Discussiones Mathematicae - General Algebra and Applications
The left invertive law makes Abel Grassmann's groupoids (briefly AGgroupoids) a very interesting ... more The left invertive law makes Abel Grassmann's groupoids (briefly AGgroupoids) a very interesting structure to study. In this paper, we define (M, N)-double-framed soft bi-ideals (briefly (M, N)-DFS bi-ideals) and (M, N)-double-framed soft generalized bi-ideals (briefly (M, N)-DFS generalized bi-ideals) of AG-groupoids and study some of its properties. We obtain some interesting results of these notions in intra-regular AG-groupoids.
Discussiones Mathematicae - General Algebra and Applications
The main purpose of this article is to study ordered semihypergroups in the context of uni-soft q... more The main purpose of this article is to study ordered semihypergroups in the context of uni-soft quasi-hyperideals. In this article, using the notion of soft-union sets in ordered semihypergroups, we introduce the concept of union-soft (uni-soft) quasi-hyperideal and the related properties 322
Background: Appendicitis is common problem treated surgically by open or laparoscopic appendectom... more Background: Appendicitis is common problem treated surgically by open or laparoscopic appendectomy. Objectives: To compare short term complications of open versus laparoscopic appendectomy. Study design: Randomized control trial Setting: Department of General Surgery, Mardan Medical Complex, MTI, Mardan. Subjects: Total 110 patients of both gender aged 20 to 40 years undergoing appendectomy were enrolled. Methodology: This study was done from 12thJuly 2020 till 11th January 2021 after approval from hospital ethical committee. Total 110 patients were enrolled and divided in open appendectomy and laparoscopic appendectomy and short term complications were noted. Results: In our study total 110 patients were enrolled and divided in two groups. The mean age of patients was 32.65±4.8 years. There were 25.5% patients in younger age group and 74.5% in elder age group. In our study population there were 26.4% males and 73.6% female patients. The mean body mass index was 30.9±5.5 kg/m2. Mean...
Journal of Ambient Intelligence and Humanized Computing
The main focus of this paper is the application of aggregation operators (AOs) in the environment... more The main focus of this paper is the application of aggregation operators (AOs) in the environment of Fermatean fuzzy soft sets (FFSS). The unique feature of the work is its application in the symptomatic treatment of the COVID-19 disease. For this purpose, the idea of FFSS is introduced which is based on the Senapati and Yagar's Fermatean fuzzy set. Next we have defined Fermatean fuzzy soft aggregation operators (FFSAOs) like, Fermatean fuzzy soft weighted averaging (FFSWA) operator, Fermatean fuzzy soft ordered weighted averaging (FFSOWA) operator, Fermatean fuzzy soft weighted geometric (FFSWG) operator and Fermatean fuzzy soft ordered weighted geometric (FFSOWG). The prominent properties of these operators are given in details. We have also developed some approaches to solve multi-criteria decision making (MCDM) problems in Fermatean fuzzy soft (FFS) information. An introduction to the novel pandemic, safety measures, and then its possible symptomatic treatment is also provided. The developed operators are utilized in the symptomatic treatment of COVID-19 disease in order to show the practical applications and importance of these AOs as well as Fermatean fuzzy soft information. The stability of the proposed work is also proved by the comparative analysis.
