Since real-world data are often inaccurate and working with fuzzy data and Z-numbers are very important and necessary, and in the real world, we need to rank and compare data, in this article, we introduce a new method for ranking Z-numbers. This ranking algorithm is based on centroid point. We evaluate the distance between the centroid points, and based on this distance, we rank the Z-numbers. The algorithm of this method has simple calculations and it provides satisfactory results for data in different conditions; we use this method in two practical examples. First, by ranking the return on assets of Tehran stock exchanges, with this method, we can choose the most risky stock and the least risky stock among the available stocks. The advantage of this method over conventional fuzzy methods is considering uncertainty and allocating credit in the opinion of experts to estimate fuzzy parameters, and in the second example, we ranked the factors which affect the productivity of tourism security. Then, by using the proposed algorithm, we introduce the most important and the least important factors for tourist security budgeting.
{"title":"Ranking the Return on Assets of Tehran Stock Exchange by a New Method Based on Z-Numbers Data","authors":"Maryam Farzam, Mozhdeh Afshar Kermani, Tofigh Allahviranloo, Azim Aminataei","doi":"10.1155/2023/2063267","DOIUrl":"https://doi.org/10.1155/2023/2063267","url":null,"abstract":"Since real-world data are often inaccurate and working with fuzzy data and Z-numbers are very important and necessary, and in the real world, we need to rank and compare data, in this article, we introduce a new method for ranking Z-numbers. This ranking algorithm is based on centroid point. We evaluate the distance between the centroid points, and based on this distance, we rank the Z-numbers. The algorithm of this method has simple calculations and it provides satisfactory results for data in different conditions; we use this method in two practical examples. First, by ranking the return on assets of Tehran stock exchanges, with this method, we can choose the most risky stock and the least risky stock among the available stocks. The advantage of this method over conventional fuzzy methods is considering uncertainty and allocating credit in the opinion of experts to estimate fuzzy parameters, and in the second example, we ranked the factors which affect the productivity of tourism security. Then, by using the proposed algorithm, we introduce the most important and the least important factors for tourist security budgeting.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135306192","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}
V. N. S. Repalle, Lateram Zawuga Hordofa, M. A. Ashebo
The article describes a new thought on the chromatic polynomial of an intuitionistic fuzzy graph which is illustrated based on α , β -level graphs. Besides, the alpha-beta fundamental set of an intuitionistic fuzzy graph is also defined with a vivid description. In addition to that, some characterizations of the chromatic polynomial of an intuitionistic fuzzy graph are specified as well verified. Furthermore, some untouched properties of the α , β -level graph are also projected and proved.
{"title":"Chromatic Polynomial of Intuitionistic Fuzzy Graphs Using α , β -Levels","authors":"V. N. S. Repalle, Lateram Zawuga Hordofa, M. A. Ashebo","doi":"10.1155/2022/9320700","DOIUrl":"https://doi.org/10.1155/2022/9320700","url":null,"abstract":"The article describes a new thought on the chromatic polynomial of an intuitionistic fuzzy graph which is illustrated based on α , β -level graphs. Besides, the alpha-beta fundamental set of an intuitionistic fuzzy graph is also defined with a vivid description. In addition to that, some characterizations of the chromatic polynomial of an intuitionistic fuzzy graph are specified as well verified. Furthermore, some untouched properties of the α , β -level graph are also projected and proved.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64788144","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}
In this study, we will introduce a new concept, which is a controlled K-operator frame for the space of all adjointable operators on a Hilbert A-module H which denoted EndA(H), where A is a C ∗-algebra. Also, we establish some results of the controlled K-operator frame in EndA(H). (e presented results are new and of interest for people working in this area. Some illustrative examples are provided to advocate the usability of our results.
