Fuzzy Mathematics

doi:10.3390/books978-3-03897-323-2

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Fuzzy Mathematics

Edited by

November 2018

286 pages

ISBN978-3-03897-322-5 (Paperback)
ISBN978-3-03897-323-2 (PDF)

https://doi.org/10.3390/books978-3-03897-323-2

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This book is a reprint of the Special Issue Fuzzy Mathematics that was published in

Computer Science & Mathematics

Engineering

Physical Sciences

Public Health & Healthcare

Summary

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems.

The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value.

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Keywords

generalized bipolar fuzzy (BF) semigroup; (α₁, α₂; β₁, β₂)-bipolar fuzzy subsemigroup; fuzzy quasi(generalized bi-, bi-) ideal; regular semigroup; hyperfuzzy set; hyperfuzzy subalgebra; hyperfuzzy ideal; hyperfuzzy set; hyperfuzzy subalgebra; length of hyperfuzzy set; length-fuzzy subalgebra; fuzzy system of linear equations (FSLEs); iterative schemes; strong and weak solutions; Hausdorff; fuzzy tensor product Bézier surface; fuzzy parametric curves; fuzzy iso-parametric curves; degree elevation algorithm; De Casteljau’s algorithm; hesitant fuzzy set; hesitant probabilistic fuzzy linguistic set; score and accuracy function; multi-criteria group decision making; aggregation operator; credibility measure; intuitionistic fuzzy variables; expected value; entropy; fuzzy incidence graphs; t-norms; connectedness; paths; cycles; trees; bridges; cutpairs; N-structure; (extended) N-hyper set; N-substructure of types 1, 2, 3, 4; entropy measure; (R,S)-norm; multi attribute decision-making; information measures; attribute weight; intuitionistic fuzzy sets; fuzzy semi-metric space; T₁-space; triangle inequality; triangular norm; pattern classification; fuzzy sets; perceptron; artificial neural networks; Lotfi A. Zadeh; Frank Rosenblatt; roughness; generalized roughness; LA-semigroup; interval-valued intuitionistic fuzzy set; intuitionistic fuzzy set; modal operator; prudence; optimal allocation; possibilistic moments; fuzzy set; interval-valued fuzzy set; “intuitionistic” fuzzy set; “pythagorean” fuzzy set; isomorphic lattices; truth values