The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Ayesha Rafiq - One of the best experts on this subject based on the ideXlab platform.
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on γ interval valued fuzzification of lagrange s theorem of γ interval valued fuzzy subGroups
IEEE Access, 2020Co-Authors: Umer Shuaib, Abdul Razaq, Hanan Alolaiyan, Muhammad Shahram Saif, Ayesha RafiqAbstract:In this paper, we present the idea of interval valued fuzzy subGroup defined over a certain t-conorm ( $\mathrm {\Gamma }$ -IVFSG) and prove that every IVFSG is $\mathrm {\Gamma }$ -IVFSG. We use this ideology to define the concepts of $\Gamma $ -IVF cosets, $\mathrm {\Gamma }$ -IVFNSG and formulate their various important algebraic characteristics. We also propose the study of the notion of level subGroups of $\mathrm {\Gamma }$ -IVFSG and investigate the condition under which a $\mathrm {\Gamma }$ -IVFS is $\Gamma $ -IVFSG. Moreover, we extend the study of this phenomenon to introduce the concept of Quotient Group of a Group $Z$ relative to the $\Gamma $ -IVFNSG and acquire a correspondence between each $\Gamma $ -IVF(N)SG of a Group $Z$ and $\Gamma $ -IVF(N)SG of its Quotient Group. Furthermore, we define the index of $\Gamma $ -IVFSG and establish the $\Gamma $ -interval valued fuzzification of Lagrange’s theorem of any $\Gamma $ -IVFSG of a finite Group $Z$ .
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On Γ-Interval Valued Fuzzification of Lagrange’s Theorem of Γ-Interval Valued Fuzzy SubGroups
IEEE Access, 2020Co-Authors: Umer Shuaib, Abdul Razaq, Hanan Alolaiyan, Muhammad Shahram Saif, Ayesha RafiqAbstract:In this paper, we present the idea of interval valued fuzzy subGroup defined over a certain t-conorm ( $\mathrm {\Gamma }$ -IVFSG) and prove that every IVFSG is $\mathrm {\Gamma }$ -IVFSG. We use this ideology to define the concepts of $\Gamma $ -IVF cosets, $\mathrm {\Gamma }$ -IVFNSG and formulate their various important algebraic characteristics. We also propose the study of the notion of level subGroups of $\mathrm {\Gamma }$ -IVFSG and investigate the condition under which a $\mathrm {\Gamma }$ -IVFS is $\Gamma $ -IVFSG. Moreover, we extend the study of this phenomenon to introduce the concept of Quotient Group of a Group $Z$ relative to the $\Gamma $ -IVFNSG and acquire a correspondence between each $\Gamma $ -IVF(N)SG of a Group $Z$ and $\Gamma $ -IVF(N)SG of its Quotient Group. Furthermore, we define the index of $\Gamma $ -IVFSG and establish the $\Gamma $ -interval valued fuzzification of Lagrange’s theorem of any $\Gamma $ -IVFSG of a finite Group $Z$ .
Umer Shuaib - One of the best experts on this subject based on the ideXlab platform.
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Algebraic Characteristics of Anti-Intuitionistic Fuzzy SubGroups Over a Certain Averaging Operator
IEEE Access, 2020Co-Authors: Dilshad Alghazzawi, Umer Shuaib, Tazeem Fatima, Abdul Razaq, Muhammad Ahsan BinyaminAbstract:In this paper, we propose the concept of $\rho $ anti-intuitionistic fuzzy sets, $\rho $ anti - intuitionistic fuzzy subGroups and prove some of their algebraic properties. We investigate a necessary and sufficient condition for a $\rho $ -anti intuitionistic fuzzy set to be a $\rho $ -anti intuitionistic fuzzy subGroup. We extend this ideology by defining the notions of $\rho $ anti-intuitionistic fuzzy coset, $\rho $ anti-intuitionistic fuzzy normal subGroup and derive some of their key algebraic characteristics. In addition, we study the Quotient Group of a Group induced by $\rho $ -anti intuitionistic fuzzy normal subGroup and establish a Group isomorphism between this newly defined Quotient Group and the Quotient Group of Group $G$ relative to its particular normal subGroup $G_{S_{\rho }}$ .
