference book by undergraduate and postgraduate students of many different engineering branches, such as electrical engineering, control engineering, electronics and communication engineering, computer sciences, and information sciences.

**Volume 1: A Unified Engineering Concept**

**Notion of Soft Computing **

Introduction

Scope for future work

**Fuzzy Sets, Fuzzy Operators and Fuzzy Relations **

Introduction

Fuzzy set

Metrics for fuzzy numbers

Difference in fuzzy set

Distance in fuzzy set

Cartesian product of fuzzy set

Operators on fuzzy set

Other operations in fuzzy set

Geometric interpretation of fuzzy sets

T-operators

Aggregation operators

Probability versus Possibility

Fuzzy event

Uncertainty

Measure of fuzziness

Type-2 fuzzy sets

Relation

**Fuzzy Logic**

Introduction

Preliminaries of logic

Lukasiewicz logic

Fuzzy logic

Fuzzy logic as viewed by Zadeh

Algebric structure in fuzzy logic

Critical appreciations on fuzzy logic

Generating logic for fuzzy set

Fuzzifying non-classical logics

Bridging the gap between fuzzy logic and quantum logic

Futuristic ambitions of fuzzy logic

**Fuzzy Implications and Fuzzy If-Then Models**

Introduction

Syntax and semantics of material implication

Fuzzy modifiers (hedges)

Linguistic truth value

Group decision making based on linguistic decision process

Linguistic assessments and combination of linguistic values

Linguistic preference relations and linguistic choice process

Fuzzy systems as function approximators

Extracting fuzzy rules from sample data points

Fuzzy basis functions

Extracting fuzzy rules from clustering of training samples

Representation of fuzzy IF-THEN rules by petri net

Transformations among various rule based fuzzy models

Losless rule reduction techniques for fuzzy system

Simplification of fuzzy rule base using similarity measure

Qualitative modeling based on fuzzy logic

**Rough Set**

Introduction

Gateway to roughset concept

Approximation spaces and set approximation

Rough membership function

Information systems

Indiscernibility relation

Some further illustration on set approximation

Dependency of attributes

Approximation and accuracy of classification

Reduction of attributes

Discernibility matrices and functions

Significance of attributes and approximate reducts

Decision rule synthesis

Case study: diagnosis of dengue based on rough set concept

Rough sets, Bayes’ rule & multivalued logic

Rough sets and data mining

Index

Volume 2: Fuzzy Reasoning and Fuzzy Control

**Fuzzy Reasoning**

Introduction

Model of approximate reasoning

Basic approach to Zadeh’s fuzzy reasoning

Extended fuzzy reasoning

Further extension of fuzzy reasoning

Generalized form of fuzzy reasoning

Application of fuzzy reasoning for prediction of radiation fog

Aggregation in fuzzy system modeling

Single Input Rule Modules (SIRMs) connected fuzzy reasoning method

Some properties of compositional rule of inference

Computation of compositional rule of inference under t-norms

Inverse approximate reasoning

Interpolative fuzzy reasoning

On generalized method-of-case inference rule

Generalized disjunctive syllogism

Ray’s bottom-up inferences

Multidimensional fuzzy reasoning based on multidimensional fuzzy implication

**Fuzzy Reasoning Based on Concept of Similarity**

Introduction

Fuzzy reasoning using similarity

Similarity based fuzzy reasoning method

Rule reduction is SBR

Proposed similarity measure

Fuzzy reasoning using similarity measures and computational rule of inference

Applications to different models

Reasoning based on total fuzzy similarity

Similarity-based bidirectional approximate reasoning

Logical approaches to fuzzy similarity-based reasoning

Fuzzy resolution based on similarity-based unification

**Fuzzy Control**

Introduction

Fuzzy controller

Illustration on basic approaches to fuzzy control

Fuzzy associative memory

Fuzzy controller design

Adaptive fuzzy controller design

Self-tuning of fuzzy controller

Single input rule module (SIRM)

Construction of PID controller by simplified fuzzy reasoning method

Fuzzy control as a fuzzy deduction system

**Concluding Remarks**

Review of the applications and future scope

Index

The volumes:

