sabahat khan - Academia.edu (original) (raw)

Papers by sabahat khan

Asian-European Journal of Mathematics

Although a lot of work has been done by algebraist on soft set theory and hyperstructure theory, ... more Although a lot of work has been done by algebraist on soft set theory and hyperstructure theory, several fundamental results of soft intersection hyperideals in LA-semihypergroups remained untouched. This paper aims at studying some structural properties of LA-semihypergroups by applying soft set theory. In this paper, we define right regular LA-semihypergroups and introduce the concept of soft generalized bi-hyperideals in LA-semihypergroups. Further, we characterize right regular LA-semihypergroups in terms of different kinds of soft right hyperideals, soft left hyperideals and soft generalized bi-hyperideals. Idempotent soft hyperideals in LA-semihypergroups are introduced and some related results on them are obtained. It is proved that in an LA-semihypergroup with left identity, the collection of all soft left hyperideals, which are idempotent forms a commutative monoid. Examples are provided to illustrate the results.

Discussiones Mathematicae - General Algebra and Applications, 2020

The main purpose of this paper is to provide an effective content of theory of ternary semigroups... more The main purpose of this paper is to provide an effective content of theory of ternary semigroups with involution by applying soft set theory concepts. In this paper, we introduce some basic terms and definitions of different ideals in ternary semigroups with involution. Further, we define soft ideals and soft filters in ternary semigroups with involution, and show how a soft set effects on a ternary semigroup with involution with the help of intersection and insertion of sets. We explore some properties using involution theoretic concepts in ternary semigroups for soft ideals and soft filters.

AIP Conference Proceedings, 2019

International Journal of Apllied Mathematics, 2018

In this paper, we introduce hesitant fuzzy ideals on ternary semigroups and define hesitant fuzzy... more In this paper, we introduce hesitant fuzzy ideals on ternary semigroups and define hesitant fuzzy left (resp. lateral, right)ideals on ternary semigroups. Here we define hesitant fuzzy point on ternary semigroups and prove some interesting results on them. We also characterize regular ternary semigroups in terms of hesitant fuzzy left, hesitant fuzzy lateral and hesitant fuzzy right ideals using hesitant fuzzy points.

Afrika Matematika, 2020

In this paper, soft intersection \varGamma -hyperideals of ordered \varGamma -semihypergr... more In this paper, soft intersection \varGamma -hyperideals of ordered \varGamma -semihypergroups over an initial universe \mathcal {V}aredefinedandsomepropertiesofthemwithsoftintersectionproductareobtained.Further,somecharacterizationsofregularandintra−regularorderedare defined and some properties of them with soft intersection product are obtained. Further, some characterizations of regular and intra-regular orderedaredefinedandsomepropertiesofthemwithsoftintersectionproductareobtained.Further,somecharacterizationsofregularandintra−regularordered\varGamma -semihypergroups in terms of soft intersection \varGamma -hyperideals are provided. We also introduce the notion of semisimple ordered \varGamma -semihypergroups. Finally, we give some characterizations of semisimple ordered \varGamma -semihypergroups in terms of soft prime and soft semiprime \varGamma -hyperideals.

In this paper, we study some useful results of ordered (p; q)-lateral ideals in ordered ternary s... more In this paper, we study some useful results of ordered (p; q)-lateral ideals in ordered ternary semigroups. Also, some properties of (p; q)-lateral simple ordered ternary semigroup have been examined. Further, we characterize the relationship between minimal (resp., maximal) ordered (p; q)- lateral ideals and (p; q)-lateral simple ordered ternary semigroups

We introduce the notions of ,-hesitant fuzzy ideal, ,-hesitant fuzzy bi-ideal and ,-hesitant fuzz... more We introduce the notions of ,-hesitant fuzzy ideal, ,-hesitant fuzzy bi-ideal and ,-hesitant fuzzy interior ideal on semigroup and characterizations of a hesitant fuzzy ideal (bi-ideal, interior ideal) with two frontiers are considered. We provide an example to show that) , ( -hesitant fuzzy ideal on S need not be a -hesitant fuzzy ideal on S. We provide conditions for a) , ( -hesitant fuzzy ideal on S to be a -hesitant fuzzy ideal on S. Moreover, we show that the hesitant intersection of two hesitant fuzzy left (right, bi-, interior) ideal with two frontiers is a hesitant fuzzy left (right, bi-, interior) ideal respectively with two frontiers.

