Pub Date : 2021-07-27DOI: 10.52280/pujm.2021.530705
Atiqe Ur Rahman, M. Saeed, Abida Hafeez
Hypersoft set (an extension of soft set) is a new mathematical tool to tackle the inadequacy of soft set for attribute-valued sets. In this study, concept of bijective hypersoft set is proposed and some of its set theoretic operations like restricted-AND and relaxed-AND, are characterized. Moreover, new operations of bijective hypersoft set such as dependency, decision system, significance of decision system, reduced decision system and decision rules in decision system, are discussed with illustrated examples. A decision making algorithm and application are discussed with the support of these proposed operations.
{"title":"Theory of Bijective Hypersoft Set with Application in Decision Making","authors":"Atiqe Ur Rahman, M. Saeed, Abida Hafeez","doi":"10.52280/pujm.2021.530705","DOIUrl":"https://doi.org/10.52280/pujm.2021.530705","url":null,"abstract":"Hypersoft set (an extension of soft set) is a new mathematical tool to tackle the inadequacy of soft set for attribute-valued sets. In\u0000this study, concept of bijective hypersoft set is proposed and some of its\u0000set theoretic operations like restricted-AND and relaxed-AND, are characterized. Moreover, new operations of bijective hypersoft set such as dependency, decision system, significance of decision system, reduced decision system and decision rules in decision system, are discussed with\u0000illustrated examples. A decision making algorithm and application are\u0000discussed with the support of these proposed operations.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117281856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-27DOI: 10.52280/pujm.2021.530704
We use the homotopy perturbation method (HPM) to construct a new iterative system for solving non-linear equations in this article. The criteria for convergence in the scheme developed are also imposed. To show the validity and reliability of our process, we compare our regime with other current procedures by looking at various test problems.
{"title":"An Efficient Two-Step Iterative Technique for Solving Non-Linear Equations","authors":"","doi":"10.52280/pujm.2021.530704","DOIUrl":"https://doi.org/10.52280/pujm.2021.530704","url":null,"abstract":"We use the homotopy perturbation method (HPM) to construct\u0000a new iterative system for solving non-linear equations in this article. The\u0000criteria for convergence in the scheme developed are also imposed. To\u0000show the validity and reliability of our process, we compare our regime\u0000with other current procedures by looking at various test problems.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116646440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-27DOI: 10.52280/pujm.2021.530701
Irfan Nazeer, T. Rashid
In this research article, we initiate the novel idea of picture fuzzy incidence graphs (PFIGs). We explain some innovative notions comprising of picture fuzzy cut-vertices, picture fuzzy bridges, picture fuzzy incidence cutpairs, and picture fuzzy incidence cut-vertices. Some rudimentary theorems and essential results are also examined in the PFIGs. Further, we determine the different concepts together with the order, size, and certain kinds of degrees in PFIG. A new type of PFIGs namely, complete picture fuzzy incidence graphs (CPFIGs) and complement of (PFIGs) are also furnished. A comparative analysis of PFIGs with fuzzy incidence graphs is also presented. Finally, an application of PFIGs in the control of illegal transportation of people from India to America is provided
{"title":"Picture Fuzzy Incidence Graphs with Application","authors":"Irfan Nazeer, T. Rashid","doi":"10.52280/pujm.2021.530701","DOIUrl":"https://doi.org/10.52280/pujm.2021.530701","url":null,"abstract":"In this research article, we initiate the novel idea of picture\u0000fuzzy incidence graphs (PFIGs). We explain some innovative notions\u0000comprising of picture fuzzy cut-vertices, picture fuzzy bridges, picture\u0000fuzzy incidence cutpairs, and picture fuzzy incidence cut-vertices. Some\u0000rudimentary theorems and essential results are also examined in the PFIGs.\u0000Further, we determine the different concepts together with the order, size,\u0000and certain kinds of degrees in PFIG. A new type of PFIGs namely,\u0000complete picture fuzzy incidence graphs (CPFIGs) and complement of\u0000(PFIGs) are also furnished. A comparative analysis of PFIGs with fuzzy\u0000incidence graphs is also presented. Finally, an application of PFIGs in\u0000the control of illegal transportation of people from India to America is\u0000provided","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124609032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-27DOI: 10.52280/pujm.2021.530702
S. Hussain, Faiza Azhar, M. Latif, Javariya Khalid
The authors have tried to prove some Ostrowski-type fractional integral inequalities for r−times differentiable functions and generalized some results which were carried out in both [6, 25]. Some applications to special means are given. The methods and techniques of this paper could further stimulate the research conducted in the field of fractional integral inequalities.
