Young Bae Jun
Department of Mathematics Education, Gyeong sang National university, Chinju, Korea
[ 1 ] - Results on Engel Fuzzy Subgroups
In the classical group theory there is an open question: Is every torsion free n-Engel group (for n ≥ 4), nilpotent?. To answer the question, Traustason [11] showed that with some additional conditions all 4-Engel groups are locally nilpotent. Here, we gave some partial answer to this question on Engel fuzzy subgroups. We show that if μ is a normal 4-Engel fuzzy subgroup of ...
[ 2 ] - More General Forms of $(alpha, beta )$-fuzzy Ideals of Ordered Semigroups
This paper consider the general forms of $(alpha,beta)$-fuzzyleft ideals (right ideals, bi-ideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. Special attention is paid to$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interiorideals) and some related pr...
[ 3 ] - Ordered semigroups characterized by their intuitionistic fuzzy bi-ideals
Fuzzy bi-ideals play an important role in the study of ordered semigroupstructures. The purpose of this paper is to initiate and study theintiuitionistic fuzzy bi-ideals in ordered semigroups and investigate thebasic theorem of intuitionistic fuzzy bi-ideals. To provide thecharacterizations of regular ordered semigroups in terms of intuitionisticfuzzy bi-ideals and to discuss the relationships ...
[ 4 ] - Some types of $(in,ivq)$-interval-valued fuzzy ideals of BCI algebras
In this paper, we introduce the notions of interval-valued and $(in,ivq)$-interval-valued fuzzy ($p$-,$q$- and $a$-) ideals of BCI algebras and investigate some of their properties. We then derive characterization theorems for these generalized interval-valued fuzzy ideals and discuss their relationship.
[ 5 ] - IDEALS OF PSEUDO MV-ALGEBRAS BASED ON VAGUE SET THEORY
The notion of vague ideals in pseudo MV-algebras is introduced,and several properties are investigated. Conditions for a vague set to be avague ideal are provided. Conditions for a vague ideal to be implicative aregiven. Characterizations of (implicative, prime) vague ideals are discussed.The smallest vague ideal containing a given vague set is established. Primeand implicative extension proper...
[ 6 ] - APPLICATIONS OF SOFT SETS IN HILBERT ALGEBRAS
The concept of soft sets, introduced by Molodtsov [20] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. In this paper, weapply the notion of the soft sets of Molodtsov to the theory of Hilbert algebras.The notion of soft Hilbert (abysmal and deductive) algebras, soft subalgebras,soft abysms and sof...
[ 7 ] - ABSORBENT ORDERED FILTERS AND THEIR FUZZIFICATIONS IN IMPLICATIVE SEMIGROUPS
The notion of absorbent ordered filters in implicative semigroupsis introduced, and its fuzzification is considered. Relations among (fuzzy) orderedfilters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicativeordered filters are stated. The extensionproperty for (fuzzy) absorbent orderedfilters is established. Conditions for (fuzzy) ordered filters to be (fuzzy)absorbent ordered ...
[ 8 ] - 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...
[ 9 ] - REDEFINED FUZZY SUBALGEBRAS OF BCK/BCI-ALGEBRAS
Using the notion of anti fuzzy points and its besideness to and nonquasi-coincidence with a fuzzy set, new concepts in anti fuzzy subalgebras in BCK/BCI-algebras are introduced and their properties and relationships are investigated.
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