{"title":"Controlled Frame for Operator in Hilbert c ∗ -Modules","authors":"H. Labrigui, A. Touri, M. Rossafi, S. Kabbaj","doi":"10.1155/2022/7296689","DOIUrl":"https://doi.org/10.1155/2022/7296689","url":null,"abstract":"In this study, we will introduce a new concept, which is a controlled K-operator frame for the space of all adjointable operators on a Hilbert A-module H which denoted EndA(H), where A is a C ∗-algebra. Also, we establish some results of the controlled K-operator frame in EndA(H). (e presented results are new and of interest for people working in this area. Some illustrative examples are provided to advocate the usability of our results.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64785320","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}
H. Q. Mohammad, Shaymaa Haleem. Ibrahem, L. Khaleel
{"title":"The Metric Chromatic Number of Zero Divisor Graph of a Ring Z n","authors":"H. Q. Mohammad, Shaymaa Haleem. Ibrahem, L. Khaleel","doi":"10.1155/2022/9069827","DOIUrl":"https://doi.org/10.1155/2022/9069827","url":null,"abstract":"","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64787713","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}
{"title":"Numerical Study of an Euler-Bernoulli Beam Stabilization Controlled in Displacement and Velocity","authors":"Brahima Yeo, Narcisse Dakouri, J. Adou","doi":"10.1155/2022/7647568","DOIUrl":"https://doi.org/10.1155/2022/7647568","url":null,"abstract":"","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64785933","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}
Bruce Masonova Solozafy Bemena, André Totohasina, Daniel Rajaonasy Feno
In epidemiology, the rule of association is used to determine the factors at the origin of diseases; implicative statistical analysis is thus a necessary tool in epidemiology too. Epidemiologists have more often chosen the so-called odds ratio measure in their studies of the quanti cation of the implicit link between an exposure and disease. In order to obtain good results, we need to be sure that the odds ratio measure is really the most relevant measure available. erefore, it is necessary to study the mathematical properties of the odds ratio. is paper proposes a comparative study of the behaviour and mathematical properties of the odds ratio measure, the measure of Guillaume–Khencha (MGK), and the normalised odd-ratio measure. We have chosen the MGK measure because the literature considers it to be a good measure for extracting implicit association rules according to its mathematical properties. e result in this paper concerns only the study of probabilistic data.
{"title":"The Effectiveness of the M G K Measure against the Odds Ratio in the Epidemiological Study","authors":"Bruce Masonova Solozafy Bemena, André Totohasina, Daniel Rajaonasy Feno","doi":"10.1155/2022/7835758","DOIUrl":"https://doi.org/10.1155/2022/7835758","url":null,"abstract":"In epidemiology, the rule of association is used to determine the factors at the origin of diseases; implicative statistical analysis is thus a necessary tool in epidemiology too. Epidemiologists have more often chosen the so-called odds ratio measure in their studies of the quanti\u0085cation of the implicit link between an exposure and disease. In order to obtain good results, we need to be sure that the odds ratio measure is really the most relevant measure available. erefore, it is necessary to study the mathematical properties of the odds ratio. is paper proposes a comparative study of the behaviour and mathematical properties of the odds ratio measure, the measure of Guillaume–Khencha (MGK), and the normalised odd-ratio measure. We have chosen the MGK measure because the literature considers it to be a good measure for extracting implicit association rules according to its mathematical properties. e result in this paper concerns only the study of probabilistic data.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64786465","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}
K. R. Cheneke, Koya Purnachandra Rao, G. K. Edessa
{"title":"A New Generalized Fractional-Order Derivative and Bifurcation Analysis of Cholera and Human Immunodeficiency Co-Infection Dynamic Transmission","authors":"K. R. Cheneke, Koya Purnachandra Rao, G. K. Edessa","doi":"10.1155/2022/7965145","DOIUrl":"https://doi.org/10.1155/2022/7965145","url":null,"abstract":"","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64786239","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}
We present some fine properties of immersions ℐ : M ⟶ N between manifolds, with particular attention to the case of immersed curves c : S 1 ⟶ ℝ n . We present new results, as well as known results but with quantitative statements (that may be useful in numerical applications) regarding tubular coordinates, neighborhoods of immersed and freely immersed curve, and local unique representations of nearby such curves, possibly “up to reparameterization.” We present examples and counterexamples to support the significance of these results. Eventually, we provide a complete and detailed proof of a result first stated in a 1991-paper by Cervera, Mascaró, and Michor: the quotient of the freely immersed curves by the action of reparameterization is a smooth (infinite dimensional) manifold.