Saudi journal of pathology and microbiology, Feb 3, 2022
Copper nanoparticles are typically in black or brown powder form. Copper nanoparticles uses in he... more Copper nanoparticles are typically in black or brown powder form. Copper nanoparticles uses in heat exchange systems, bioscience, anti-microbial materials, Aluminum is extremely harmful to fish in the acid conditions. The primary targeted organ of fish is gill, and death is influenced by a variety of respiratory, osmo-regulatory, and ion regulatory dysfunction. To understand the effect of heavy metals on the aquatic biota, it is necessary to characterize the methods readily accessible to aquatic species for heavy metal mobility, immobilization, and excretion. The severe Ag toxicity to fish is very lower in the seawater than in the freshwater. Tetrodotoxin is a highly poisonous toxin located primarily in gonads and liver of some fishes, including pufferfishes, toadfish and globefish as well as some shellfish, octopus, and amphibian species. Fish exposed to Cr for the first time displayed a variety of behavioural alterations, including loss of appetite, irregular swimming, changing in colour and mucous discharge. It is much more complicated than genome of humans because zebrafish possess two more sets of chromosomes than humans. Glutathione peroxidase and Catalase are anti-oxidant enzymes that have long been used to assess anti-oxidant injury and stress reaction.
We theoretically present the physical realization of one dimensional (1D) atom localization by su... more We theoretically present the physical realization of one dimensional (1D) atom localization by superposition of three standing wave fields in a four-level tripod atomic configuration. The most interesting result that we observe is the variation of the bandwidth of the localization peaks with the intensity of the space independent Rabi frequency. A sharp single and double localized peaks are observed at different direction of the wave numbers. The bandwidth of a localized peak is reduced as the intensity of the space independent Rabi frequency goes on increasing, which corresponds to the reduction in the uncertainty. These results will hopefully contribute to the development of current high tech-applications.
Journal of Algebraic Hyperstructures and Logical Algebras, Nov 30, 1999
In this paper, we introduce the concept of unionsoft (briefly, uni-soft) bi-hyperideal of an orde... more In this paper, we introduce the concept of unionsoft (briefly, uni-soft) bi-hyperideal of an ordered semihypergroup. The notions of prime (strongly prime, semiprime, irreducible, and strongly irreducible) uni-soft bi-hyperideals in ordered semihypergroups are introduced and related properties are investigated. Numerous examples of these notions are given. The relationship between prime and strongly prime, irreducible and strongly irreducible uni-soft bi-hyperideals are considered and characterizations of these concepts are established. Regular and intra-regular ordered semihypergroups are characterized in terms of these notions.
Molodtsov’s soft set theory is a new mathematical model dealing with uncertainty from a parameter... more Molodtsov’s soft set theory is a new mathematical model dealing with uncertainty from a parameterization point of view. In soft set theory, the problem of setting the membership function does not arise, which makes the theory easily applied to many different fields. In this paper, we introduce the notions of uni-soft ordered AG-groupoids, uni-soft left (right) ideals in an ordered AG-groupoids and the related properties are discussed. Characterizations of uni-soft ordered AG-groupoids, uni-soft left (right) ideals are studied. The concepts of uni-soft products and uni-soft regular ordered AG-groupoids are investigated and using the notions of uni-soft left and right ideals, the conditions for a regular ordered AG-groupoids are given. In the last section of this paper, we discuss the concept of a concave soft set and introduce the notion of a critical soft points in ordered AG-groupoids.
International Journal of Algebra and Statistics, 2018
Theory of soft sets proposed by Molodtsov as a general framework for reasoning about vague concep... more Theory of soft sets proposed by Molodtsov as a general framework for reasoning about vague concepts is a powerful mathematical tool for modelling various types of uncertainties. In this paper, we introduce the notions of intersectional soft subsemihypergroup, intersectional soft left (lateral, right) hyperideal of ordered ternary semihypergroups and related properties are investigated. We present characterizations of right weakly regular ordered ternary semihypergroups by means of intersectional hyperideals.