{"title":"OSTROWSKI-TYPE FRACTIONAL INTEGRAL INEQUALITIES FOR\u0000r−TIMES DIFFERENTIABLE h−CONVEX FUNCTIONS","authors":"S. Hussain, Faiza Azhar, M. Latif, Javariya Khalid","doi":"10.52280/pujm.2021.530702","DOIUrl":"https://doi.org/10.52280/pujm.2021.530702","url":null,"abstract":"The authors have tried to prove some Ostrowski-type fractional\u0000integral inequalities for r−times differentiable functions and generalized\u0000some results which were carried out in both [6, 25]. Some applications to\u0000special means are given. The methods and techniques of this paper could\u0000further stimulate the research conducted in the field of fractional integral\u0000inequalities.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116191182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-27DOI: 10.52280/pujm.2021.530703
Nisar Ahmad, Syed Aleem Shah, W. K. Mashwani, Nasim Ullah
In this paper we elaborated the concept that on what conditions left almost semigroup (LA-Semigroup), right almost semigroup (RA-Semigroup) and a groupoid become commutative and further extended these results on medial, LA-Group and RA-Group. We proved that the relation of LA-Semigroup with left double displacement semigroup (LDD-semigroup), RA-Semigroup with left double displacement semigroup (RDD-semigroup) is only commutative property. We highlighted the errors in the recently developed results on LA-Semigroup and semigroup [17, 1, 18] and proved that example discussed in [18] is semigroup with left identity but not paramedial. We extended results on locally associative LA-Semigroup explained in [20, 21] towards LA-Semigroup and RA-Semigroup with left zero and right zero respectively. We also discussed results on n-dimensional LA-Semigroup, n-dimensional RASemigroup, non commutative finite medials with three or more than three left or right identities and finite as well as infinite commutative idempotent medials not studied in literature.
{"title":"Corrections and Extensions in Left and Right Almost Semigroups","authors":"Nisar Ahmad, Syed Aleem Shah, W. K. Mashwani, Nasim Ullah","doi":"10.52280/pujm.2021.530703","DOIUrl":"https://doi.org/10.52280/pujm.2021.530703","url":null,"abstract":"In this paper we elaborated the concept that on what conditions left almost semigroup (LA-Semigroup), right almost semigroup\u0000(RA-Semigroup) and a groupoid become commutative and further extended these results on medial, LA-Group and RA-Group. We proved\u0000that the relation of LA-Semigroup with left double displacement semigroup (LDD-semigroup), RA-Semigroup with left double displacement\u0000semigroup (RDD-semigroup) is only commutative property. We highlighted the errors in the recently developed results on LA-Semigroup and\u0000semigroup [17, 1, 18] and proved that example discussed in [18] is semigroup with left identity but not paramedial. We extended results on locally\u0000associative LA-Semigroup explained in [20, 21] towards LA-Semigroup\u0000and RA-Semigroup with left zero and right zero respectively. We also\u0000discussed results on n-dimensional LA-Semigroup, n-dimensional RASemigroup, non commutative finite medials with three or more than three\u0000left or right identities and finite as well as infinite commutative idempotent\u0000medials not studied in literature.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132280409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-25DOI: 10.52280/pujm.2021.530603
Amna Shujahuddin, Muhammad Salim Khan, Haider Ali
In the image processing, noise is referred to as the visual distortion. This undesirable by-product may be captured in an image due to unpreventable assorted reasons. The interference of natural phenomena and technical problem, such as small sensor size, long exposure time, low ISO, shadow noise etc., can pollute image. The presence of noise images affects image processing outputs that include segmentation. Segmentation for noisy images is the major concern. To tackle this issue, we propose a modernistic model that is able neutralize the negative effects of outlier using the characteristic of kernel function by different approaches such as linear approach and quadratic approach for global segmentation. Moreover the weight function is used for local segmentation of noisy images. Comparing with classical models, the proposed technique shows robust performance. In comparison with the wellknown models such as Chan-Vese (CV) model , Yongfei Wu and Chuanjiang He (Wu-He) model and Chunming Li (Li) model we conclude that performance of our new model is much better.