Advances in Intelligent Systems and Computing, 2018

In this paper, we introduce soft hyperideals in ordered LAsemihypergroups through new approach an... more In this paper, we introduce soft hyperideals in ordered LAsemihypergroups through new approach and investigate some useful results. Further, we define right regular ordered LA-semihypergroup and characterize right regular ordered LA-semihypergroups using soft hyperideals.

The aim of this paper is to apply the concept of fuzzification on prime hyperideals and semiprime... more The aim of this paper is to apply the concept of fuzzification on prime hyperideals and semiprime hyperideals in po-ternary semihypergroups and look for some of their related characteristics. Moreover, a number of characterizations for intra-regular po-ternary semihypergroups had been given by using the concept of fuzzy hyperideals.

Harmony Search and Nature Inspired Optimization Algorithms, 2018

In this paper, we introduce soft hyperideals in LA-semihypergroups through new approach and inves... more In this paper, we introduce soft hyperideals in LA-semihypergroups through new approach and investigate some useful results. Further, we characterize regular and intra-regular LA-semihypergroups using soft hyperideals.

The aim of this paper is to introduce a new concept of an ordered (m; (p; q); n)-bi ideal of an o... more The aim of this paper is to introduce a new concept of an ordered (m; (p; q); n)-bi ideal of an ordered tenary semigroup. Some classical results in ordered ternary semigroups are given. We also consider the minimal ordered (m; (p; q); n)-bi ideals in ordered ternary semigroups. In particular, the (m; (p; q); n)-bi simple ordered ternary semigroups are dened and some of their properties are explored. As a conse- quence, we will show that the regular ordered ternary semigroups can be characterized by using various generalised ideals.

In this paper, the notions of extension of hesitant fuzzy ideals, hesitant fuzzy prime ideals, he... more In this paper, the notions of extension of hesitant fuzzy ideals, hesitant fuzzy prime ideals, hesitant fuzzy semiprime ideals and hesitant 3-prime fuzzy ideals in po-semigroups are introduced with some of their properties are investigated. We discuss the relationship between between prime(semi prime) ideals and 3-prime ideals in po-semigroup by means of the extensions hesitant fuzzy ideals.

In this paper, we introduce generalised quasi-ideals in ordered ternary semigroups. Also, we defi... more In this paper, we introduce generalised quasi-ideals in ordered ternary semigroups. Also, we define ordered m-right ideals, ordered (p, q)-lateral ideals and ordered n-left ideals in ordered ternary semigroups and studied the relation between them. Some intersection properties of ordered (m, (p, q), n)-quasi ideals are examined. We also characterize these notions in terms of minimal ordered (m, (p, q), n)-quasi-ideals in ordered ternary semigroups. Moreover, m-right simple, (p, q)-lateral simple, n-left simple, and (m, (p, q), n)-quasi simple ordered ternary semigroups are defined and some properties of them are studied.

Journal of Discrete Mathematical Sciences and Cryptography, 2020

Advances in Fuzzy Systems, 2018

We apply the hesitant fuzzy sets theory to Γ-semigroups and provide some characterizations of hes... more We apply the hesitant fuzzy sets theory to Γ-semigroups and provide some characterizations of hesitant fuzzy left (right and bi-) ideals. We introduce the hesitant fuzzy left (resp., right and two-sided) ideal, hesitant fuzzy bi-ideal, and hesitant fuzzy interior ideal in Γ-semigroup and study some properties of them. Finally, a characterization of a simple Γ-semigroup by means of a hesitant fuzzy simple Γ-semigroup is obtained.

