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Solvable groups derived from fuzzy hypergroups

E Mohammadzadeh, T Nozari
<span title="">2015</span> <span class="release-stage">unpublished</span>
In this paper we introduce the smallest equivalence relation ξ * on a finite fuzzy hypergroup S such that the quotient group S/ξ * , the set of all equivalence classes, is a solvable group.  ...  The characterization of solvable groups via strongly regular relation is investigated and several results on the topic are presented.  ...  ξ * on a finite fuzzy hypergroup S such that H/ξ * is a solvable group.  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180424220421/http://eiris.it/ojs/index.php/ratiomathematica/article/viewFile/22/pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/5e/80/5e8092723741a5bb5dccaace26b354f729b44a60.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a>

Solvable groups derived from fuzzy hypergroups

E Mohammadzadeh, T Nozari
<span title="">2015</span> <i > RATIO MATHEMATICA </i> &nbsp; <span class="release-stage">unpublished</span>
In this paper we introduce the smallest equivalence relation ξ * on a finite fuzzy hypergroup S such that the quotient group S/ξ * , the set of all equivalence classes, is a solvable group.  ...  The characterization of solvable groups via strongly regular relation is investigated and several results on the topic are presented.  ...  ξ * on a finite fuzzy hypergroup S such that H/ξ * is a solvable group.  ... 
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Results on (Engel, Solvable, Nilpotent) Fuzzy Subpolygroups

ELAHE MOHAMMADZADEH, Faculty of Science, Payame Noor University, RAJAB ALI BORZOOEI, Shahid Beheshti University, Tehran, Iran
<span title="">2021</span> <i title="University Library in Kragujevac"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tnomswj7izf5lokp2km2nwvsai" style="color: black;">Kragujevac Journal of Mathematics</a> </i> &nbsp;
Finally we investigate the relations among solvable and nilpotent fuzzy subpolygroups with Engel fuzzy subpolygroups.  ...  Furthermore, we introduce the notions of solvable and nilpotent fuzzy subpolygroups and we get some of their properties.  ...  Moreover, we obtain a necessary and sufficient condition between solvable fuzzy subpolygroups and the solvable group P/ ∼, the group of equivalence classes derived from a fuzzy subpolygroup of P .  ... 
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Page 3290 of Mathematical Reviews Vol. , Issue 2000e [page]

<span title="">2000</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
He shows that every solvable group contains a solvable fuzzy subgroup and that every fuzzy subgroup of a solvable group is solvable.  ...  (ET-ZAGS; Zagazig) Restudy of fuzzy factor groups and fuzzy solvable groups. (English summary) J. Fuzzy Math. 7 (1999), no. 2, 311-320.  ... 
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On $\alpha$-solvable fundamental groups

F. Mohammadzadeh, Elahe Mohammadzadeh
<span title="2021-05-01">2021</span> <i title="CMV Verlag"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/r76eippidfeu5de6zqxnuakree" style="color: black;">Journal of Algebraic Hyperstructures and Logical Algebras</a> </i> &nbsp;
We introduce a specific kind of equivalence relation ξ * α n on a fuzzy hypergroup S such that the quotient S/ξ * α n , the set of all equivalence classes, is an α-solvable group.  ...  This helps us to introduce the α-solvable fundamental relation ξ * α . In particular, we obtain an equivalent condition with transitivity of ξ α . Article Information  ...  Characterization of α-solvable groups via a fuzzy strongly regular relation We introduce a new fuzzy strongly regular relation on an FHG such that the quotient group is an α-solvable group.  ... 
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Investigate Of Fuzzy Semi-simple Lie Algebra

A. Taleshian, F. Khaniani, A. A. Hosseinzadeh
<span title="2010-12-25">2010</span> <i title="International Scientific Research Publications MY SDN. BHD."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bmhn5xzzqzfevooumwiffmuzfm" style="color: black;">Journal of Mathematics and Computer Science</a> </i> &nbsp;
In this paper we have tried apply the concepts of fuzzy set to lie algebras and fuzzy ideals of lie algebras in order to provide suitable conditions to introduce the solvable fuzzy ideals, we use zadeh's  ...  extension principle the aim of this paper is to introduce and study new definition for fuzzy lie algebras and fuzzy semi-simple of lie algebras.  ...  Introduction The notion of a fuzzy subset of a nonempty set was introduced by zadeh [5] . So Rosenfeld introduced the concept of a fuzzy subgroup of a group [4] .  ... 
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Length functions and fuzzy groups