{"title":"Mathematical Model for Single and Multiple Object Extraction","authors":"Amna Shujahuddin, Muhammad Salim Khan, Haider Ali","doi":"10.52280/pujm.2021.530603","DOIUrl":"https://doi.org/10.52280/pujm.2021.530603","url":null,"abstract":"In the image processing, noise is referred to as the visual distortion. This undesirable by-product may be captured in\u0000an image due to unpreventable assorted reasons. The interference\u0000of natural phenomena and technical problem, such as small sensor\u0000size, long exposure time, low ISO, shadow noise etc., can pollute\u0000image. The presence of noise images affects image processing outputs that include segmentation. Segmentation for noisy images is\u0000the major concern. To tackle this issue, we propose a modernistic\u0000model that is able neutralize the negative effects of outlier using\u0000the characteristic of kernel function by different approaches such\u0000as linear approach and quadratic approach for global segmentation. Moreover the weight function is used for local segmentation\u0000of noisy images. Comparing with classical models, the proposed\u0000technique shows robust performance. In comparison with the wellknown models such as Chan-Vese (CV) model , Yongfei Wu and\u0000Chuanjiang He (Wu-He) model and Chunming Li (Li) model we\u0000conclude that performance of our new model is much better.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128937122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-25DOI: 10.52280/pujm.2021.530604
M. Saeed, Asad Mehmood, Amna Anwar
Chen [24] introduced the extension of TOPSIS in the fuzzy structure, while this article stretches the modern approach of TOPSIS to the intuitionistic fuzzy framework. Linguistic terms are used in this study to evaluate the weight of each criterion and the rating of alternatives in the context of a triangular intuitionistic fuzzy number. A new intuitionistic fuzzy positive ideal solution (IFPIS) and intuitionistic fuzzy negative ideal solution (IFNIS) are proposed in this model of extended TOPSIS. Euclidean distance is introduced between two triangular intuitionistic fuzzy numbers to calculate separation between each alternative to both (IFPIS) and (IFNIS). The proposed model’s mechanism is presented with the help of an algorithm, and then it is applied to the personal selection problem. Finally, a comparative study is given between this model and other TOPSIS techniques.
