[Studies in Fuzziness and Soft Computing] Recent Developments in Fuzzy Logic and Fuzzy Sets Volume 391 (Dedicated to Lotfi A. Zadeh) ||

This book provides a timely and comprehensive overview of current theories and methods in fuzzy logic, as well as relevant applications in a variety of fields of science and technology. Dedicated to Lotfi A. Zadeh on his one year death anniversary, the book goes beyond a pure commemorative text. Yet, it offers a fresh perspective on a number of relevant topics, such as computing with words, theory of perceptions, possibility theory, and decision-making in a fuzzy environment. Written by Zadeh’s closest colleagues and friends, the different chapters are intended both as a timely reference guide and a source of inspiration for scientists, developers and researchers who have been dealing with fuzzy sets or would like to learn more about their potential for their future research. Contents Fuzziness in Information Extracted from Tweets’ Hashtags and Keywords 1 Introduction 2 Hashtags and Clustering 2.1 Tweet and Hashtags 2.2 Fuzzy Sets 2.3 Fuzzy Clustering 2.4 Cluster Quality and Visualization 3 Collected Data 3.1 Hashtag Data 3.2 Presidential Election 2012 Data 4 Hashtag Data: Analysis of Popularity and Changes 4.1 Popularity Analysis 4.2 Analysis of Changes 5 Analysis of Election Data 5.1 Hashtags and Keywords of Tweets 5.2 Analysis of Tweets 5.3 Party Signatures 5.4 Similarities Between Party Signatures 6 Conclusion References Why Triangular and Trapezoid Membership Functions: A Simple Explanation 1 Ubiquity of Triangular and Trapezoid Membership Functions 2 Main Idea 3 First Formalization and the First Set of Results 4 Second Formalization and the Second Set of Results 5 Proofs References Statistical Approach to Fuzzy Cognitive Maps 1 Introduction 2 Fuzzy Cognitive Maps 3 Statistical Approach to Fuzzy Cognitive Maps 3.1 Stage 1, the Linear Nontransformed FCM Model 3.2 Stage 2, the Transformed FCM Model 3.3 The Liquid Tank Model 4 Conclusions References Probabilistic and More General Uncertainty-Based (e.g., Fuzzy) Approaches to Crisp Clustering Explain the Empirical Success of the K-Sets Algorithm 1 Clustering by Similarity: Formulation of the Practical Problem 2 The Main Idea Behind Clustering-by-Similarity 3 Probabilistic Approach: Towards the Precise Formulation of the Problem 4 Probabilistic Approach: Precise Formulation of the Problem, Resulting Clustering Algorithm, and Their Relation to K-Sets Algorithm and Its Foundations 5 Towards a More General Uncertainty-Based Approach 6 What if We Have Disproportionate Clusters? 7 Disproportionate Clusters: Probabilistic Case 8 Disproportionate Clusters: Case of General Uncertainty 9 Conclusion References Semi-supervised Learning to Rank with Nonlinear Preference Model 1 Introduction 2 Problem Statement 3 Semi-supervized Learning to Rank 3.1 Linear Pointwise Semi-supervised Ranking Learning 3.2 Nonlinear Kernel-Based Pointwise Semi-supervised Ranking Learning 3.3 Pairwise Ranking Learning 4 Learning to Rank Using Aggregated Data 4.1 Ranking Learning on Clusters Problem 4.2 Semi-supervised Clustering in Feature Space 4.3 Recurrent Ranking Learning on Clusters Using Stream Dataset 5 Conclusion References The Concept of Linguistic Variable Revisited 1 Introduction 2 Preliminaries 3 Semantics of Linguistic Expressions 3.1 Possible Worlds, Intension and Extension 3.2 Formalization of the Meaning of Linguistic Expressions 4 Linguistic Variable 4.1 Linguistic Framework 4.2 Evaluative Linguistic Expressions 4.3 Modified Definition of Linguistic Variable 4.4 Fuzzy Numbers 5 Conclusion References On the Z-Numbers 1 Introduction 2 Computation with Z-Numbers 2.1 Sum of Z-Numbers ( Ax ,Rx ) and ( Ay ,Ry ) [1] 2.2 Subtraction of Z-Numbers ( Ax ,Rx ) and ( Ay ,Ry ) [1] 2.3 Multiplication of Z-Numbers ( Ax ,Rx ) and ( Ay ,Ry ) [1] 2.4 Division of Z-Numbers ( Ax ,Rx ) and ( Ay ,Ry ) [1] 3 Ranking of Z-Numbers 3.1 Z-Numbers Ranking Algorithm by Sigmoid Function 3.2 Z-Numbers Ranking Algorithm by Sigmoid Function Based on the Combination of Convex 4 Z-Number Linear Regression (ZLR) Estimates Using Neural Network [5] 4.1 First State 4.2 Second State 5 The Definition of a Derivative-Based Z-Number [11] 5.1 Z-Number Initial Value Problem (ZIVP) 5.2 Numerical Examples (Economics Example) 6 Conclusions References Fuzzy Normed Linear Spaces 1 Introduction 2 Preliminaries 3 Katsaras's Type Fuzzy Norm 4 Felbin's Type Fuzzy Norm 5 Bag-Samanta's Type Fuzzy Norm 6 Convergence in Fuzzy Normed Linear Spaces 7 Fuzzy Continuous Linear Operators in Fuzzy Normed Linear Spaces 8 Conclusions References A Calculation Model of Hierarchical Multiplex Structure with Fuzzy Inference for VRSD Problem 1 Introduction 2 VRSDP/SD Problem and Its Formulation 2.1 Description of the VRSDP/SD Problem 2.2 Constants and Variables in VRSD Problem 2.3 Constraints for VRSD Problem 2.4 Evaluation for VRSDP/SD Problem 2.5 Objectives Solving VRSDP/SD Problem 3 HIMS Calculation Model 3.1 Strategy in Atomic Level of HIMS 3.2 Strategy in Molecular Level 3.3 Fuzzy Inference in Individual Level 3.4 Evaluation and Selection 3.5 The Implementation of HIMS Model 4 Experiments and Discussion 4.1 Experiment (1): Working with All Vehicles 4.2 Experiment (2): Working with just Number 4.3 Analysis of Experimental Results 5 Conclusion References Designing the Researchers’ Management Decision Support System Based on Fuzzy Logic 1 Introduction 2 Modeling of Researchers’ Activity Assessment 3 The Technique for the Assessment of Researchers’ Activity Based on the Fuzzy Relation Model 4 Functional Blocks of Researchers’ Performance Assessment System 5 Conclusion References