Note: Intro -- Preface -- Acknowledgements -- Contents -- 1 Matrix Games with Interval Payoffs -- 1.1 Matrix Games with Interval Payoffs -- 1.2 Existing Mathematical Formulation of Matrix Games with Interval Payoffs -- 1.3 Literature Review of Matrix Game with Interval Payoffs -- 1.4 Arithmetic Operations over Intervals -- 1.5 Flaws of the Existing Methods -- 1.6 Invalidity of Existing Mathematical Formulation of Matrix Games with Interval Payoffs -- 1.6.1 Existing Method to Obtain Mathematical Formulation of Matrix Games with Interval Payoffs -- 1.6.2 Mathematically Incorrect Assumptions Considered in the Existing Method -- 1.7 Minimum and Maximum of Intervals -- 1.7.1 Minimum of Intervals -- 1.7.2 Maximum of Intervals -- 1.8 Proposed Gaurika Method -- 1.8.1 Minimum Expected Gain of Player I -- 1.8.2 Maximum Expected Loss of Player II -- 1.9 Numerical Examples -- 1.9.1 Existing Numerical Example Considered by Nayak and Pal -- 1.9.2 Existing Numerical Example Considered by Li et al. -- 1.10 Conclusion -- References -- 2 Matrix Games with Fuzzy Payoffs -- 2.1 Matrix Games with Fuzzy Payoffs -- 2.2 Preliminaries -- 2.2.1 Some Basic Definitions -- 2.2.2 Arithmetic Operations of Trapezoidal Fuzzy Numbers -- 2.2.3 Comparison of Fuzzy Numbers -- 2.3 Existing Mathematical Formulation of Matrix Games with Fuzzy Payoffs -- 2.4 Literature Review of Matrix Games with Fuzzy Payoffs -- 2.5 Flaws of the Existing Methods -- 2.6 Invalidity of Existing Mathematical Formulation of Matrix Games with Fuzzy Payoffs -- 2.7 Proposed Mehar Method -- 2.7.1 Minimum Expected Gain of Player I -- 2.7.2 Maximum Expected Loss of Player II -- 2.8 Numerical Example -- 2.8.1 Minimum Expected Gain of Player I -- 2.8.2 Maximum Expected Loss of Player II -- 2.9 Conclusion -- References -- 3 Constrained Matrix Games with Fuzzy Payoffs -- 3.1 Constrained Matrix Games with Fuzzy Payoffs. , 3.2 Existing Mathematical Formulation of Constrained Matrix Games with Fuzzy Payoffs -- 3.3 Literature Review of Constrained Matrix Games with Fuzzy Payoffs -- 3.4 Flaws of the Existing Methods -- 3.5 Proposed Vaishnavi Method -- 3.5.1 Minimum Expected Gain of Player I -- 3.5.2 Maximum Expected Loss of Player II -- 3.6 Numerical Examples -- 3.6.1 Existing Numerical Example Considered by Li and Hong -- 3.6.2 Existing Numerical Example Considered by Li and Cheng -- 3.7 Conclusion -- References -- 4 Matrix Games with Intuitionistic Fuzzy Payoffs -- 4.1 Matrix Games with Intuitionistic Fuzzy Payoffs -- 4.2 Preliminaries -- 4.2.1 Basic Definitions -- 4.2.2 Arithmetic Operations over Trapezoidal Vague Sets -- 4.3 Existing Mathematical Formulation of Matrix Games with Intuitionistic Fuzzy Payoffs -- 4.4 Literature Review of Matrix Games with Intuitionistic Fuzzy Payoffs -- 4.5 Flaws of the Existing Methods -- 4.6 Proposed Ambika Methods -- 4.6.1 Ambika Method-I -- 4.6.2 Ambika Method-II -- 4.6.3 Ambika Method-III -- 4.6.4 Ambika Method-IV -- 4.7 Numerical Examples -- 4.7.1 Existing Numerical Example Considered by Nan et al. -- 4.7.2 Existing Numerical Example Considered by Li et al. -- 4.7.3 Existing Numerical Example Considered by Nan et al. -- 4.7.4 Existing Numerical Example Considered by Nan et al. -- 4.8 Conclusion -- References -- 5 Bimatrix Games with Intuitionistic Fuzzy Payoffs -- 5.1 The Difference-Index Based Ranking Method -- 5.2 Maximum of Trapezoidal Intuitionistic Fuzzy Numbers -- 5.3 Flaws in the Existing Mathematical Formulation of Bimatrix Games with Intuitionistic Fuzzy Payoffs -- 5.3.1 Mathematical Formulation of Bimatrix Games with Intuitionistic Fuzzy Payoffs -- 5.3.2 Mathematically Incorrect Assumption Considered by Li and Yang -- 5.4 Exact Solution of Bimatrix Games with Intuitionistic Fuzzy Payoffs. , 5.4.1 Exact Mathematical Formulation of Bimatrix Games with Intuitionistic Fuzzy Payoffs -- 5.4.2 Proposed Mehar Method -- 5.4.3 Convergence of the Proposed Mehar Method -- 5.5 Numerical Example -- 5.6 Conclusion -- References -- 6 Future Scope -- References.

