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ROUGH PRIME IDEALS AND ROUGH FUZZY PRIME IDEALS IN GAMMA-SEMIGROUPS
Chinram, Ronnason Korean Mathematical Society 2009 대한수학회논문집 Vol.24 No.3
The notion of rough sets was introduced by Z. Pawlak in the year 1982. The notion of a $\Gamma$-semigroup was introduced by M. K. Sen in the year 1981. In 2003, Y. B. Jun studied the roughness of sub$\Gamma$-semigroups, ideals and bi-ideals in i-semigroups. In this paper, we study rough prime ideals and rough fuzzy prime ideals in $\Gamma$-semigroups.
Generalized Transformation Semigroups Whose Sets of Quasi-ideals and Bi-ideals Coincide
Chinram, Ronnason Department of Mathematics 2005 Kyungpook mathematical journal Vol.45 No.2
Let BQ be the class of all semigroups whose bi-ideals are quasi-ideals. It is known that regular semigroups, right [left] 0-simple semigroups and right [left] 0-simple semigroups belong to BQ. Every zero semigroup is clearly a member of this class. In this paper, we characterize when generalized full transformation semigroups and generalized Baer-Levi semigroups are in BQ in terms of the cardinalities of sets.
Pythagorean fuzzy implicative/comparative/shift UP-filters of UP-algebras with approximations
Akarachai Satirad,Ronnason Chinram,Pongpun Julath,Aiyared Iampan 한국지능시스템학회 2023 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.23 No.1
The aim of this paper is to introduce new types of Pythagorean fuzzy sets (PFSs) in UP-algebras, which we will call a Pythagorean fuzzy implicative UP-filter (PFIUPF), a Pythagorean fuzzy comparative UP-filter (PFCUPF), and a Pythagorean fuzzy shift UP-filter (PFSUPF). In addition, we will also discuss the relationship between some assertions of PFSs and PFIUPFs (resp., PFCUPFs, PFSUPFs) in UP-algebras and find sufficient conditions for studying the generalizations of three PFSs in UP-algebras. As a result of the study, we found their generalization as follows: every PFCUPF and every PFSUPF are a PFUPF, and every PFIUPF is a PFUPI. Moreover, we study upper and lower approximations of PFSs.
MAGNIFYING ELEMENTS IN A SEMIGROUP OF TRANSFORMATIONS PRESERVING EQUIVALENCE RELATION
Kaewnoi, Thananya,Petapirak, Montakarn,Chinram, Ronnason The Kangwon-Kyungki Mathematical Society 2019 한국수학논문집 Vol.27 No.2
Let X be a nonempty set, ${\rho}$ be an equivalence on X, T(X) be the semigroup of all transformations from X into itself, and $T_{\rho}(X)=\{f{\in}T(X)|(x,y){\in}{\rho}{\text{ implies }}((x)f,\;(y)f){\in}{\rho}\}$. In this paper, we investigate some necessary and sufficient conditions for elements in $T_{\rho}(X)$ to be left or right magnifying.
STRUCTURES OF INVOLUTION Г-SEMIHYPERGROUPS
( Naveed Yaqoob ),( Jian Tang ),( Ronnason Chinram ) 호남수학회 2018 호남수학학술지 Vol.40 No.1
In this paper, structure of involution Г-semihypergroup is in-troduced and some theorems about this concept are stated and proved. The concept of Г-hyperideal in involution Г-semihypergroup is defined and some of their properties are studied. Some results on regular Г*-semihypergroups and fuzzy Г*-semihypergroups are also provided.
STRUCTURES OF INVOLUTION Γ-SEMIHYPERGROUPS
Yaqoob, Naveed,Tang, Jian,Chinram, Ronnason The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.1
In this paper, structure of involution ${\Gamma}$-semihypergroup is introduced and some theorems about this concept are stated and proved. The concept of ${\Gamma}$-hyperideal in involution ${\Gamma}$-semihypergroup is defined and some of their properties are studied. Some results on regular ${\Gamma}^*$-semihypergroups and fuzzy ${\Gamma}^*$-semihypergroups are also provided.
Pythagorean fuzzy soft sets over UP-algebras
Akarachai Satirad,Rukchart Prasertpong,Pongpun Julatha,Ronnason Chinram,Aiyared Iampan 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.3
This paper aims to apply the concept of Pythagorean fuzzy soft sets (PFSSs) to UP-algebras. Then we introduce five types of PFSSs over UP-algebras, study their generalization, and provide illustrative examples. In addition, we study the results of four operations of two PFSSs over UP-algebras, namely, the union, the restricted union, the intersection, and the extended intersection. Finally, we will also discuss $t$-level subsets of PFSSs over UP-algebras to study the relationships between PFSSs and special subsets of UP-algebras.