The objective of this project was to assist New Jersey Motor Vehicle Commission in determining th... more The objective of this project was to assist New Jersey Motor Vehicle Commission in determining the feasibility of a removable visual marker for Graduated Drivers License (GDL) drivers. The NJ Teen Driver Safety Study Commission issued a report to the Governor and Legislature in March of 2008 in response to concerns over the growing level of fatalities and teen driver injuries in New Jersey. One of the recommendations from the Commission’s report identifies the need to mark vehicles operated by mostly teen Graduated Driver License (GDL) drivers to aid in enforcement of the GDL law. Six technologies were identified to meet the requirement for a removable tag on the vehicle license plate. After review of documents and discussion with vendors two technologies were field tested, a hook-and-loop, or Velcro, fastener, and a magnetic fastener. Both had two pieces, a base which attached to the license plate with adhesive and a top piece with a reflective sticker. Based on the field test and further review of product specifications, the hook-and-loop fastener is recommended as the preferred technology for this application. A retroreflective sticker was tested as well. Both the durability and the visibility of the stickers tested were not satisfactory. A draft specification was prepared to help address these deficiencies when the stickers are put out to bid. A focus group was held to discuss enforcement strategies and it was agreed that no identification was required on the sticker, only a solid color. It is proposed that the successful vendor conduct a field test of the attachment devices and the stickers, prior to full deployment, using approximately 500-1000 devices.
Purpose Awareness about plagiarism is essential for the evasion of intellectual mendacity, inculc... more Purpose Awareness about plagiarism is essential for the evasion of intellectual mendacity, inculcation of academic integrity and assurance of quality research. Maintaining high standards regarding academic integrity is a major challenge for higher education and research organizations. In Pakistan, resident doctors are required to submit a dissertation to the College of Physicians and Surgeons. The purpose of this study is to examine this cohort’s awareness of plagiarism and to determine the effectiveness of the library literacy (IL) programme towards the prevention of plagiarism. Design/methodology/approach Using the quantitative approach, a cross-sectional survey method was used. A convenience sample of postgraduate resident doctors was randomly recruited from two hospitals in Peshawar, Pakistan. Questionnaires were used for data collection. Descriptive and inferential statistics were used for data analyses. Findings The findings revealed that while resident doctors were aware of t...
Objective: To determine the role of mini-percutaneus nephrolithotomy in the renal stones manageme... more Objective: To determine the role of mini-percutaneus nephrolithotomy in the renal stones management and its post-operative complications.
In this paper, we apply the concept of double-framed soft sets to Abel-Grassmann’s hypergroupoids... more In this paper, we apply the concept of double-framed soft sets to Abel-Grassmann’s hypergroupoids (AG-hypergroupoids). We define double-framed soft AG-hypergroupoids (DFS AG-hypergroupoids) and double-framed soft left (respectively, right) (briefly DFS-left (respectively, DFS-right)) hyperideals of AG-hypergroupoids. It is shown that an idempotent DFS-left hyperideal is a DFS-hyperideal. Also a DFS right hyperideal becomes DFS hyperideal when pure left identity is adjoined to an AG-hypergroupoid, but the converse is not true. We also discuss some properties of these hyperideals in regular AG-hypergroupoids.
Many applications use the Global Positioning System data that provide rich context information fo... more Many applications use the Global Positioning System data that provide rich context information for multiple purposes. Easier availability and access of Global Positioning System data can facilitate various mobile applications, and one of such applications is to infer the mobility of a user. Most existing works for inferring users’ transportation modes need the combination of Global Positioning System data and other types of data such as accelerometer and Global System for Mobile Communications. However, the dependency of the applications to use data sources other than the Global Positioning System makes the use of application difficult if peer data source is not available. In this paper, we introduce a new generic framework for the inference of transportation mode by only using the Global Positioning System data. Our contribution is threefold. First, we propose a new method for Global Positioning System trajectory data preprocessing using grid probability distribution function. Seco...
In this paper, we introduce double-framed soft bi-ideals (briefly DFS bi-ideals) and double-frame... more In this paper, we introduce double-framed soft bi-ideals (briefly DFS bi-ideals) and double-framed soft generalized bi-ideals (briefly DFS generalized bi-ideals) in AG-groupoids and some properties of them are investigated. Several characterizations of intra-regular AG-groupoids in terms of DFS left (resp. right) ideals, DFS bi-ideals, DFS generalized bi-ideals and semiprime class of them are provided.
