Besides well-known "defects", the book introduces and studies new ones, such as: measures of noncompactness for fuzzy sets; fuzzy and intuitionistic entropies; the defect of (sub, super)additivity; complementarity; monotonicity for set functions; the defect of convexity; monotonicity; differentiability for real functions; the defect of equality for inequalities; the defect of orthogonality for sets and defects of properties for linear operators in normed spaces; defects of properties (commutativity, associativity, etc.) for binary operations; defects of orthogonality and parallelness in Euclidean and non-Euclidean geometries; defects of integer, perfect, prime and amicable numbers; the defect of tautology in fuzzy logic.

Contents:

• Defect of Property in Set Theory
• Defect of Property in Topology
• Defect of Property in Measure Theory
• Defect of Property in Real Function Theory
• Defect of Property in Functional Analysis
• Defect of Property in Algebra
• Miscellaneous

"... this is the first book on a comprehensive treatment of defect analysis. It is a well-written book and no doubt will fill a need in the general literature on this topic."

“This book is a good overview of the theory of quantitative characterisations, the introduced concepts are elegant and the methods of proof are (the authors believe) ‘rather’ elementary. This makes the material accessible to undergraduate and graduate students, while researchers may find the new concepts very motivating.”

“This monograph brings a lot of interesting observations, motivation for deeper look on the real fullfilment of several important properties when modelling some practical problem … it is surely a good handbook-like source in general mathematics for all researchers trying to fit their quantitative models to real data.”