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on γ interval valued fuzzification of lagrange s theorem of γ interval valued fuzzy subGroups
IEEE Access, 2020Co-Authors: Umer Shuaib, Abdul Razaq, Hanan Alolaiyan, Muhammad Shahram Saif, Ayesha RafiqAbstract:In this paper, we present the idea of interval valued fuzzy subGroup defined over a certain t-conorm ( $\mathrm {\Gamma }$ -IVFSG) and prove that every IVFSG is $\mathrm {\Gamma }$ -IVFSG. We use this ideology to define the concepts of $\Gamma $ -IVF cosets, $\mathrm {\Gamma }$ -IVFNSG and formulate their various important algebraic characteristics. We also propose the study of the notion of level subGroups of $\mathrm {\Gamma }$ -IVFSG and investigate the condition under which a $\mathrm {\Gamma }$ -IVFS is $\Gamma $ -IVFSG. Moreover, we extend the study of this phenomenon to introduce the concept of Quotient Group of a Group $Z$ relative to the $\Gamma $ -IVFNSG and acquire a correspondence between each $\Gamma $ -IVF(N)SG of a Group $Z$ and $\Gamma $ -IVF(N)SG of its Quotient Group. Furthermore, we define the index of $\Gamma $ -IVFSG and establish the $\Gamma $ -interval valued fuzzification of Lagrange’s theorem of any $\Gamma $ -IVFSG of a finite Group $Z$ .
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On Γ-Interval Valued Fuzzification of Lagrange’s Theorem of Γ-Interval Valued Fuzzy SubGroups
IEEE Access, 2020Co-Authors: Umer Shuaib, Abdul Razaq, Hanan Alolaiyan, Muhammad Shahram Saif, Ayesha RafiqAbstract:In this paper, we present the idea of interval valued fuzzy subGroup defined over a certain t-conorm ( $\mathrm {\Gamma }$ -IVFSG) and prove that every IVFSG is $\mathrm {\Gamma }$ -IVFSG. We use this ideology to define the concepts of $\Gamma $ -IVF cosets, $\mathrm {\Gamma }$ -IVFNSG and formulate their various important algebraic characteristics. We also propose the study of the notion of level subGroups of $\mathrm {\Gamma }$ -IVFSG and investigate the condition under which a $\mathrm {\Gamma }$ -IVFS is $\Gamma $ -IVFSG. Moreover, we extend the study of this phenomenon to introduce the concept of Quotient Group of a Group $Z$ relative to the $\Gamma $ -IVFNSG and acquire a correspondence between each $\Gamma $ -IVF(N)SG of a Group $Z$ and $\Gamma $ -IVF(N)SG of its Quotient Group. Furthermore, we define the index of $\Gamma $ -IVFSG and establish the $\Gamma $ -interval valued fuzzification of Lagrange’s theorem of any $\Gamma $ -IVFSG of a finite Group $Z$ .
M Woronowicz - One of the best experts on this subject based on the ideXlab platform.
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A torsion-free abelian Group of finite rank exists whose Quotient Group modulo the square subGroup is not a nil-Group
Quaestiones Mathematicae, 2017Co-Authors: R R Andruszkiewicz, M WoronowiczAbstract:The first example of a finite rank torsion-free abelian Group A such that the Quotient Group of A modulo the square subGroup of A is not a nil-Group is indicated (in both cases of associative and g...
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a torsion free abelian Group exists whose Quotient Group modulo the square subGroup is not a nil Group
Bulletin of The Australian Mathematical Society, 2016Co-Authors: R R Andruszkiewicz, M WoronowiczAbstract:The first example of a torsion-free abelian Group such that the Quotient Group of modulo the square subGroup is not a nil-Group is indicated (for both associative and general rings). In particular, the answer to the question posed by Stratton and Webb [‘Abelian Groups, nil modulo a subGroup, need not have nil Quotient Group’, Publ. Math. Debrecen 27 (1980), 127–130] is given for torsion-free Groups. A new method of constructing indecomposable nil-Groups of any rank from to is presented. Ring multiplications on -pure subGroups of the additive Group of the ring of -adic integers are investigated using only elementary methods.
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A torsion-free abelian Group exists whose Quotient Group modulo the square subGroup is not a \(nil\)-Group
Bulletin of the Australian Mathematical Society, 2016Co-Authors: R R Andruszkiewicz, M WoronowiczAbstract:The first example of a torsion-free abelian Group $(A,+,0)$ such that the Quotient Group of $A$ modulo the square subGroup is not a nil-Group is indicated (for both associative and general rings). In particular, the answer to the question posed by Stratton and Webb [‘Abelian Groups, nil modulo a subGroup, need not have nil Quotient Group’, Publ. Math. Debrecen 27 (1980), 127–130] is given for torsion-free Groups. A new method of constructing indecomposable nil-Groups of any rank from $2$ to $2^{\aleph _{0}}$ is presented. Ring multiplications on $p$ -pure subGroups of the additive Group of the ring of $p$ -adic integers are investigated using only elementary methods.