The main motivation behind this paper is to study some structural properties of a non-associative... more The main motivation behind this paper is to study some structural properties of a non-associative structure Abel Grassmann's groupoid (AG-groupoid) in terms of double-framed soft sets (DFS sets) as it hasn't attracted much attention compared to associative structures. An AG-groupoid can be referred to as a non-associative semigroup, as the main difference between a semigroup and an AG-groupoid is the switching of an associative law. In this paper, we introduce the concept of (M, N)-double-framed soft ideals (briefly, (M, N)-DFS ideal) of AG-groupoids and investigate some properties of these notions. We have shown that every (M, N)-DFS ideal is (M, N)-DFS AG-groupoid but the converse is not true. This is shown with the help of an example. We also discuss the properties of (M, N)-DFS ideals in regular AG-groupoids. Moreover a decision making algorithm based on DFS-sets is given.
Molodtsov's soft set theory is a new mathematical model for dealing with uncertainty from a param... more Molodtsov's soft set theory is a new mathematical model for dealing with uncertainty from a parameterization point of view. In soft set theory, the problem of setting the membership function does not arise, which makes the theory easily applied to many different fields. In this paper, we discuss a new approach to soft sets and compare soft sets to the related concepts of ordered semihypergroups. We define int-soft generalized bi-hyperideals in ordered semihypergroups and characterize regular and left weakly regular ordered semihypergroups by the properties of their int-soft generalized bi-hyperideals. Keywords Soft set • Regular • Left weakly regular ordered semihypergroups • Left (resp., right, bi-and generalized bi-)hyperideals • Int-soft left (resp., right, bi-and generalized bi-)hyperideals in ordered semihypergroups 1 Introduction Algebraic hyperstructures represent a natural extension of classical algebraic structures, and they were originally proposed in 1934 by a French mathematician Marty (1934), at Communicated by V. Loia.
Discussiones Mathematicae - General Algebra and Applications
The left invertive law makes Abel Grassmann's groupoids (briefly AGgroupoids) a very interesting ... more The left invertive law makes Abel Grassmann's groupoids (briefly AGgroupoids) a very interesting structure to study. In this paper, we define (M, N)-double-framed soft bi-ideals (briefly (M, N)-DFS bi-ideals) and (M, N)-double-framed soft generalized bi-ideals (briefly (M, N)-DFS generalized bi-ideals) of AG-groupoids and study some of its properties. We obtain some interesting results of these notions in intra-regular AG-groupoids.
Discussiones Mathematicae - General Algebra and Applications
The main purpose of this article is to study ordered semihypergroups in the context of uni-soft q... more The main purpose of this article is to study ordered semihypergroups in the context of uni-soft quasi-hyperideals. In this article, using the notion of soft-union sets in ordered semihypergroups, we introduce the concept of union-soft (uni-soft) quasi-hyperideal and the related properties 322
Background: Appendicitis is common problem treated surgically by open or laparoscopic appendectom... more Background: Appendicitis is common problem treated surgically by open or laparoscopic appendectomy. Objectives: To compare short term complications of open versus laparoscopic appendectomy. Study design: Randomized control trial Setting: Department of General Surgery, Mardan Medical Complex, MTI, Mardan. Subjects: Total 110 patients of both gender aged 20 to 40 years undergoing appendectomy were enrolled. Methodology: This study was done from 12thJuly 2020 till 11th January 2021 after approval from hospital ethical committee. Total 110 patients were enrolled and divided in open appendectomy and laparoscopic appendectomy and short term complications were noted. Results: In our study total 110 patients were enrolled and divided in two groups. The mean age of patients was 32.65±4.8 years. There were 25.5% patients in younger age group and 74.5% in elder age group. In our study population there were 26.4% males and 73.6% female patients. The mean body mass index was 30.9±5.5 kg/m2. Mean...
