Bijan Davvaz
Yazd University
[ 1 ] - Cat$^1$-polygroups and pullback cat$^1$-polygroups
In this paper, we give the notions of crossed polymodule and cat$^1$-polygroup as a generalization of Loday's definition. Then, we define the pullback cat$^1$-polygroup and we obtain some results in this respect. Specially, we prove that by a pullback cat$^1$-polygroup we can obtain a cat$^1$-group.
[ 2 ] - On nilpotent and solvable polygroups
Applications of hypergroups have mainly appeared in special subclasses. One of the important subclasses is the class of polygroups. In this paper, we study the notions of nilpotent and solvable polygroups by using the notion of heart of polygroups. In particular, we give a necessary and sufficient condition between nilpotent (solvable) polygroups and fundamental groups.
[ 3 ] - Application of fundamental relations on n-ary polygroups
The class of $n$-ary polygroups is a certain subclass of $n$-ary hypergroups, a generalization of D{"o}rnte $n$-arygroups and a generalization of polygroups. The$beta^*$-relation and the $gamma^*$-relation are the smallestequivalence relations on an $n$-ary polygroup $P$ such that$P/beta^*$ and $P/gamma^*$ are an $n$-ary group and acommutative $n$-ary group, respectively. We use the $beta^*$-...
[ 4 ] - NEW TYPES OF FUZZY n-ARY SUBHYPERGROUPS OF AN n-ARY HYPERGROUP
In this paper, the new notions of ``belongingness ($in_{gamma}$)"and ``quasi-coincidence ($q_delta$)" of a fuzzy point with a fuzzyset are introduced. By means of this new idea, the concept of$(alpha,beta)$-fuzzy $n$-ary subhypergroup of an $n$-aryhypergroup is given, where $alpha,betain{in_{gamma}, q_{delta},in_{gamma}wedge q_{delta}, ivq}$, andit is shown that, in 16 kinds of $(alpha,beta...
[ 5 ] - Fuzzy $h$-ideal of Matrix Hemiring $S_{2}=left( begin{array}{cc} R & Gamma S & L end{array} right)$
The purpose of this paper is to study matrix hemiring $S_{2}$ via fuzzy subsets and fuzzy $h$-ideals.
[ 6 ] - ATANASSOV'S INTUITIONISTIC FUZZY GRADE OF I.P.S. HYPERGROUPS OF ORDER LESS THAN OR EQUAL TO 6
In this paper we determine the sequences of join spaces and Atanassov's intuitionistic fuzzy sets associated with all i.p.s. hypergroups of order less than or equal to 6, focusing on the calculation of their lengths.
[ 7 ] - FUZZY ORDERED SETS AND DUALITY FOR FINITE FUZZY DISTRIBUTIVE LATTICES
The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley space...
[ 9 ] - ON ($epsilon, epsilon vee q$)-FUZZY IDEALS OF BCI-ALGEBRAS
The aim of this paper is to introduce the notions of ($epsilon, epsilon vee q$)-fuzzy p-ideals, ($epsilon, epsilon vee q$)-fuzzy q-ideals and ($epsilon, epsilon vee q$)-fuzzy a-ideals in BCIalgebras and to investigate some of their properties. Several characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of BCI-algebras i...
[ 10 ] - ON ( $alpha, beta$ )-FUZZY Hv-IDEALS OF H_{v}-RINGS
Using the notion of “belongingness ($epsilon$)” and “quasi-coincidence (q)” of fuzzy points with fuzzy sets, we introduce the concept of an ($ alpha, beta$)- fuzzyHv-ideal of an Hv-ring, where , are any two of {$epsilon$, q,$epsilon$ $vee$ q, $epsilon$ $wedge$ q} with $ alpha$ $neq$ $epsilon$ $wedge$ q. Since the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy Hv-ideals is an important and ...
[ 11 ] - GENERALIZED FUZZY POLYGROUPS
small Polygroups are multi-valued systems that satisfy group-likeaxioms. Using the notion of “belonging ($epsilon$)” and “quasi-coincidence (q)” offuzzy points with fuzzy sets, the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy subpolygroups isintroduced. The study of ($epsilon$, $epsilon$ $vee$ q)-fuzzy normal subpolygroups of a polygroupare dealt with. Characterization and some of the fundam...
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