ENGLISH

Uncertainty Data in Interval-valued Fuzzy Set Theory

By Barbara Pękala

Book information

Publisher
Springer
Year
2019
ISBN
978-3-319-93910-0
Language
english
Format
PDF
Filesize
1 MB (1554568 bytes)
Pages
187\187
Time added
2018-10-18 09:20:29

Description

Preface......Page 3 Contents......Page 8 1 Intro to Fuzzy Sets......Page 10 Fuzzy Sets......Page 11 Fuzzy Negations......Page 14 Basic Operations on Fuzzy Sets......Page 15 Triangular Norms......Page 17 Aggregation Functions......Page 18 Extensions of Fuzzy Sets......Page 20 Interval-valued Fuzzy Sets......Page 21 Atanassov Intuitionistic Fuzzy Sets......Page 26 2 Interval-Valued Fuzzy Relations......Page 30 Interval Orders......Page 31 Interval-valued Fuzzy Negation......Page 33 Interval-valued Aggregation Functions......Page 34 Interval-valued Ordered Weighted Averaging Operator......Page 41 Interval-valued Fuzzy Implication with Respect to Partial or Linear Order......Page 43 Atanassov Operators......Page 44 Basic Properties of the Composition......Page 46 Powers of Interval-valued Fuzzy Relations......Page 54 Properties of Interval-valued Fuzzy Relations......Page 57 Class of Equivalent Interval-valued Fuzzy Relations......Page 59 Other Properties of Interval-valued Fuzzy Relations......Page 72 Possible & Necessary Comparability Relations......Page 78 Possible & Necessary Aggregation Functions......Page 85 Possible & Necessary Properties of Interval-valued Fuzzy Relations......Page 87 Transitive Closures......Page 91 3 Applications......Page 99 Decision Making Problem......Page 100 Preferences......Page 104 Construction of Interval-valued Preference Structure......Page 111 N-Reciprocity. Generalized Reciprocity......Page 115 Preservation of N-Reciprocity by different Operations......Page 117 Transitivity Properties & N-Reciprocity......Page 122 Approximate Reasoning......Page 137 General Modus Ponens Property......Page 139 Method for Inference in Approximate Reasoning based on Interval-valued Fuzzy Sets & their Characteristics......Page 146 Problem Description......Page 149 2-Fuzzification. Construction of Intervals from Ignorance Function......Page 150 Inference. Rule Base......Page 152 2-Deffuzzification......Page 155 Analyzing Behaviour of different Aggregation Functions when accomplishing Inference Process......Page 156 Studying Effect of Aggregation Functions in the whole System......Page 157 Reference to other Methods......Page 158 4 Summary & open Problems......Page 160 Appendix Codes......Page 164 Refs......Page 172 Index......Page 185

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