{"title":"An extension of TOPSIS based on linguistic terms in triangular intuitionistic\u0000fuzzy structure","authors":"M. Saeed, Asad Mehmood, Amna Anwar","doi":"10.52280/pujm.2021.530604","DOIUrl":"https://doi.org/10.52280/pujm.2021.530604","url":null,"abstract":"Chen [24] introduced the extension of TOPSIS in the fuzzy\u0000structure, while this article stretches the modern approach of TOPSIS to\u0000the intuitionistic fuzzy framework. Linguistic terms are used in this study\u0000to evaluate the weight of each criterion and the rating of alternatives in\u0000the context of a triangular intuitionistic fuzzy number. A new intuitionistic fuzzy positive ideal solution (IFPIS) and intuitionistic fuzzy negative ideal solution (IFNIS) are proposed in this model of extended TOPSIS. Euclidean distance is introduced between two triangular intuitionistic fuzzy numbers to calculate separation between each alternative to both\u0000(IFPIS) and (IFNIS). The proposed model’s mechanism is presented with\u0000the help of an algorithm, and then it is applied to the personal selection\u0000problem. Finally, a comparative study is given between this model and\u0000other TOPSIS techniques.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127002062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-25DOI: 10.52280/pujm.2021.530605
M. Jamil, R. Khan, K. Shah
A wave phenomena evolved day after day, as various concepts regarding waves appeared with the passage of time. These phenomena are generally modelled mathematically by partial differential equations (PDEs). In this research, we investigate the exact analytical solutions of one and two dimensional linear dissipative wave equations which are modelled by second order PDEs with use of some initial and boundary conditions. We use double Laplace transform (DLT) and triple Laplace transform (TLT) methods to determine these exact analytical solutions. We provide examples with figures to test effectiveness of this scheme of Laplace transform
{"title":"Exact Analytical Solutions of Linear Dissipative Wave Equations via Laplace\u0000Transform Method","authors":"M. Jamil, R. Khan, K. Shah","doi":"10.52280/pujm.2021.530605","DOIUrl":"https://doi.org/10.52280/pujm.2021.530605","url":null,"abstract":"A wave phenomena evolved day after day, as various concepts\u0000regarding waves appeared with the passage of time. These phenomena\u0000are generally modelled mathematically by partial differential equations\u0000(PDEs). In this research, we investigate the exact analytical solutions\u0000of one and two dimensional linear dissipative wave equations which are\u0000modelled by second order PDEs with use of some initial and boundary\u0000conditions. We use double Laplace transform (DLT) and triple Laplace\u0000transform (TLT) methods to determine these exact analytical solutions.\u0000We provide examples with figures to test effectiveness of this scheme of\u0000Laplace transform","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129524408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-25DOI: 10.52280/pujm.2021.530602
Muhammad Kashif Maqbool, M. S. Bosan, Abdul Rauf Khan, Zaheer Ahmad
: In our present paper, topological groups are being discussed, where the relations with counter examples built the interest in the generalized structure. Some of these structures have also been converted into the other structures using topological isomorphism. In our work, the identity element plays the important role in lieu of arbitrary element. The role of topology has the more interest in our discipline.
{"title":"Relations on topologized groups","authors":"Muhammad Kashif Maqbool, M. S. Bosan, Abdul Rauf Khan, Zaheer Ahmad","doi":"10.52280/pujm.2021.530602","DOIUrl":"https://doi.org/10.52280/pujm.2021.530602","url":null,"abstract":": In our present paper, topological groups are being discussed,\u0000where the relations with counter examples built the interest in the generalized structure. Some of these structures have also been converted into the\u0000other structures using topological isomorphism. In our work, the identity\u0000element plays the important role in lieu of arbitrary element. The role of\u0000topology has the more interest in our discipline.","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115792742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-24DOI: 10.52280/pujm.2021.530601
H. Irmak
The principal goal of this scientific note is first to compose various rational types functions directly connecting to a variety of multivalently functions with complex coefficients, which are regular in certain domains in the complex plane, and then to designate numerous argument properties associating with certain applications of those (multivalent) functions
{"title":"A variety of multivalently analytic functions with complex coefficients and some\u0000argument properties of their applications","authors":"H. Irmak","doi":"10.52280/pujm.2021.530601","DOIUrl":"https://doi.org/10.52280/pujm.2021.530601","url":null,"abstract":"The principal goal of this scientific note is first to compose\u0000various rational types functions directly connecting to a variety of multivalently\u0000functions with complex coefficients, which are regular in certain\u0000domains in the complex plane, and then to designate numerous argument\u0000properties associating with certain applications of those (multivalent)\u0000functions","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128221379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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