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2 results on '"i-octahedron ideal"'

1. Octahedron Subgroups and Subrings

Author

Jeong-Gon Lee, Young Bae Jun, and Kul Hur

Subjects
octahedron set, i-octahedron subgroupoid, i-octahedron ideal, i-sup-property, i-octahedron subgroup, i-octahedron subring, Mathematics, QA1-939
Abstract

In this paper, we define the notions of i-octahedron groupoid and i-OLI [resp., i-ORI and i-OI], and study some of their properties and give some examples. Also we deal with some properties for the image and the preimage of i-octahedron groupoids [resp., i-OLI, i-ORI and i-OI] under a groupoid homomorphism. Next, we introduce the concepts of i-octahedron subgroup and normal subgroup of a group and investigate some of their properties. In particular, we obtain a characterization of an i-octahedron subgroup of a group. Finally, we define an i-octahedron subring [resp., i-OLI, i-ORI and i-OI] of a ring and find some of their properties. In particular, we obtain two characterizations of i-OLI [resp., i-ORI and i-OI] of a ring and a skew field, respectively.

Published
2020
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2. Fuzzy Sets, Fuzzy Logic and Their Applications 2020.

Author

Voskoglou, Michael and Voskoglou, Michael

Subjects
Mathematics & science, Research & information: general, B-spline surface model function, Bayesian probabilities, FAHP, FCOPRAS, FTOPSIS, GEFS, Hyers-Ulam stability, RDM fuzzy arithmetic, SEFS, Schauder fixed point theorem, alternative fixed point theorem, bipolar fuzzy topology, bipolar gradation of closedness, bipolar gradation of openness, bipolar gradation preserving map, defuzzification, distance measure, dynamic random access memory, embedding method, entropy, fuzzification, fuzzy AHP, fuzzy TOPSIS, fuzzy arithmetic, fuzzy calculus, fuzzy collaborative forecasting, fuzzy difference equations, fuzzy differential equations, fuzzy implication, fuzzy intersection, fuzzy linear system, fuzzy logic, fuzzy logic (FL), fuzzy logic connectives, fuzzy max-T algebra, fuzzy measures, fuzzy nonlinear systems, fuzzy normed linear space, fuzzy number, fuzzy number vector, fuzzy parametric form, fuzzy relations: fuzzy sets, fuzzy set, fuzzy soft set, fuzzy statistics, governance, hexagonal fuzzy number, homomorphism of graph products, i-octahedron ideal, i-octahedron subgroupoid, i-octahedron subring, i-sup-property, i-octahedron subgroup, inductive and deductive reasoning, information measure, interval eigenvector, interval matrix, interval-valued fuzzy competition graph, interval-valued fuzzy neighbourhood graph, interval-valued fuzzy p competition graph, interval-valued m-step fuzzy competition graph, intuitionistic fuzzy normed spaces, law of importation, least fuzzy negation, linguistic terms for fuzzy variable, management system, max-min algebra, max-min composition, max-Łukasiewicz algebra, measure of non-compactness, min-max composition, mixed continuous-discrete model, monotone measures, monotone statistical parameters, multi-fuzzy set, multi-fuzzy soft set, multidimensional fuzzy arithmetic, neutrosophic set, octahedron set, ordering property, parametric solvability, partial consensus, pexider type functional equation, plithogenic set, probability and statistics, product spaces, scientific method, shopping mall site selection, similarity measure, similarity measure of ℒℳℱ??, site selection, soft set, strong interval eigenvector, strongly generalized Hukuhara differentiability, t-conditionality, t-norm, time value of money, type-2 fuzzy set, type-reduction, Łukasiewicz triangular norm, α-migrativity, ℒℳℱ??
Abstract

Summary: The present book contains the 24 total articles accepted and published in the Special Issue "Fuzzy Sets, Fuzzy Logic and Their Applications, 2020" of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity.

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