In this paper, we present some basic notions of simple ordered semihypergroups and regular ordered Krasner hyperrings and prove some results in this respect. In addition, we describe pure hyperideals of ordered Krasne...In this paper, we present some basic notions of simple ordered semihypergroups and regular ordered Krasner hyperrings and prove some results in this respect. In addition, we describe pure hyperideals of ordered Krasner hyperrings and investigate some properties of them. Finally, some results concerning purely prime hyperideals are proved.展开更多
In this paper, we consider an application of hyperstructure theory in biological inher- itance in which we deal with n-ary hyperstructures associated to the genotypes of the second generation F2 for n ： 2, 3, 4. Firs...In this paper, we consider an application of hyperstructure theory in biological inher- itance in which we deal with n-ary hyperstructures associated to the genotypes of the second generation F2 for n ： 2, 3, 4. First, we define a hyperoperation × （mating） on F2 and prove that it is a cyclic Hv-semigroup under the defined hyperoperation. Then we define a ternary hyperstructure f associated to the genotypes of F2 and prove that （F2, f） is a ternary Hv-semigroup. Finally, we define a 4-ary hyperstructure g associated to the genotypes of F2 and prove that （F2, g） is a 4-ary Hv-semigroup.展开更多
Vougiouklis ＆ Vougiouklis have proposed the replacement of Likert scales, usually used in questionnaires, with a bar. With this proposal a discrete situation is replaced by a fuzzy one. There are identified certain a...Vougiouklis ＆ Vougiouklis have proposed the replacement of Likert scales, usually used in questionnaires, with a bar. With this proposal a discrete situation is replaced by a fuzzy one. There are identified certain advantages concerning the use of the bar as compared to that of a scale during both the stages of filling-in as well as processing a questionnaire. The main advantage associated with business research requirements is the fact that it is expected to be much quicker to fill in and much easier to explain to participants. The bar provides the potential for different types of processing Likert scales cannot. Therefore the researchers are allowed to ascertain that the given answers follow not only the already suggested and used Gauss distribution but also a parabola distribution as it will be suggested in present paper, and which is expected to give the researcher the opportunity to ＂correct＂ this tendency. Therefore, a possibility of choosing amongst a number of alternatives is offered, by utilizing fuzzy logic in the same way as it has already been done in industry and combining mathematical models with multivalued operations.展开更多
The hyperoperations, called theta-operations （δ）, are motivated from the usual property, which the derivative has on the derivation of a product of functions. Using any map on a set, one can define δ-operations. I...The hyperoperations, called theta-operations （δ）, are motivated from the usual property, which the derivative has on the derivation of a product of functions. Using any map on a set, one can define δ-operations. In this paper, we continue our study on the δ-operations on groupoids, rings, fields and vector spaces or on the corresponding hyperstructures. Using δ-operations one obtains, mainly, Hwstructures, which form the largest class of the hyperstructures. For representation theory of hyperstructures, by hypermatrices, one needs special Hv-rings or Hy-fields, so these hyperstructures can be used. Moreover, we study the relation of these δ-structures with other classes of hyperstructures, especially with the Hv-structures.展开更多
Mendel, the father of genetics took the first steps in defining ＂contrasting characters, genotypes in F1 and F2... and setting different laws＂. The genotypes of F2 is dependent on the type of its parents genotype an...Mendel, the father of genetics took the first steps in defining ＂contrasting characters, genotypes in F1 and F2... and setting different laws＂. The genotypes of F2 is dependent on the type of its parents genotype and it follows certain roles. Purpose of this paper is to analyze the second generation genotypes of monohybrid and a dihybrid with a mathematical structure. We use the concept of Hv-semigroup structure in the F2-genotypes with cross oper- ation and prove that this is an Hv-semigroup. We determine the kinds of number of the Hv-subsemigroups of F2-genotypes.展开更多
The concept of an HX-group is an upgrade of the concept of a group,in which a new operation is defined on the family of non-empty subsets of a group.If this new support set together with the new operation is a group,t...The concept of an HX-group is an upgrade of the concept of a group,in which a new operation is defined on the family of non-empty subsets of a group.If this new support set together with the new operation is a group,then we call it an HX-group.On the other hand,a hyperoperation is a mapping having the same codomain as the operation of an HX-group,i.e.,the family of non-empty subsets of the initial set,but a different domain-the set itself.This could be(and was indeed)a source of confusion,which is clarified in this paper.Moreover,HX-groups naturally lead to constructions of hypergroups.The links between these two algebraic concepts are presented,with the aim of reviving the old notion of an HX-group in the current research on algebraic hyperstructures.One of such existing links and one newly established link are also discussed.展开更多
基金supported by a Grant of National Natural Science Foundation of China(Grant Nos.11461025and 11561023)
文摘In this paper, we present some basic notions of simple ordered semihypergroups and regular ordered Krasner hyperrings and prove some results in this respect. In addition, we describe pure hyperideals of ordered Krasner hyperrings and investigate some properties of them. Finally, some results concerning purely prime hyperideals are proved.
