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Fuzzy Mathematics

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ISBN: 9783038973225 9783038973232 Year: Pages: 286 DOI: 10.3390/books978-3-03897-323-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General) --- Mathematics
Added to DOAB on : 2018-11-28 11:26:53
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Abstract

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.

Discrete Mathematics and Symmetry

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ISBN: 9783039281909 9783039281916 Year: Pages: 458 DOI: 10.3390/books978-3-03928-191-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2020-04-07 23:07:08
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Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group.

Keywords

strongly regular graph --- automorphism group --- orbit matrix --- binary polyhedral group --- icosahedron --- dodecahedron --- 600-cell --- Electric multiple unit trains --- high-level maintenance planning --- time window --- 0–1 programming model --- particle swarm algorithm --- fixed point --- split-quaternion --- quadratic polynomial --- split-octonion --- neutrosophic set --- neutrosophic rough set --- pessimistic (optimistic) multigranulation neutrosophic approximation operators --- complete lattice --- rough set --- matroid --- operator --- attribute reduction --- graded rough sets --- rough intuitionistic fuzzy sets --- dominance relation --- logical conjunction operation --- logical disjunction operation --- multi-granulation --- planar point set --- convex polygon --- disjoint holes --- fuzzy logic --- pseudo-BCI algebra --- quasi-maximal element --- KG-union --- quasi-alternating BCK-algebra --- quality function deployment --- engineering characteristics --- group decision making --- 2-tuple --- metro station --- emergency routes --- graph partitioning --- graph clustering --- invariant measures --- partition comparison --- finite automorphism groups --- graph automorphisms --- Fuzzy sets --- ring --- normed space --- fuzzy normed ring --- fuzzy normed ideal --- fuzzy implication --- quantum B-algebra --- q-filter --- quotient algebra --- basic implication algebra --- Detour–Harary index --- maximum --- unicyclic --- bicyclic --- cacti --- three-way decisions --- intuitionistic fuzzy sets --- multi-granulation rough intuitionistic fuzzy sets --- granularity importance degree --- complexity --- Chebyshev polynomials --- gear graph --- pyramid graphs --- edge detection --- Laplacian operation --- regularization --- parameter selection --- performance evaluation --- aggregation operator --- triangular norm --- ?-convex set --- atom-bond connectivity index --- geometric arithmetic index --- line graph --- generalized bridge molecular graph --- graceful labeling --- edge graceful labeling --- edge even graceful labeling --- polar grid graph --- graph --- good drawing --- crossing number --- join product --- cyclic permutation --- nonlinear --- synchronized --- linear discrete --- chaotic system --- algorithm --- generalized permanental polynomial --- coefficient --- co-permanental --- isoperimetric number --- random graph --- intersection graph --- social network --- Abel–Grassmann’s groupoid (AG-groupoid) --- Abel–Grassmann’s group (AG-group) --- involution AG-group --- commutative group --- filter --- graceful labeling --- edge even graceful labeling --- cylinder grid graph --- selective maintenance --- multi-state system --- human reliability --- optimization --- genetic algorithm --- hypernear-ring --- multitransformation --- embedding --- distance matrix (spectrum) --- distance signlees Laplacian matrix (spectrum) --- (generalized) distance matrix --- spectral radius --- transmission regular graph --- graph --- good drawing --- crossing number --- join product --- cyclic permutation --- cyclic associative groupoid (CA-groupoid) --- cancellative --- variant CA-groupoids --- decomposition theorem --- construction methods

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