Journal of Discrete Mathematical Sciences and Cryptography, 2019

The aim of this paper is to apply fuzzy sets in hyperstructure theory. We initiate fuzzy hyperide... more The aim of this paper is to apply fuzzy sets in hyperstructure theory. We initiate fuzzy hyperideals over po-ternary semihypergroups and explore some related properties. We introduce the concept of po-fuzzy point in po-ternary semihypergroups. Moreover, we give a number of characterizations for regular po-ternary semihypergroups by using the concept of fuzzy hyperideals.

International Journal of Pure and Apllied Mathematics, 2017

The concept of covered ideal in semigroups has been introduced by I. Fabrici[1]. In this paper, w... more The concept of covered ideal in semigroups has been introduced by I. Fabrici[1]. In this paper, we introduce covered Γ-ideal in po-Γ-semigroups. We study some results based on covered Γ-ideals in po-Γ-semigroup.

Kragujevac Journal of Mathematics, 2020

This paper is a contribution to the study of the effective content of LAhyperstructure. In this p... more This paper is a contribution to the study of the effective content of LAhyperstructure. In this paper, we introduce the notion of soft interior-hyperideals. Further, we give several basic properties of these notions and provide different important characterizations in terms of soft interior hyperideals.

European Journal of Mathematics and Applications, 2022

In this paper, we introduce G-hyperideal, G-prime hyperideal, G-prime-bihyperideal, and G-weakly ... more In this paper, we introduce G-hyperideal, G-prime hyperideal, G-prime-bihyperideal, and G-weakly prime hyperideal in ordered semihypergroups and we also define G-regular ordered hypersemigroups as well as G-semisimple ordered hypersemigroups. Thereby, we extend the results to the broader and abstract setting of ordered hypersemigroups, this also strengthens previous generalizations relating to rings, semigroups and other algebraic structures.

Asian-European Journal of Mathematics

Although a lot of work has been done by algebraist on soft set theory and hyperstructure theory, ... more Although a lot of work has been done by algebraist on soft set theory and hyperstructure theory, several fundamental results of soft intersection hyperideals in LA-semihypergroups remained untouched. This paper aims at studying some structural properties of LA-semihypergroups by applying soft set theory. In this paper, we define right regular LA-semihypergroups and introduce the concept of soft generalized bi-hyperideals in LA-semihypergroups. Further, we characterize right regular LA-semihypergroups in terms of different kinds of soft right hyperideals, soft left hyperideals and soft generalized bi-hyperideals. Idempotent soft hyperideals in LA-semihypergroups are introduced and some related results on them are obtained. It is proved that in an LA-semihypergroup with left identity, the collection of all soft left hyperideals, which are idempotent forms a commutative monoid. Examples are provided to illustrate the results.

Discussiones Mathematicae - General Algebra and Applications, 2020

The main purpose of this paper is to provide an effective content of theory of ternary semigroups... more The main purpose of this paper is to provide an effective content of theory of ternary semigroups with involution by applying soft set theory concepts. In this paper, we introduce some basic terms and definitions of different ideals in ternary semigroups with involution. Further, we define soft ideals and soft filters in ternary semigroups with involution, and show how a soft set effects on a ternary semigroup with involution with the help of intersection and insertion of sets. We explore some properties using involution theoretic concepts in ternary semigroups for soft ideals and soft filters.

AIP Conference Proceedings, 2019

International Journal of Apllied Mathematics, 2018

In this paper, we introduce hesitant fuzzy ideals on ternary semigroups and define hesitant fuzzy... more In this paper, we introduce hesitant fuzzy ideals on ternary semigroups and define hesitant fuzzy left (resp. lateral, right)ideals on ternary semigroups. Here we define hesitant fuzzy point on ternary semigroups and prove some interesting results on them. We also characterize regular ternary semigroups in terms of hesitant fuzzy left, hesitant fuzzy lateral and hesitant fuzzy right ideals using hesitant fuzzy points.