Note: Intro -- Contents -- Preface -- Chapter 1 -- Introduction and Applications of Microbial Products in the Food Processing Industry -- Abstract -- 1. Aspartase -- 2. Asparaginase -- 3. Naringinase -- 4. Inulinases -- 5. Pullulanases -- 6. Proteases -- 7. Cellulases, Xylanases and Pectinase -- 8. Laccase -- 9. Microbial Polysaccharides -- 10. Amylase -- 11. Microbial Pigments -- 12. Lipase -- 13. Organic Acids -- Conclusion -- References -- Chapter 2 -- Microbial Inulinases and Pullulanases in the Food Industry -- Abstract -- 1. Introduction -- 2. Inulinases -- 3. Microbial Inulinase Producers -- 4. Applications of Inulinases -- 4.1. High Fructose Syrup -- 4.2. Fructooligosaccharides (FOSs) -- 4.3. Miscellaneous Applications -- 5. Pullulanases -- 6. Microbial Sources of Pullulanases -- 7. Applications of Pullulanases -- 7.1. Starch Saccharification -- 7.2. Preparation of Resistant Starch -- 7.3. As an Antistaling Agent in Bakery Products -- 7.4. Miscellaneous Applications -- Conclusion -- References -- Chapter 3 -- The Role of Microbial Proteases in Food Industry: Recent Trends and Future Perspectives -- Abstract -- 1. Introduction -- 2. Classification of Microbial Proteases -- 2.1. Serine Proteases -- 2.1.1. Chymotrypsin-Like protesases -- 2.1.2. Subtilisin-Like serine proteases -- 2.2. Aspartate Proteases -- 2.3. Cysteine Proteases/Thiol Proteases -- 2.4. Metalloproteases -- 2.5. Threonine Proteases -- 2.6. Glutamic Acid Proteases -- 3. Sources of Proteases -- 3.1. Animal Proteases -- 3.2. Plant Proteases -- 3.3. Microbial Proteases -- 4. Protease Production from Microbes -- 5. Downstream Processing -- 6. Improving Protease Performance for Industrial Applications -- 6.1. Enzyme Immobilization -- 6.2. Improving Protease Performance by Directed Evolution and Protein Engineering -- 7. Protease Assay. , 8. Applications of Proteases in Food Industry -- 8.1. Baking Industry -- 8.2. Dairy Industry -- 8.3. Meat Industry -- 8.4. Hydrolysis of Soybean Protein -- 8.5. Beverage Industry -- 9. Miscellaneous Applications of Proteases -- 10. Future Perspectives -- References -- Chapter 4 -- Laccases: A Polyphenol Oxidase for the Fruit Processing Industry -- Abstract -- 1. Introduction -- 2. Inducers for Fungal Laccase: Properties and Activity -- 3. Polyphenol Oxidase -- 3.1. Laccase -- 3.2. Catechol Oxidase -- 3.3. Tyrosinase -- 4. Laccase Applications -- 5. Laccase in Fruit Processing Industry -- 6. Problem of Enzymatic Browning in Fruit Juice -- 7. Prevention of Enzymatic Browning -- 7.1. Fruit Juice Stabilization by Elimination/Transformation of Phenolic Compounds Using Free Laccase -- 7.2. Fruit Juice Stabilization by Elimination/Transformation of Phenolic Compounds Using Immobilized Laccase -- 7.3. Inactivation of Natural Polyphenol Oxidase -- Conclusion -- References -- Chapter 5 -- α-Amylase: Microbial Sources, Production and Applications in the Food Processing Industry -- Abstract -- 1. Introduction -- 2. Broad Categories of Amylases -- 3. Microbial sources of α-amylase -- 4. Microbial Production of α-Amylase -- 5. Applications ofα-Amylase in Food Industry -- 6. Applications of Amylases in Other Industries -- 6.1. Starch Hydrolysis -- 6.2. Inhibition and Removal of Staphylococcus aureus Biofilms by Use of Alpha-Amylase -- 6.3. Paper