{"title":"Neighborhoods and Manifolds of Immersed Curves","authors":"A. Mennucci","doi":"10.1155/2021/6974292","DOIUrl":"https://doi.org/10.1155/2021/6974292","url":null,"abstract":"We present some fine properties of immersions \u0000 \u0000 ℐ\u0000 :\u0000 M\u0000 ⟶\u0000 N\u0000 \u0000 between manifolds, with particular attention to the case of immersed curves \u0000 \u0000 c\u0000 :\u0000 \u0000 \u0000 S\u0000 \u0000 \u0000 1\u0000 \u0000 \u0000 ⟶\u0000 \u0000 \u0000 ℝ\u0000 \u0000 \u0000 n\u0000 \u0000 \u0000 \u0000 . We present new results, as well as known results but with quantitative statements (that may be useful in numerical applications) regarding tubular coordinates, neighborhoods of immersed and freely immersed curve, and local unique representations of nearby such curves, possibly “up to reparameterization.” We present examples and counterexamples to support the significance of these results. Eventually, we provide a complete and detailed proof of a result first stated in a 1991-paper by Cervera, Mascaró, and Michor: the quotient of the freely immersed curves by the action of reparameterization is a smooth (infinite dimensional) manifold.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64764622","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}
Hydrodynamic interactions of a two-solid microspheres system in a viscous incompressible fluid at low Reynolds number is investigated analytically. One of the spheres is conducting and assumed to be actively in motion under the action of an external oscillator field, and as the result, the other nonconducting sphere moves due to the induced flow oscillation of the surrounding fluid. The fluid flow past the spheres is described by the Stokes equation and the governing equation in the vector form for the two-sphere system is solved asymptotically using the two-timing method. For illustrations, applying a simple oscillatory external field, a systematic description of the average velocity of each sphere is formulated. The trajectory of the sphere was found to be inversely proportional to the frequency of the external field. The results demonstrated that no collisions occur between the spheres as the system moves in a circular motion with a fixed separation distance.
{"title":"On the Motion of Two Microspheres in a Stokes Flow Driven by an External Oscillator Field","authors":"Mohammed M. Al-Hatmi, A. Purnama","doi":"10.1155/2021/9211272","DOIUrl":"https://doi.org/10.1155/2021/9211272","url":null,"abstract":"Hydrodynamic interactions of a two-solid microspheres system in a viscous incompressible fluid at low Reynolds number is investigated analytically. One of the spheres is conducting and assumed to be actively in motion under the action of an external oscillator field, and as the result, the other nonconducting sphere moves due to the induced flow oscillation of the surrounding fluid. The fluid flow past the spheres is described by the Stokes equation and the governing equation in the vector form for the two-sphere system is solved asymptotically using the two-timing method. For illustrations, applying a simple oscillatory external field, a systematic description of the average velocity of each sphere is formulated. The trajectory of the sphere was found to be inversely proportional to the frequency of the external field. The results demonstrated that no collisions occur between the spheres as the system moves in a circular motion with a fixed separation distance.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64768635","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}
Let be the complex Grassmann manifold of -linear subspaces in . We compute rational relative Gottlieb groups of the embedding and show that the -sequence is exact if
让Gr。n是在n上的k个线性子空间的复数Grassmann流形。我们计算嵌入i的有理相对Gottlieb群:Gr k, nn + r，并证明当r≥k n时G -序列是精确的−k。
{"title":"Relative Gottlieb Groups of Embeddings between Complex Grassmannians","authors":"J. Gatsinzi","doi":"10.1155/2021/1417769","DOIUrl":"https://doi.org/10.1155/2021/1417769","url":null,"abstract":"<jats:p>Let <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mtext>Gr</mtext>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> be the complex Grassmann manifold of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>k</mi>\u0000 </math>\u0000 </jats:inline-formula>-linear subspaces in <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℂ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msup>\u0000 </math>\u0000 </jats:inline-formula>. We compute rational relative Gottlieb groups of the embedding <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mi>i</mi>\u0000 <mo>:</mo>\u0000 <mtext>Gr</mtext>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>⟶</mo>\u0000 <mtext>Gr</mtext>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mi>r</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> and show that the <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <mi>G</mi>\u0000 </math>\u0000 </jats:inline-formula>-sequence is exact if <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <mi>r</mi>\u0000 <mo>≥</mo>\u0000 <mi>k</mi>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mi","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64755579","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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