Afrika Matematika, 2020

In this paper, soft intersection \varGamma -hyperideals of ordered \varGamma -semihypergr... more In this paper, soft intersection \varGamma -hyperideals of ordered \varGamma -semihypergroups over an initial universe \mathcal {V}aredefinedandsomepropertiesofthemwithsoftintersectionproductareobtained.Further,somecharacterizationsofregularandintra−regularorderedare defined and some properties of them with soft intersection product are obtained. Further, some characterizations of regular and intra-regular orderedaredefinedandsomepropertiesofthemwithsoftintersectionproductareobtained.Further,somecharacterizationsofregularandintra−regularordered\varGamma -semihypergroups in terms of soft intersection \varGamma -hyperideals are provided. We also introduce the notion of semisimple ordered \varGamma -semihypergroups. Finally, we give some characterizations of semisimple ordered \varGamma -semihypergroups in terms of soft prime and soft semiprime \varGamma -hyperideals.

In this paper, we study some useful results of ordered (p; q)-lateral ideals in ordered ternary s... more In this paper, we study some useful results of ordered (p; q)-lateral ideals in ordered ternary semigroups. Also, some properties of (p; q)-lateral simple ordered ternary semigroup have been examined. Further, we characterize the relationship between minimal (resp., maximal) ordered (p; q)- lateral ideals and (p; q)-lateral simple ordered ternary semigroups

We introduce the notions of ,-hesitant fuzzy ideal, ,-hesitant fuzzy bi-ideal and ,-hesitant fuzz... more We introduce the notions of ,-hesitant fuzzy ideal, ,-hesitant fuzzy bi-ideal and ,-hesitant fuzzy interior ideal on semigroup and characterizations of a hesitant fuzzy ideal (bi-ideal, interior ideal) with two frontiers are considered. We provide an example to show that) , ( -hesitant fuzzy ideal on S need not be a -hesitant fuzzy ideal on S. We provide conditions for a) , ( -hesitant fuzzy ideal on S to be a -hesitant fuzzy ideal on S. Moreover, we show that the hesitant intersection of two hesitant fuzzy left (right, bi-, interior) ideal with two frontiers is a hesitant fuzzy left (right, bi-, interior) ideal respectively with two frontiers.

Advances in Intelligent Systems and Computing, 2018

In this paper, we introduce soft hyperideals in ordered LAsemihypergroups through new approach an... more In this paper, we introduce soft hyperideals in ordered LAsemihypergroups through new approach and investigate some useful results. Further, we define right regular ordered LA-semihypergroup and characterize right regular ordered LA-semihypergroups using soft hyperideals.

The aim of this paper is to apply the concept of fuzzification on prime hyperideals and semiprime... more The aim of this paper is to apply the concept of fuzzification on prime hyperideals and semiprime hyperideals in po-ternary semihypergroups and look for some of their related characteristics. Moreover, a number of characterizations for intra-regular po-ternary semihypergroups had been given by using the concept of fuzzy hyperideals.

Harmony Search and Nature Inspired Optimization Algorithms, 2018

In this paper, we introduce soft hyperideals in LA-semihypergroups through new approach and inves... more In this paper, we introduce soft hyperideals in LA-semihypergroups through new approach and investigate some useful results. Further, we characterize regular and intra-regular LA-semihypergroups using soft hyperideals.

The aim of this paper is to introduce a new concept of an ordered (m; (p; q); n)-bi ideal of an o... more The aim of this paper is to introduce a new concept of an ordered (m; (p; q); n)-bi ideal of an ordered tenary semigroup. Some classical results in ordered ternary semigroups are given. We also consider the minimal ordered (m; (p; q); n)-bi ideals in ordered ternary semigroups. In particular, the (m; (p; q); n)-bi simple ordered ternary semigroups are dened and some of their properties are explored. As a conse- quence, we will show that the regular ordered ternary semigroups can be characterized by using various generalised ideals.