Industry and Textile Industry -- 6.4. Detergent Industry -- 6.5. Fuel Alcohol Production -- Acknowledgment -- References -- Chapter 6 -- Food Industry Based Applications of Cellulases, Xylanases and Pectinases -- Abstract -- 1. Introduction -- 2. Cellulases, Xylanases -- and Pectinases Production -- 3. Applications of Cellulases, Xylanases and Pectinases -- 3.1. Cellulases, Xylanases and Pectinases in Food Industry. , 3.1.1. Fruit and Vegetable Juices Extraction and Clarification -- 3.1.2. Improvement of Aroma and Volatile Properties Fruits and Vegetables -- 3.1.3. Improvement of Bakery Products Quality -- 3.1.4. Oil Extraction -- 3.1.5. Improved Tea and Coffee Fermentation -- 3.2. Lignocellulolytic Enzymes in Animal Feed Industry -- 3.3. Lignocellulolytic Enzymes in Beer and Wine Industry -- Conclusion -- References -- Chapter 7 -- Microbial Pigments as Potent Bicolor and Their Applications in Food Industries -- Abstract -- 1. Introduction -- 2. Microbial Pigments -- 3. Role of Pigments in Living Organism -- 3.1. Role of Pigments in Microbes -- 3.2. Role of Pigments in Animals -- 3.3. Role of Pigments in Plants -- 3.4. Pigments as Indicators of Pollution -- 3.5. Pigments in Disease Control and Human Health -- 4. Classification of Pigments -- 4.1. Types and Classes of Microbial Pigments -- 4.1.1. On the Basis of Origin -- 4.1.2. On the Basis of Color -- 4.1.3. On the Basis of Solubility -- 4.1.4. On the Basis of Production -- 5. Advantages of Microbial Pigments over Synthetic Pigments -- 6. Substrates for Production of Microbial Pigments -- 7. Extraction and Characterization of Microbial Pigments -- 8. Application of Biocolors -- 8.1. Pharmaceutical Industry -- 8.2. Pigments in Food and Nutrition -- 8.3. Textile Industry -- 8.4. Nutritional Supplements -- 8.5. Printing Industry -- 8.6. Food Colorants -- 8.7. Bio-Indicators -- 9. Future Perspective and Scope of Advancement of Microbial Pigments -- Conclusion -- References -- Chapter 8 -- The Role of Microbial Polysaccharides in the Food Industry -- Abstract -- 1. Introduction -- 2. Xanthan Gum -- 3. Pullulan -- 4. Curdlan -- 5. Gellan -- 6. Alginates -- 7. Dextran -- 8. Bacterial Cellulose -- 9. Role of Different Microbial Polysaccharides in Food Processing -- 9.1. Xanthan Gum -- 9.2. Pullulan -- 9.3. Curdlan. , 9.4. Gellan -- 9.5. Alginate -- 9.6. Dextran -- 9.7. Bacterial Cellulose -- Conclusion -- References -- Chapter 9 -- Organic Acids: Microbial Sources, Production and Applications -- Abstract -- 1. Introduction -- 2. Microbial Sources and Production of Organic Acids -- 3. Applications of Organic Acids in Food Industry -- References -- Chapter 10 -- Aspartase, Asparaginase and Naringinase: Current Status and Perspectives for the Food Industry -- Abstract -- 1. Introduction -- 2. Aspartase -- 2.1. Aspartase Producing Bacterial Strains -- 2.2. Production of Microbial Aspartase -- 2.3. Applications of Aspartase in Food Industry -- 3. Asparaginase -- 3.1. Microbial Sources of Asparaginase -- 3.2. Applications of Asparaginase in Food Industries -- 4. Naringinase -- 4.1. Naringin: A Flavonoid -- 4.2. Naringin Hydrolysis -- 4.3. Production of Naringinase -- 4.4. Application of Naringinase in Food Industry -- 5. Future Perspectives -- References -- About the Editors -- Index -- Blank Page.