文摘In this paper, we consider an application of hyperstructure theory in biological inher- itance in which we deal with n-ary hyperstructures associated to the genotypes of the second generation F2 for n ： 2, 3, 4. First, we define a hyperoperation × （mating） on F2 and prove that it is a cyclic Hv-semigroup under the defined hyperoperation. Then we define a ternary hyperstructure f associated to the genotypes of F2 and prove that （F2, f） is a ternary Hv-semigroup. Finally, we define a 4-ary hyperstructure g associated to the genotypes of F2 and prove that （F2, g） is a 4-ary Hv-semigroup.
文摘Vougiouklis ＆ Vougiouklis have proposed the replacement of Likert scales, usually used in questionnaires, with a bar. With this proposal a discrete situation is replaced by a fuzzy one. There are identified certain advantages concerning the use of the bar as compared to that of a scale during both the stages of filling-in as well as processing a questionnaire. The main advantage associated with business research requirements is the fact that it is expected to be much quicker to fill in and much easier to explain to participants. The bar provides the potential for different types of processing Likert scales cannot. Therefore the researchers are allowed to ascertain that the given answers follow not only the already suggested and used Gauss distribution but also a parabola distribution as it will be suggested in present paper, and which is expected to give the researcher the opportunity to ＂correct＂ this tendency. Therefore, a possibility of choosing amongst a number of alternatives is offered, by utilizing fuzzy logic in the same way as it has already been done in industry and combining mathematical models with multivalued operations.
文摘The hyperoperations, called theta-operations （δ）, are motivated from the usual property, which the derivative has on the derivation of a product of functions. Using any map on a set, one can define δ-operations. In this paper, we continue our study on the δ-operations on groupoids, rings, fields and vector spaces or on the corresponding hyperstructures. Using δ-operations one obtains, mainly, Hwstructures, which form the largest class of the hyperstructures. For representation theory of hyperstructures, by hypermatrices, one needs special Hv-rings or Hy-fields, so these hyperstructures can be used. Moreover, we study the relation of these δ-structures with other classes of hyperstructures, especially with the Hv-structures.
文摘Mendel, the father of genetics took the first steps in defining ＂contrasting characters, genotypes in F1 and F2... and setting different laws＂. The genotypes of F2 is dependent on the type of its parents genotype and it follows certain roles. Purpose of this paper is to analyze the second generation genotypes of monohybrid and a dihybrid with a mathematical structure. We use the concept of Hv-semigroup structure in the F2-genotypes with cross oper- ation and prove that this is an Hv-semigroup. We determine the kinds of number of the Hv-subsemigroups of F2-genotypes.
基金The first author acknowledges the financial support from the Slovenian Research Agency(research core funding No.P1-0285)The second author was supported by the FEKT-S-17-4225 grant of Brno University of Technology.
文摘The concept of an HX-group is an upgrade of the concept of a group,in which a new operation is defined on the family of non-empty subsets of a group.If this new support set together with the new operation is a group,then we call it an HX-group.On the other hand,a hyperoperation is a mapping having the same codomain as the operation of an HX-group,i.e.,the family of non-empty subsets of the initial set,but a different domain-the set itself.This could be(and was indeed)a source of confusion,which is clarified in this paper.Moreover,HX-groups naturally lead to constructions of hypergroups.The links between these two algebraic concepts are presented,with the aim of reviving the old notion of an HX-group in the current research on algebraic hyperstructures.One of such existing links and one newly established link are also discussed.