Journal of Ambient Intelligence and Humanized Computing
The main focus of this paper is the application of aggregation operators (AOs) in the environment... more The main focus of this paper is the application of aggregation operators (AOs) in the environment of Fermatean fuzzy soft sets (FFSS). The unique feature of the work is its application in the symptomatic treatment of the COVID-19 disease. For this purpose, the idea of FFSS is introduced which is based on the Senapati and Yagar's Fermatean fuzzy set. Next we have defined Fermatean fuzzy soft aggregation operators (FFSAOs) like, Fermatean fuzzy soft weighted averaging (FFSWA) operator, Fermatean fuzzy soft ordered weighted averaging (FFSOWA) operator, Fermatean fuzzy soft weighted geometric (FFSWG) operator and Fermatean fuzzy soft ordered weighted geometric (FFSOWG). The prominent properties of these operators are given in details. We have also developed some approaches to solve multi-criteria decision making (MCDM) problems in Fermatean fuzzy soft (FFS) information. An introduction to the novel pandemic, safety measures, and then its possible symptomatic treatment is also provided. The developed operators are utilized in the symptomatic treatment of COVID-19 disease in order to show the practical applications and importance of these AOs as well as Fermatean fuzzy soft information. The stability of the proposed work is also proved by the comparative analysis.
Saudi journal of pathology and microbiology, Feb 3, 2022
Copper nanoparticles are typically in black or brown powder form. Copper nanoparticles uses in he... more Copper nanoparticles are typically in black or brown powder form. Copper nanoparticles uses in heat exchange systems, bioscience, anti-microbial materials, Aluminum is extremely harmful to fish in the acid conditions. The primary targeted organ of fish is gill, and death is influenced by a variety of respiratory, osmo-regulatory, and ion regulatory dysfunction. To understand the effect of heavy metals on the aquatic biota, it is necessary to characterize the methods readily accessible to aquatic species for heavy metal mobility, immobilization, and excretion. The severe Ag toxicity to fish is very lower in the seawater than in the freshwater. Tetrodotoxin is a highly poisonous toxin located primarily in gonads and liver of some fishes, including pufferfishes, toadfish and globefish as well as some shellfish, octopus, and amphibian species. Fish exposed to Cr for the first time displayed a variety of behavioural alterations, including loss of appetite, irregular swimming, changing in colour and mucous discharge. It is much more complicated than genome of humans because zebrafish possess two more sets of chromosomes than humans. Glutathione peroxidase and Catalase are anti-oxidant enzymes that have long been used to assess anti-oxidant injury and stress reaction.
We theoretically present the physical realization of one dimensional (1D) atom localization by su... more We theoretically present the physical realization of one dimensional (1D) atom localization by superposition of three standing wave fields in a four-level tripod atomic configuration. The most interesting result that we observe is the variation of the bandwidth of the localization peaks with the intensity of the space independent Rabi frequency. A sharp single and double localized peaks are observed at different direction of the wave numbers. The bandwidth of a localized peak is reduced as the intensity of the space independent Rabi frequency goes on increasing, which corresponds to the reduction in the uncertainty. These results will hopefully contribute to the development of current high tech-applications.
Journal of Algebraic Hyperstructures and Logical Algebras, Nov 30, 1999
In this paper, we introduce the concept of unionsoft (briefly, uni-soft) bi-hyperideal of an orde... more In this paper, we introduce the concept of unionsoft (briefly, uni-soft) bi-hyperideal of an ordered semihypergroup. The notions of prime (strongly prime, semiprime, irreducible, and strongly irreducible) uni-soft bi-hyperideals in ordered semihypergroups are introduced and related properties are investigated. Numerous examples of these notions are given. The relationship between prime and strongly prime, irreducible and strongly irreducible uni-soft bi-hyperideals are considered and characterizations of these concepts are established. Regular and intra-regular ordered semihypergroups are characterized in terms of these notions.