Markku Niemenmaa
<span title="">1987</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7a65khxirfbfljbnqng5zzeslu" style="color: black;">Journal of Mathematical Analysis and Applications</a> </i> &nbsp;
Since the class of finite solvable groups contains, e.g., the class of finite cyclic groups, Theorem 4.1 is a generalization of Theorem 3.4 of Das [Z]. LEMMA 1.1 (Das[2, p. 265-j).  ...  INTRODUCTION Fuzzy sets were introduced by Zadeh [7] in 1965 and fuzzy groups by Rosenfeld [4] in 1971.  ... 
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At-least At-most Modifications in a Space with Fuzzy Preoreder

Irina Perfilieva
<span title="">2013</span> <i title="Atlantis Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/q47jwxc36zhozejiwja7mtgcsu" style="color: black;">Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology</a> </i> &nbsp;
Keywords: monotonous fuzzy rule base, system of fuzzy relation equations, "at least" ("at most") quantifiers, fuzzy preorder, criterion of solvability Abstract In this paper, we utilize the theory of solvability  ...  of systems of fuzzy relation equations in a space with fuzzy preorder and propose a justification of solvability of systems that are modified with "at least" ("at most") quantifiers.  ...  Irrespective of the used composition, the obtained results can be divided into two groups: the first containing solvability criteria (see [3-6, 9, 12, 14-16] ), and the second containing various characterizations  ... 
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E-fuzzy groups

Branka Budimirović, Vjekoslav Budimirović, Branimir Šešelja, Andreja Tepavčević
<span title="">2016</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wcbukkuh2vbrpcbz2f4z2a2g6u" style="color: black;">Fuzzy sets and systems (Print)</a> </i> &nbsp;
We prove basic features of E -fuzzy groups: properties of the unit and inverses, cancellability, solvability of equations, subgroup properties and others.  ...  Tepavčević E-Fuzzy Groups Abstract Abstract An E -fuzzy group is a lattice-valued algebraic structure, defined on a crisp algebra which is not necessarily a group.  ...  Tepavčević E-Fuzzy Groups  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200321092244/http://www.math.sk/fsta2014/presentations/BudimirovicBudimirovicSeseljaTepavcevic.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/9a/fb/9afbc7661d3570336031650791c8bf2a3624a6e9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.fss.2015.03.011"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Page 4402 of Mathematical Reviews Vol. , Issue 94h [page]

<span title="">1994</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Summary: “Solvability of fuzzy groups is defined and the concept is tested for various fuzzy groups.  ...  fuzzy groups.  ... 
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Page 5154 of Mathematical Reviews Vol. , Issue 2004g [page]

<span title="">2004</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
(CZ-OSUN-FZM: Ostrava); Gottwald, Siegfried (D-LEIP-LP: Leipzig Solvability and approximate solvability of fuzzy relation equations. (English summary) Fuzzy logic in systems modelling. Int. J. Gen.  ...  Summary: “We give a discussion of approximate solvability of a system of fuzzy relation equations.  ... 
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Page 938 of Mathematical Reviews Vol. , Issue 2002B [page]

<span title="">2002</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
is solvable.  ...  Since any finite loop Q with solvable multiplication group M(Q) is a solvable loop the author finally obtains the following theorem: A finite loop Q whose inner mapping group /(Q) has order 2p where p  ... 
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Page 196 of Mathematical Reviews Vol. , Issue 97A [page]

<span title="">1997</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
In this paper, 20 GROUP THEORY AND GENERALIZATIONS 196 the author shows that if Q is finite and M(Q) is solvable, then Q is solvable. (The converse is false; there is a counterexample of order 10.)  ...  Robinson (1-GAIT; Atlanta, GA) 97a:20115 20N05 20D10 20F16 Vesanen, Ari (FIN-OUL; Oulu) Solvable groups and loops. J. Algebra 180 (1996), no. 3, 862-876.  ... 
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Page 1781 of Mathematical Reviews Vol. , Issue 2000c [page]

<span title="">2000</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Summary: “Using the concept of fuzzy spaces, we study fuzzy rings, fuzzy ideals and fuzzy ring homomorphisms. The fuzzy quotient ring is introduced by using fuzzy ideals.  ...  (By a result of Kukin in the 1970s every solvable Lie algebra with a countable set of generators can be embedded in a 2-generated solvable Lie algebra [G. P.  ... 
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Page 39 of Mathematical Reviews Vol. , Issue 92a [page]

<span title="">1992</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
:05002 criteria of solvability are satisfied.  ...  Next, some types of fuzzy relation equations are studied and the problems of solvability are considered.” 92a:04010 04A72 03B52 Perfil‘eva, I. G. Applications of the theory of fuzzy sets.  ... 
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