Abdul Razaq - One of the best experts on this subject based on the ideXlab platform.
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Algebraic Characteristics of Anti-Intuitionistic Fuzzy SubGroups Over a Certain Averaging Operator
IEEE Access, 2020Co-Authors: Dilshad Alghazzawi, Umer Shuaib, Tazeem Fatima, Abdul Razaq, Muhammad Ahsan BinyaminAbstract:In this paper, we propose the concept of $\rho $ anti-intuitionistic fuzzy sets, $\rho $ anti - intuitionistic fuzzy subGroups and prove some of their algebraic properties. We investigate a necessary and sufficient condition for a $\rho $ -anti intuitionistic fuzzy set to be a $\rho $ -anti intuitionistic fuzzy subGroup. We extend this ideology by defining the notions of $\rho $ anti-intuitionistic fuzzy coset, $\rho $ anti-intuitionistic fuzzy normal subGroup and derive some of their key algebraic characteristics. In addition, we study the Quotient Group of a Group induced by $\rho $ -anti intuitionistic fuzzy normal subGroup and establish a Group isomorphism between this newly defined Quotient Group and the Quotient Group of Group $G$ relative to its particular normal subGroup $G_{S_{\rho }}$ .
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on γ interval valued fuzzification of lagrange s theorem of γ interval valued fuzzy subGroups
IEEE Access, 2020Co-Authors: Umer Shuaib, Abdul Razaq, Hanan Alolaiyan, Muhammad Shahram Saif, Ayesha RafiqAbstract:In this paper, we present the idea of interval valued fuzzy subGroup defined over a certain t-conorm ( $\mathrm {\Gamma }$ -IVFSG) and prove that every IVFSG is $\mathrm {\Gamma }$ -IVFSG. We use this ideology to define the concepts of $\Gamma $ -IVF cosets, $\mathrm {\Gamma }$ -IVFNSG and formulate their various important algebraic characteristics. We also propose the study of the notion of level subGroups of $\mathrm {\Gamma }$ -IVFSG and investigate the condition under which a $\mathrm {\Gamma }$ -IVFS is $\Gamma $ -IVFSG. Moreover, we extend the study of this phenomenon to introduce the concept of Quotient Group of a Group $Z$ relative to the $\Gamma $ -IVFNSG and acquire a correspondence between each $\Gamma $ -IVF(N)SG of a Group $Z$ and $\Gamma $ -IVF(N)SG of its Quotient Group. Furthermore, we define the index of $\Gamma $ -IVFSG and establish the $\Gamma $ -interval valued fuzzification of Lagrange’s theorem of any $\Gamma $ -IVFSG of a finite Group $Z$ .
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On Γ-Interval Valued Fuzzification of Lagrange’s Theorem of Γ-Interval Valued Fuzzy SubGroups
IEEE Access, 2020Co-Authors: Umer Shuaib, Abdul Razaq, Hanan Alolaiyan, Muhammad Shahram Saif, Ayesha RafiqAbstract:In this paper, we present the idea of interval valued fuzzy subGroup defined over a certain t-conorm ( $\mathrm {\Gamma }$ -IVFSG) and prove that every IVFSG is $\mathrm {\Gamma }$ -IVFSG. We use this ideology to define the concepts of $\Gamma $ -IVF cosets, $\mathrm {\Gamma }$ -IVFNSG and formulate their various important algebraic characteristics. We also propose the study of the notion of level subGroups of $\mathrm {\Gamma }$ -IVFSG and investigate the condition under which a $\mathrm {\Gamma }$ -IVFS is $\Gamma $ -IVFSG. Moreover, we extend the study of this phenomenon to introduce the concept of Quotient Group of a Group $Z$ relative to the $\Gamma $ -IVFNSG and acquire a correspondence between each $\Gamma $ -IVF(N)SG of a Group $Z$ and $\Gamma $ -IVF(N)SG of its Quotient Group. Furthermore, we define the index of $\Gamma $ -IVFSG and establish the $\Gamma $ -interval valued fuzzification of Lagrange’s theorem of any $\Gamma $ -IVFSG of a finite Group $Z$ .
Hartmut Führ - One of the best experts on this subject based on the ideXlab platform.
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Hausdorff--Young Inequalities for Group Extensions
Canadian Mathematical Bulletin, 2006Co-Authors: Hartmut FührAbstract:AbstractThis paper studies Hausdorff–Young inequalities for certain Group extensions, by use of Mackey's theory. We consider the case in which the dual action of the Quotient Group is free almost everywhere. This result applies in particular to yield a Hausdorff–Young inequality for nonunimodular Groups.