Molodtsov’s soft set theory is a new mathematical model dealing with uncertainty from a parameter... more Molodtsov’s soft set theory is a new mathematical model dealing with uncertainty from a parameterization point of view. In soft set theory, the problem of setting the membership function does not arise, which makes the theory easily applied to many different fields. In this paper, we introduce the notions of uni-soft ordered AG-groupoids, uni-soft left (right) ideals in an ordered AG-groupoids and the related properties are discussed. Characterizations of uni-soft ordered AG-groupoids, uni-soft left (right) ideals are studied. The concepts of uni-soft products and uni-soft regular ordered AG-groupoids are investigated and using the notions of uni-soft left and right ideals, the conditions for a regular ordered AG-groupoids are given. In the last section of this paper, we discuss the concept of a concave soft set and introduce the notion of a critical soft points in ordered AG-groupoids.
International Journal of Algebra and Statistics, 2018
Theory of soft sets proposed by Molodtsov as a general framework for reasoning about vague concep... more Theory of soft sets proposed by Molodtsov as a general framework for reasoning about vague concepts is a powerful mathematical tool for modelling various types of uncertainties. In this paper, we introduce the notions of intersectional soft subsemihypergroup, intersectional soft left (lateral, right) hyperideal of ordered ternary semihypergroups and related properties are investigated. We present characterizations of right weakly regular ordered ternary semihypergroups by means of intersectional hyperideals.
The objective of this project was to assist New Jersey Motor Vehicle Commission in determining th... more The objective of this project was to assist New Jersey Motor Vehicle Commission in determining the feasibility of a removable visual marker for Graduated Drivers License (GDL) drivers. The NJ Teen Driver Safety Study Commission issued a report to the Governor and Legislature in March of 2008 in response to concerns over the growing level of fatalities and teen driver injuries in New Jersey. One of the recommendations from the Commission’s report identifies the need to mark vehicles operated by mostly teen Graduated Driver License (GDL) drivers to aid in enforcement of the GDL law. Six technologies were identified to meet the requirement for a removable tag on the vehicle license plate. After review of documents and discussion with vendors two technologies were field tested, a hook-and-loop, or Velcro, fastener, and a magnetic fastener. Both had two pieces, a base which attached to the license plate with adhesive and a top piece with a reflective sticker. Based on the field test and further review of product specifications, the hook-and-loop fastener is recommended as the preferred technology for this application. A retroreflective sticker was tested as well. Both the durability and the visibility of the stickers tested were not satisfactory. A draft specification was prepared to help address these deficiencies when the stickers are put out to bid. A focus group was held to discuss enforcement strategies and it was agreed that no identification was required on the sticker, only a solid color. It is proposed that the successful vendor conduct a field test of the attachment devices and the stickers, prior to full deployment, using approximately 500-1000 devices.
Purpose Awareness about plagiarism is essential for the evasion of intellectual mendacity, inculc... more Purpose Awareness about plagiarism is essential for the evasion of intellectual mendacity, inculcation of academic integrity and assurance of quality research. Maintaining high standards regarding academic integrity is a major challenge for higher education and research organizations. In Pakistan, resident doctors are required to submit a dissertation to the College of Physicians and Surgeons. The purpose of this study is to examine this cohort’s awareness of plagiarism and to determine the effectiveness of the library literacy (IL) programme towards the prevention of plagiarism. Design/methodology/approach Using the quantitative approach, a cross-sectional survey method was used. A convenience sample of postgraduate resident doctors was randomly recruited from two hospitals in Peshawar, Pakistan. Questionnaires were used for data collection. Descriptive and inferential statistics were used for data analyses. Findings The findings revealed that while resident doctors were aware of t...
Objective: To determine the role of mini-percutaneus nephrolithotomy in the renal stones manageme... more Objective: To determine the role of mini-percutaneus nephrolithotomy in the renal stones management and its post-operative complications.