In this paper, the notions of extension of hesitant fuzzy ideals, hesitant fuzzy prime ideals, he... more In this paper, the notions of extension of hesitant fuzzy ideals, hesitant fuzzy prime ideals, hesitant fuzzy semiprime ideals and hesitant 3-prime fuzzy ideals in po-semigroups are introduced with some of their properties are investigated. We discuss the relationship between between prime(semi prime) ideals and 3-prime ideals in po-semigroup by means of the extensions hesitant fuzzy ideals.

In this paper, we introduce generalised quasi-ideals in ordered ternary semigroups. Also, we defi... more In this paper, we introduce generalised quasi-ideals in ordered ternary semigroups. Also, we define ordered m-right ideals, ordered (p, q)-lateral ideals and ordered n-left ideals in ordered ternary semigroups and studied the relation between them. Some intersection properties of ordered (m, (p, q), n)-quasi ideals are examined. We also characterize these notions in terms of minimal ordered (m, (p, q), n)-quasi-ideals in ordered ternary semigroups. Moreover, m-right simple, (p, q)-lateral simple, n-left simple, and (m, (p, q), n)-quasi simple ordered ternary semigroups are defined and some properties of them are studied.

Journal of Discrete Mathematical Sciences and Cryptography, 2020

Advances in Fuzzy Systems, 2018

We apply the hesitant fuzzy sets theory to Γ-semigroups and provide some characterizations of hes... more We apply the hesitant fuzzy sets theory to Γ-semigroups and provide some characterizations of hesitant fuzzy left (right and bi-) ideals. We introduce the hesitant fuzzy left (resp., right and two-sided) ideal, hesitant fuzzy bi-ideal, and hesitant fuzzy interior ideal in Γ-semigroup and study some properties of them. Finally, a characterization of a simple Γ-semigroup by means of a hesitant fuzzy simple Γ-semigroup is obtained.

Journal of Discrete Mathematical Sciences and Cryptography, 2019

The aim of this paper is to apply fuzzy sets in hyperstructure theory. We initiate fuzzy hyperide... more The aim of this paper is to apply fuzzy sets in hyperstructure theory. We initiate fuzzy hyperideals over po-ternary semihypergroups and explore some related properties. We introduce the concept of po-fuzzy point in po-ternary semihypergroups. Moreover, we give a number of characterizations for regular po-ternary semihypergroups by using the concept of fuzzy hyperideals.

International Journal of Pure and Apllied Mathematics, 2017

The concept of covered ideal in semigroups has been introduced by I. Fabrici[1]. In this paper, w... more The concept of covered ideal in semigroups has been introduced by I. Fabrici[1]. In this paper, we introduce covered Γ-ideal in po-Γ-semigroups. We study some results based on covered Γ-ideals in po-Γ-semigroup.

Kragujevac Journal of Mathematics, 2020

This paper is a contribution to the study of the effective content of LAhyperstructure. In this p... more This paper is a contribution to the study of the effective content of LAhyperstructure. In this paper, we introduce the notion of soft interior-hyperideals. Further, we give several basic properties of these notions and provide different important characterizations in terms of soft interior hyperideals.

European Journal of Mathematics and Applications, 2022

In this paper, we introduce G-hyperideal, G-prime hyperideal, G-prime-bihyperideal, and G-weakly ... more In this paper, we introduce G-hyperideal, G-prime hyperideal, G-prime-bihyperideal, and G-weakly prime hyperideal in ordered semihypergroups and we also define G-regular ordered hypersemigroups as well as G-semisimple ordered hypersemigroups. Thereby, we extend the results to the broader and abstract setting of ordered hypersemigroups, this also strengthens previous generalizations relating to rings, semigroups and other algebraic structures.