• Discuss the present state of art of soft computing

• Include the existing application areas of soft computing

• Present original research contributions

• Discuss the future scope of work in soft computing

**Volume 1: A Unified Engineering Concept**

**Notion of Soft Computing **

Introduction

Scope for future work

**Fuzzy Sets, Fuzzy Operators and Fuzzy Relations **

Introduction

Fuzzy set

Metrics for fuzzy numbers

Difference in fuzzy set

Distance in fuzzy set

Cartesian product of fuzzy set

Operators on fuzzy set

Other operations in fuzzy set

Geometric interpretation of fuzzy sets

T-operators

Aggregation operators

Probability versus Possibility

Fuzzy event

Uncertainty

Measure of fuzziness

Type-2 fuzzy sets

Relation

**Fuzzy Logic**

Introduction

Preliminaries of logic

Lukasiewicz logic

Fuzzy logic

Fuzzy logic as viewed by Zadeh

Algebric structure in fuzzy logic

Critical appreciations on fuzzy logic

Generating logic for fuzzy set

Fuzzifying non-classical logics

Bridging the gap between fuzzy logic and quantum logic

Futuristic ambitions of fuzzy logic

**Fuzzy Implications and Fuzzy If-Then Models**

Introduction

Syntax and semantics of material implication

Fuzzy modifiers (hedges)

Linguistic truth value

Group decision making based on linguistic decision process

Linguistic assessments and combination of linguistic values

Linguistic preference relations and linguistic choice process

Fuzzy systems as function approximators

Extracting fuzzy rules from sample data points

Fuzzy basis functions

Extracting fuzzy rules from clustering of training samples

Representation of fuzzy IF-THEN rules by petri net

Transformations among various rule based fuzzy models

Losless rule reduction techniques for fuzzy system

Simplification of fuzzy rule base using similarity measure

Qualitative modeling based on fuzzy logic

**Rough Set**

Introduction

Gateway to roughset concept

Approximation spaces and set approximation

Rough membership function

Information systems

Indiscernibility relation

Some further illustration on set approximation

Dependency of attributes

Approximation and accuracy of classification

Reduction of attributes

Discernibility matrices and functions

Significance of attributes and approximate reducts

Decision rule synthesis

Case study: diagnosis of dengue based on rough set concept

Rough sets, Bayes’ rule & multivalued logic

Rough sets and data mining

Index

Volume 2: Fuzzy Reasoning and Fuzzy Control

**Fuzzy Reasoning**

Introduction

Model of approximate reasoning

Basic approach to Zadeh’s fuzzy reasoning

Extended fuzzy reasoning

Further extension of fuzzy reasoning

Generalized form of fuzzy reasoning

Application of fuzzy reasoning for prediction of radiation fog

Aggregation in fuzzy system modeling

Single Input Rule Modules (SIRMs) connected fuzzy reasoning method

Some properties of compositional rule of inference

Computation of compositional rule of inference under t-norms

Inverse approximate reasoning

Interpolative fuzzy reasoning

On generalized method-of-case inference rule

Generalized disjunctive syllogism

Ray’s bottom-up inferences

Multidimensional fuzzy reasoning based on multidimensional fuzzy implication

**Fuzzy Reasoning Based on Concept of Similarity**

Introduction

Fuzzy reasoning using similarity

Similarity based fuzzy reasoning method

Rule reduction is SBR

Proposed similarity measure

Fuzzy reasoning using similarity measures and computational rule of inference

Applications to different models

Reasoning based on total fuzzy similarity

Similarity-based bidirectional approximate reasoning

Logical approaches to fuzzy similarity-based reasoning

Fuzzy resolution based on similarity-based unification

**Fuzzy Control**

Introduction

Fuzzy controller

Illustration on basic approaches to fuzzy control

Fuzzy associative memory

Fuzzy controller design

Adaptive fuzzy controller design

Self-tuning of fuzzy controller

Single input rule module (SIRM)

Construction of PID controller by simplified fuzzy reasoning method

Fuzzy control as a fuzzy deduction system

**Concluding Remarks**

Review of the applications and future scope

Index

The volumes:

• Discuss the present state of art of soft computing

• Include the existing application areas of soft computing

• Present original research contributions

• Discuss the future scope of work in soft computing

**Volume 1: A Unified Engineering Concept**

**Notion of Soft Computing **

Introduction

Scope for future work

**Fuzzy Sets, Fuzzy Operators and Fuzzy Relations **

Introduction

Fuzzy set

Metrics for fuzzy numbers

Difference in fuzzy set

Distance in fuzzy set

Cartesian product of fuzzy set

Operators on fuzzy set

Other operations in fuzzy set

Geometric interpretation of fuzzy sets

T-operators

Aggregation operators

Probability versus Possibility

Fuzzy event

Uncertainty

Measure of fuzziness

Type-2 fuzzy sets

Relation

**Fuzzy Logic**

Introduction

Preliminaries of logic

Lukasiewicz logic

Fuzzy logic

Fuzzy logic as viewed by Zadeh

Algebric structure in fuzzy logic

Critical appreciations on fuzzy logic

Generating logic for fuzzy set

Fuzzifying non-classical logics

Bridging the gap between fuzzy logic and quantum logic

Futuristic ambitions of fuzzy logic

**Fuzzy Implications and Fuzzy If-Then Models**

Introduction

Syntax and semantics of material implication

Fuzzy modifiers (hedges)

Linguistic truth value

Group decision making based on linguistic decision process

Linguistic assessments and combination of linguistic values

Linguistic preference relations and linguistic choice process

Fuzzy systems as function approximators

Extracting fuzzy rules from sample data points

Fuzzy basis functions

Extracting fuzzy rules from clustering of training samples

Representation of fuzzy IF-THEN rules by petri net

Transformations among various rule based fuzzy models

Losless rule reduction techniques for fuzzy system

Simplification of fuzzy rule base using similarity measure

Qualitative modeling based on fuzzy logic

**Rough Set**

Introduction

Gateway to roughset concept

Approximation spaces and set approximation

Rough membership function

Information systems

Indiscernibility relation

Some further illustration on set approximation

Dependency of attributes

Approximation and accuracy of classification

Reduction of attributes

Discernibility matrices and functions

Significance of attributes and approximate reducts

Decision rule synthesis

Case study: diagnosis of dengue based on rough set concept

Rough sets, Bayes’ rule & multivalued logic

Rough sets and data mining

Index

Volume 2: Fuzzy Reasoning and Fuzzy Control

**Fuzzy Reasoning**

Introduction

Model of approximate reasoning

Basic approach to Zadeh’s fuzzy reasoning

Extended fuzzy reasoning

Further extension of fuzzy reasoning

Generalized form of fuzzy reasoning

Application of fuzzy reasoning for prediction of radiation fog

Aggregation in fuzzy system modeling

Single Input Rule Modules (SIRMs) connected fuzzy reasoning method

Some properties of compositional rule of inference

Computation of compositional rule of inference under t-norms

Inverse approximate reasoning

Interpolative fuzzy reasoning

On generalized method-of-case inference rule

Generalized disjunctive syllogism

Ray’s bottom-up inferences

Multidimensional fuzzy reasoning based on multidimensional fuzzy implication

**Fuzzy Reasoning Based on Concept of Similarity**

Introduction

Fuzzy reasoning using similarity

Similarity based fuzzy reasoning method

Rule reduction is SBR

Proposed similarity measure

Fuzzy reasoning using similarity measures and computational rule of inference

Applications to different models

Reasoning based on total fuzzy similarity

Similarity-based bidirectional approximate reasoning

Logical approaches to fuzzy similarity-based reasoning

Fuzzy resolution based on similarity-based unification

**Fuzzy Control**

Introduction

Fuzzy controller

Illustration on basic approaches to fuzzy control

Fuzzy associative memory

Fuzzy controller design

Adaptive fuzzy controller design

Self-tuning of fuzzy controller

Single input rule module (SIRM)

Construction of PID controller by simplified fuzzy reasoning method

Fuzzy control as a fuzzy deduction system

**Concluding Remarks**

Review of the applications and future scope

Index

The volumes:

• Discuss the present state of art of soft computing

• Include the existing application areas of soft computing

• Present original research contributions

• Discuss the future scope of work in soft computing

**Volume 1: A Unified Engineering Concept**

**Notion of Soft Computing **

Introduction

Scope for future work

**Fuzzy Sets, Fuzzy Operators and Fuzzy Relations **

Introduction

Fuzzy set

Metrics for fuzzy numbers

Difference in fuzzy set

Distance in fuzzy set

Cartesian product of fuzzy set

Operators on fuzzy set

Other operations in fuzzy set

Geometric interpretation of fuzzy sets

T-operators

Aggregation operators

Probability versus Possibility

Fuzzy event

Uncertainty

Measure of fuzziness

Type-2 fuzzy sets

Relation

**Fuzzy Logic**

Introduction

Preliminaries of logic

Lukasiewicz logic

Fuzzy logic

Fuzzy logic as viewed by Zadeh

Algebric structure in fuzzy logic

Critical appreciations on fuzzy logic

Generating logic for fuzzy set

Fuzzifying non-classical logics

Bridging the gap between fuzzy logic and quantum logic

Futuristic ambitions of fuzzy logic

**Fuzzy Implications and Fuzzy If-Then Models**

Introduction

Syntax and semantics of material implication

Fuzzy modifiers (hedges)

Linguistic truth value

Group decision making based on linguistic decision process

Linguistic assessments and combination of linguistic values

Linguistic preference relations and linguistic choice process

Fuzzy systems as function approximators

Extracting fuzzy rules from sample data points

Fuzzy basis functions

Extracting fuzzy rules from clustering of training samples

Representation of fuzzy IF-THEN rules by petri net

Transformations among various rule based fuzzy models

Losless rule reduction techniques for fuzzy system

Simplification of fuzzy rule base using similarity measure

Qualitative modeling based on fuzzy logic

**Rough Set**

Introduction

Gateway to roughset concept

Approximation spaces and set approximation

Rough membership function

Information systems

Indiscernibility relation

Some further illustration on set approximation

Dependency of attributes

Approximation and accuracy of classification

Reduction of attributes

Discernibility matrices and functions

Significance of attributes and approximate reducts

Decision rule synthesis

Case study: diagnosis of dengue based on rough set concept

Rough sets, Bayes’ rule & multivalued logic

Rough sets and data mining

Index

Volume 2: Fuzzy Reasoning and Fuzzy Control

**Fuzzy Reasoning**

Introduction

Model of approximate reasoning

Basic approach to Zadeh’s fuzzy reasoning

Extended fuzzy reasoning

Further extension of fuzzy reasoning

Generalized form of fuzzy reasoning

Application of fuzzy reasoning for prediction of radiation fog

Aggregation in fuzzy system modeling

Single Input Rule Modules (SIRMs) connected fuzzy reasoning method

Some properties of compositional rule of inference

Computation of compositional rule of inference under t-norms

Inverse approximate reasoning

Interpolative fuzzy reasoning

On generalized method-of-case inference rule

Generalized disjunctive syllogism

Ray’s bottom-up inferences

Multidimensional fuzzy reasoning based on multidimensional fuzzy implication

**Fuzzy Reasoning Based on Concept of Similarity**

Introduction

Fuzzy reasoning using similarity

Similarity based fuzzy reasoning method

Rule reduction is SBR

Proposed similarity measure

Fuzzy reasoning using similarity measures and computational rule of inference

Applications to different models

Reasoning based on total fuzzy similarity

Similarity-based bidirectional approximate reasoning

Logical approaches to fuzzy similarity-based reasoning

Fuzzy resolution based on similarity-based unification

**Fuzzy Control**

Introduction

Fuzzy controller

Illustration on basic approaches to fuzzy control

Fuzzy associative memory

Fuzzy controller design

Adaptive fuzzy controller design

Self-tuning of fuzzy controller

Single input rule module (SIRM)

Construction of PID controller by simplified fuzzy reasoning method

Fuzzy control as a fuzzy deduction system

**Concluding Remarks**

Review of the applications and future scope

Index