Facets of Uncertainties and Applications: ICFUA, Kolkata, India, December 2013 (Springer Proceedings in Mathematics & Statistics Book 125)

Since the emergence of the formal concept of probability theory in the seventeenth century, uncertainty has been perceived solely in terms of probability theory. However, this apparently unique link between uncertainty and probability theory has come under investigation a few decades back. Uncertainties are nowadays accepted to be of various kinds. Uncertainty in general could refer to different sense like not certainly known, questionable, problematic, vague, not definite or determined, ambiguous, liable to change, not reliable. In Indian languages, particularly in Sanskrit-based languages, there are other higher levels of uncertainties. It has been shown that several mathematical concepts such as the theory of fuzzy sets, theory of rough sets, evidence theory, possibility theory, theory of complex systems and complex network, theory of fuzzy measures and uncertainty theory can also successfully model uncertainty. Front Matter....Pages i-xiv Front Matter....Pages 1-1 Rough Sets and Other Mathematics: Ten Research Programs....Pages 3-15 Dealing with Uncertainty: From Rough Sets to Interactive Rough-Granular Computing....Pages 17-32 An Evolutionary Approach to Secondary Membership Function Selection in Generalized Type-2 Fuzzy Sets....Pages 33-50 Specificity Based Defuzzification in Approximate Reasoning....Pages 51-61 Proto-Fuzzy Concepts Generation Technique Using Fuzzy Graph....Pages 63-74 Front Matter....Pages 75-75 Open World Models: A View from Rough Set Theory....Pages 77-86 Approximate Reasoning Under Type-2 Fuzzy Logics....Pages 87-97 Approximation Dialectics of Proto-Transitive Rough Sets....Pages 99-109 Front Matter....Pages 111-111 A Probabilistic Approach to Information System and Rough Set Theory....Pages 113-123 Uncertainty Analysis of Contaminant Transportation Through Ground Water Using Fuzzy-Stochastic Response Surface....Pages 125-134 Development of a Fuzzy Random Health Risk Model....Pages 135-152 Uncertainty Analysis of Retardation Factor Using Monte Carlo, Fuzzy Set and Hybrid Approach....Pages 153-163 Front Matter....Pages 165-165 Two Person Interaction Detection Using Kinect Sensor....Pages 167-176 An Improved Genetic Algorithm and Its Application in Constrained Solid TSP in Uncertain Environments....Pages 177-200 A Novel Soft Theoretic AHP Model for Project Management in Multi-criteria Decision Making Problem....Pages 201-213 An Application of Weighted Neutrosophic Soft Sets in a Decision-Making Problem....Pages 215-223 Approximate Reasoning in Management of Hypertension....Pages 225-233 The Hesitant Fuzzy Soft Set and Its Application in Decision-Making....Pages 235-247 On Fuzzy Ideal Cone Method to Capture Entire Fuzzy Nondominated Set of Fuzzy Multi-criteria Optimization Problems with Fuzzy Parameters....Pages 249-260 A Bi-Objective Solid Transportation Model Under Uncertain Environment....Pages 261-275 Front Matter....Pages 165-165 A Food Web Population Model in Deterministic and Stochastic Environment....Pages 277-292 Computational Method for High-Order Weighted Fuzzy Time Series Forecasting Based on Multiple Partitions....Pages 293-302 Portfolio Selection with Possibilistic Kurtosis....Pages 303-313 Conflicting Bifuzzy Preference Relations Based Method for Multi Criteria Decision Making Problems....Pages 315-323 A Linear Goal Programming Method for Solving Chance-Constrained Multiobjective Problems with Interval Data Uncertainty....Pages 325-343 Part II Logic of UncertaintyOpen World Models: A View from Rough Set Theory; 1 Introduction; 2 Open World Information Systems; 3 A Logic for Open World Information Systems; 3.1 Syntax; 3.2 Semantics; 4 Conclusions; References; Approximate Reasoning Under Type-2 Fuzzy Logics; 1 Introduction; 2 Definition and Basic Concepts; 3 Approximate Reasoning; 3.1 Computational Procedure; 3.2 Similarity Based Approximate Reasoning; 4 Measures of Prediction; 5 Conclusion; References; Approximation Dialectics of Proto-Transitive Rough Sets; 1 Introduction; 2 Approximations and Definite Elements in PRAX 3.1 Approximate Reasoning with Specificity Based Defuzzification4 A Case Study on DC Motor; 5 Conclusion; References; Proto-Fuzzy Concepts Generation Technique Using Fuzzy Graph; 1 Introduction; 2 Mathematical Background--Explanations on the Fundamentals Applied; 2.1 Basics of Fuzzy Logic and Fuzzy Graph; 2.2 Fuzzy Contexts and Fuzzy Concepts; 3 Proposed Fuzzy Graph Based Proto-Fuzzy Concepts Generation Technique; 3.1 Fuzzy Graph Defined for a Formal Context; 3.2 Generation of t-Concepts; 3.3 Proto-Fuzzy Concepts Determination from the Graph of Fuzzy Context; 4 Conclusion; References 5.1 Experimental Environment5.2 Optimization of Objective Function and Constraint to Evaluate Secondary Membership; 5.3 Case Study in Emotion Recognition; 5.4 Relative Performance Analysis; 6 Conclusion; References; Specificity Based Defuzzification in Approximate Reasoning; 1 Introduction; 2 Defuzzification Procedure; 2.1 Center-of-Area/Gravity Defuzzification (COA/COG); 2.2 Center of Sums Defuzzification (COS); 2.3 Height Defuzzification Method (HM); 2.4 Center of Largest Area (COLA); 2.5 First of Maxima (FOM); 2.6 Middle of Maxima (MOM); 3 Specificity Measure--Defuzzification 3.1 Complex Granules and Computations Over Complex Granules3.2 Agent Interactions and Communication Languages; 4 Adaptive Judgment: Toward Efficiency Management in Interactive Computations Over Complex Granules; 5 Conclusions; References; An Evolutionary Approach to Secondary Membership Function Selection in Generalized Type-2 Fuzzy Sets; 1 Introduction; 2 Preliminaries on Type-2 Fuzzy Sets; 3 An Overview of Differential Evolution Algorithm; 3.1 Mutation; 3.2 Crossover; 3.3 Selection; 4 Secondary Membership Evaluation in the Settings of an Optimization Problem; 5 Experiments Preface; Contents; About the Editors; Part I Uncertainty Modelling ; Rough Sets and Other Mathematics: Ten Research Programs; 1 Information from Data and Information as Metaphor; 2 Algebras of Rough Sets; 3 Purely Relational Approximation Operators; 4 Approximation by Means of Neighborhoods; 5 Conclusions; References; Dealing with Uncertainty: From Rough Sets to Interactive Rough-Granular Computing; 1 Introduction; 2 Rough Sets and Uncertainty; 2.1 Uncertainty in Object Perception; 2.2 Uncertainty in Concept Perception; 3 IRGC and Uncertainty