Note: Intro -- Contents -- 1 Introduction -- 1.1 A Brief Literature Review -- 1.2 Outline of the Book -- References -- 2 A Brief Introduction to Fuzzy Sets -- 2.1 Basic Definitions and Properties of Fuzzy Sets -- 2.2 Basic Set-Theoretic Operations on Fuzzy Sets -- 2.3 Fuzzy Relations -- 2.4 Fuzzy Numbers and Fuzzy Arithmetic -- 2.5 Fuzzy Events and Their Probabilities -- 2.6 Defuzzification of Fuzzy Sets -- References -- 3 A Brief Introduction to Fuzzy Optimization and Fuzzy Mathematical Programming -- 3.1 Introductory Remarks -- 3.2 Main Approaches to Fuzzy Optimization -- 3.3 Bellman and Zadeh's General Approach to Decision Making Under Fuzziness -- 3.4 Using the α-cuts of the Fuzzy Feasible Set -- 3.5 Fuzzy Mathematical Programming -- 3.6 Fuzzy Linear Programming -- 3.7 Fuzzy Linear Programming with Fuzzy Constraints -- 3.8 Fuzzy Coefficients in the Objective Function -- 3.9 Fuzzy Coefficients in the Technological Matrix -- References -- 4 New Methods for Solving Fully Fuzzy Transportation Problems with Trapezoidal Fuzzy Parameters -- 4.1 Preliminaries -- 4.1.1 Basic Definitions Related to Fuzzy Numbers -- 4.1.2 Arithmetic Operations on the Trapezoid Fuzzy Numbers -- 4.2 A Fuzzy Linear Programming Formulation of the Balanced Fully Fuzzy Transportation Problem -- 4.3 Existing Methods for Finding a Fuzzy Optimal Solution of the Fully Fuzzy Transportation Problem -- 4.4 Liu and Kao's Method -- 4.4.1 Fully Fuzzy Transportation Problems with the Inequality Constraints -- 4.4.2 Fully Fuzzy Transportation Problems with Equality Constraints -- 4.5 A Critical Analysis of the Existing Methods -- 4.6 On Some New Methods for Solving the Fully Fuzzy Transportation Problem -- 4.6.1 A New Method Based on a Fuzzy Linear Programming Formulation -- 4.6.2 Method Based on the Tabular Representation -- 4.6.3 Advantages of the Proposed Methods over the Existing Methods. , 4.7 An Illustrative Example -- 4.7.1 Fuzzy Optimal Solution Using the Method Based on Fuzzy Linear Programming Formulation -- 4.7.2 Fuzzy Optimal Solution Using the Method Based on Tabular Representation -- 4.7.3 Interpretation of Results -- 4.8 Case Study -- 4.8.1 Description of the Problem -- 4.8.2 Results Obtained -- 4.8.3 Interpretation of Results -- 4.9 Concluding Remarks -- References -- 5 New Methods for Solving the Fully Fuzzy Transportation Problems with the LR Flat Fuzzy Numbers -- 5.1 Preliminaries -- 5.2 Basic Definitions -- 5.3 Arithmetic Operations on the LR Flat Fuzzy Numbers -- 5.4 Solution of the Fully Fuzzy Transportation Problems with Parameters Represented by the LR Fuzzy Numbers or LR Flat Fuzzy Numbers -- 5.5 New Methods -- 5.5.1 Method Based on Fuzzy Linear Programming -- 5.5.2 Method Based on the Tabular Representation -- 5.5.3 Main Advantages of the Proposed Methods -- 5.6 Illustrative Example -- 5.6.1 Determination of the Fuzzy Optimal Solution Using the Method Based on the Fuzzy Linear Programming -- 5.6.2 Determination of the Fuzzy Optimal Solution Using the Method