In this paper, we apply the concept of double-framed soft sets to Abel-Grassmann’s hypergroupoids... more In this paper, we apply the concept of double-framed soft sets to Abel-Grassmann’s hypergroupoids (AG-hypergroupoids). We define double-framed soft AG-hypergroupoids (DFS AG-hypergroupoids) and double-framed soft left (respectively, right) (briefly DFS-left (respectively, DFS-right)) hyperideals of AG-hypergroupoids. It is shown that an idempotent DFS-left hyperideal is a DFS-hyperideal. Also a DFS right hyperideal becomes DFS hyperideal when pure left identity is adjoined to an AG-hypergroupoid, but the converse is not true. We also discuss some properties of these hyperideals in regular AG-hypergroupoids.
Many applications use the Global Positioning System data that provide rich context information fo... more Many applications use the Global Positioning System data that provide rich context information for multiple purposes. Easier availability and access of Global Positioning System data can facilitate various mobile applications, and one of such applications is to infer the mobility of a user. Most existing works for inferring users’ transportation modes need the combination of Global Positioning System data and other types of data such as accelerometer and Global System for Mobile Communications. However, the dependency of the applications to use data sources other than the Global Positioning System makes the use of application difficult if peer data source is not available. In this paper, we introduce a new generic framework for the inference of transportation mode by only using the Global Positioning System data. Our contribution is threefold. First, we propose a new method for Global Positioning System trajectory data preprocessing using grid probability distribution function. Seco...
In this paper, we introduce double-framed soft bi-ideals (briefly DFS bi-ideals) and double-frame... more In this paper, we introduce double-framed soft bi-ideals (briefly DFS bi-ideals) and double-framed soft generalized bi-ideals (briefly DFS generalized bi-ideals) in AG-groupoids and some properties of them are investigated. Several characterizations of intra-regular AG-groupoids in terms of DFS left (resp. right) ideals, DFS bi-ideals, DFS generalized bi-ideals and semiprime class of them are provided.
The main motivation behind this paper is to study some structural properties of a non-associative... more The main motivation behind this paper is to study some structural properties of a non-associative structure Abel Grassmann's groupoid (AG-groupoid) in terms of double-framed soft sets (DFS sets) as it hasn't attracted much attention compared to associative structures. An AG-groupoid can be referred to as a non-associative semigroup, as the main difference between a semigroup and an AG-groupoid is the switching of an associative law. In this paper, we introduce the concept of (M, N)-double-framed soft ideals (briefly, (M, N)-DFS ideal) of AG-groupoids and investigate some properties of these notions. We have shown that every (M, N)-DFS ideal is (M, N)-DFS AG-groupoid but the converse is not true. This is shown with the help of an example. We also discuss the properties of (M, N)-DFS ideals in regular AG-groupoids. Moreover a decision making algorithm based on DFS-sets is given.
Molodtsov's soft set theory is a new mathematical model for dealing with uncertainty from a param... more Molodtsov's soft set theory is a new mathematical model for dealing with uncertainty from a parameterization point of view. In soft set theory, the problem of setting the membership function does not arise, which makes the theory easily applied to many different fields. In this paper, we discuss a new approach to soft sets and compare soft sets to the related concepts of ordered semihypergroups. We define int-soft generalized bi-hyperideals in ordered semihypergroups and characterize regular and left weakly regular ordered semihypergroups by the properties of their int-soft generalized bi-hyperideals. Keywords Soft set • Regular • Left weakly regular ordered semihypergroups • Left (resp., right, bi-and generalized bi-)hyperideals • Int-soft left (resp., right, bi-and generalized bi-)hyperideals in ordered semihypergroups 1 Introduction Algebraic hyperstructures represent a natural extension of classical algebraic structures, and they were originally proposed in 1934 by a French mathematician Marty (1934), at Communicated by V. Loia.
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