On Intuitionistic Fuzzy Sets TheoryThis book aims to be a comprehensive and accurate survey of state-of-art research on intuitionistic fuzzy sets theory and could be considered a continuation and extension of the author ́s previous book on Intuitionistic Fuzzy Sets, published by Springer in 1999 (Atanassov, Krassimir T., Intuitionistic Fuzzy Sets, Studies in Fuzziness and soft computing, ISBN 978-3-7908-1228-2, 1999). Since the aforementioned book has appeared, the research activity of the author within the area of intuitionistic fuzzy sets has been expanding into many directions. The results of the author ́s most recent work covering the past 12 years as well as the newest general ideas and open problems in this field have been therefore collected in this new book. |
Contents
| 1 | |
Operations and Relations over IFSs | 17 |
Geometrical Interpretations of IFSs | 37 |
Modal and Topological Operators Defined over IFSs | 53 |
Extended Modal Operators | 77 |
Other Types of Operators | 112 |
Norms and Metrics over IFSs or Their Elements | 133 |
Other editions - View all
Common terms and phrases
algorithms asterisk Atanassov Axiom bijective bpr,qs Cartesian product cells commutative monoid construct Conway's Game criteria defined definitions discussed elements equality estimations evaluation example experts extended modal operators Fa,ß fA(x fixed Fuzzy Sets Theory geometrical interpretation given graph Ha,ß IF-interpretation IFSs IFTree IFTS implications and negations Insg(A introduced intuitionistic fuzzy implications intuitionistic fuzzy negations Intuitionistic Fuzzy Sets intuitionistic logic Ja,ß logic max(a max(VA(x measurement tool membership and non-membership min(a min(b min(µA(x modal logic modal operators natural number norms Notes on Intuitionistic obtain Obviously Open problem ordinary fuzzy sets pairs placed on square range(A real numbers respectively satisfy Section separate squares sg(a sg(VA(x subtraction Table Theorem three IFSS topological operators transformation triangle Trifon Trifonov VA(x VA(y values VB(x vc(x Vi,j Vi,k µA(x µB(x µE(X µi,j