Based on the Tabular Representation -- 5.6.3 Interpretation of Results -- 5.7 A Comparative Study -- 5.8 Concluding Remarks -- References -- 6 New Improved Methods for Solving the Fully Fuzzy Transshipment Problems with Parameters Given as the LR Flat Fuzzy Numbers -- 6.1 Fuzzy Linear Programming Formulation of the Balanced Fully Fuzzy Transshipment Problems -- 6.2 Outline of the Ghatee and Hashemi Method -- 6.3 On Some Limitations of the Existing Methods -- 6.4 New Methods -- 6.4.1 New Method Based on the Fuzzy Linear Programming Formulation -- 6.4.2 New Method Based on the Tabular Representation -- 6.4.3 Advantages of the New Methods -- 6.5 Illustrative Example. , 6.5.1 Determination of the Optimal Solution Using the Method Based on the Fuzzy Linear Programming Formulation -- 6.5.2 Determination of the Optimal Solution Using the Method Based on the Tabular Representation -- 6.5.3 Interpretation of Results -- 6.6 A Comparative Study -- 6.7 A Case Study -- 6.8 Concluding Remarks -- References -- 7 New Methods for Solving Fully Fuzzy Solid Transportation Problems with LR Fuzzy Parameters -- 7.1 Fuzzy Linear Programming Formulation of the Balanced Fully Fuzzy Solid Transportation Problems -- 7.2 Liu and Kao's Method -- 7.3 Some Shortcomings of Liu and Kao's Method -- 7.4 Limitations of the Methods Proposed in the Previous Chapters -- 7.5 New Methods -- 7.5.1 New Method Based on the Fuzzy Linear Programming Formulation -- 7.5.2 New Method Based on the Tabular Representation -- 7.5.3 Advantages of the New Methods -- 7.6 Illustrative Example -- 7.6.1 Determination of the Fuzzy Optimal Solution Using the New Method Based on the Fuzzy Linear Programming Formulation -- 7.6.2 Determination of the Fuzzy Optimal Solution Using the New Method Based on the Tabular Representation -- 7.6.3 Interpretation of Results -- 7.7 A Comparative Study -- 7.8 A Case Study -- 7.8.1 Problem Description -- 7.8.2 Results -- 7.8.3 Interpretation of Results -- 7.9 Concluding Remarks -- References -- 8 New Methods for Solving Fully Fuzzy Solid Transshipment Problems with LR Flat Fuzzy Numbers -- 8.1 New Fuzzy Linear Programming Formulation of the Balanced Fully Fuzzy Solid Transshipment Problem -- 8.2 Limitations of the Existing Method and Methods Proposed in Previous Chapters -- 8.3 New Methods -- 8.3.1 New Method Based on the Fuzzy Linear Programming Formulation -- 8.3.2 New Method Based on the Tabular Representation -- 8.3.3 Advantages of the New Methods -- 8.4 Illustrative Example. , 8.4.1 Determination of the Fuzzy Optimal Solution of the Fully Fuzzy Solid Transshipment Problem Using the Method Based on the Fuzzy Linear Programming Formulation -- 8.4.2 Determination of the Fuzzy Optimal Solution of the Fully Fuzzy Solid Transshipment Problem Using the Method Based on the Tabular Representation -- 8.4.3 Interpretation of Results -- 8.5 A Comparison of Results Obtained -- 8.6 Concluding Remarks -- References -- 9 Conclusions and Future Research Directions -- References.