Linear programming problems with integers, are issues in which some or all decision variables are restricted to be their values are correct values, and here these models can be solved by neglecting the constraints of integers and then rotating the fractional values of the optimal solution to obtain correct values, paying attention to the need for the resulting solution to belong to the accepted solutions area, but this procedure can lead to the desired purpose if the number of variables is small, but if there is a number We do not guarantee to obtain an optimal correct solution for the model, even if all the solution combinations are tested, knowing that in the model that contains a variable n a set of solutions 2n must be tried, and if we can rotate, the correct solution will be an approximate solution, in order to obtain more accurate integer values, we present in this research a study in which we use binary integer variables to build the neutrosophic linear mathematical model. The importance of this study lies in providing solutions to many practical problems that require solutions with integers and we will clarify all the above by building a mathematical model for the problem of the mixture of products using binary integer variables and neutrosophic values.
{"title":"Neutrosophic Mathematical Model of Product Mixture Problem Using Binary Integer Mutant","authors":"A. Admin","doi":"10.54216/jnfs.060206","DOIUrl":"https://doi.org/10.54216/jnfs.060206","url":null,"abstract":"Linear programming problems with integers, are issues in which some or all decision variables are restricted to be their values are correct values, and here these models can be solved by neglecting the constraints of integers and then rotating the fractional values of the optimal solution to obtain correct values, paying attention to the need for the resulting solution to belong to the accepted solutions area, but this procedure can lead to the desired purpose if the number of variables is small, but if there is a number We do not guarantee to obtain an optimal correct solution for the model, even if all the solution combinations are tested, knowing that in the model that contains a variable n a set of solutions 2n must be tried, and if we can rotate, the correct solution will be an approximate solution, in order to obtain more accurate integer values, we present in this research a study in which we use binary integer variables to build the neutrosophic linear mathematical model. The importance of this study lies in providing solutions to many practical problems that require solutions with integers and we will clarify all the above by building a mathematical model for the problem of the mixture of products using binary integer variables and neutrosophic values.","PeriodicalId":438286,"journal":{"name":"Journal of Neutrosophic and Fuzzy Systems","volume":"1 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113932796","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}
There are several mathematical theorem and other equation which is used frequently. However many researchers or scholar unable to prove them mathematically. One of the famous example is Pythagrous theorem, Budhayana, Pingala, Fibonacci series or even (a+b)2=a2+b2+2ab. It is indeed requirement to understand the basic proof of thiese mathematical theorem and its contradictory. This paper tried to provide some basic proof for these famous theorem and its relations with existing approaches for various applications.
{"title":"A Note on Basic Proof of Some Famous Mathematical Theorem and Its Illustration","authors":"Prempratap Singh","doi":"10.54216/jnfs.030105","DOIUrl":"https://doi.org/10.54216/jnfs.030105","url":null,"abstract":"There are several mathematical theorem and other equation which is used frequently. However many researchers or scholar unable to prove them mathematically. One of the famous example is Pythagrous theorem, Budhayana, Pingala, Fibonacci series or even (a+b)2=a2+b2+2ab. It is indeed requirement to understand the basic proof of thiese mathematical theorem and its contradictory. This paper tried to provide some basic proof for these famous theorem and its relations with existing approaches for various applications.","PeriodicalId":438286,"journal":{"name":"Journal of Neutrosophic and Fuzzy Systems","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115422049","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 began a novel technique to dealing with the Neutrosophic Pythagorean shortest route problem in a network in this paper by representing each edge weight as a triangular fuzzy Pythagorean number with dependent Neutrosophic components and Pythagorean fuzzy graph condition.0≤μ_1 (v_i^' )^2+β_1 (v_i^' )^2+σ_1 (v_i^' )^2≤2. The main purpose of this article is to show how to use Neutrosophic Pythagorean fuzzy graphs. As a result, we created the proposed method, which also delivers the shortest path length from the source node (SN) to the destination node by using a ranking function for the Neutrosophic Pythagorean fuzzy Triangular number. Finally, an illustrative instance is supplied for validation.
{"title":"Neutrosophic Pythagorean Fuzzy Shortest Path in a Network","authors":"M. Basha, M. M. Jabarulla, Broumi Said","doi":"10.54216/jnfs.060103","DOIUrl":"https://doi.org/10.54216/jnfs.060103","url":null,"abstract":"We began a novel technique to dealing with the Neutrosophic Pythagorean shortest route problem in a network in this paper by representing each edge weight as a triangular fuzzy Pythagorean number with dependent Neutrosophic components and Pythagorean fuzzy graph condition.0≤μ_1 (v_i^' )^2+β_1 (v_i^' )^2+σ_1 (v_i^' )^2≤2. The main purpose of this article is to show how to use Neutrosophic Pythagorean fuzzy graphs. As a result, we created the proposed method, which also delivers the shortest path length from the source node (SN) to the destination node by using a ranking function for the Neutrosophic Pythagorean fuzzy Triangular number. Finally, an illustrative instance is supplied for validation.","PeriodicalId":438286,"journal":{"name":"Journal of Neutrosophic and Fuzzy Systems","volume":"138 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116394129","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}
Recently, precise measurement of uncertainty of data with fuzzy attributes is considered as one of the main problems. For this purpose, fuzzy sets, intuitionistic fuzzy sets, and neutrosophic set theory are extensively introduced. The problem arises in computing the complement of true or false membership values in the case of indeterminacy. Instead of indeterminacy as discussed in neutrosophic set theory, it can be completely true, partially true, or partially false. To deal with this, the theory of ambiguous sets has recently been introduced. A real-time example of dealing with unconsciousness and ambiguousness in relation to human perception is discussed, illustrating the motivation of the ambiguous set theory. Finally, this study focuses on the definition of the ambiguous set, its mathematical representation, and the associated concepts.
{"title":"Ambiguous Set Theory: A New Approach to Deal with Unconsciousness and Ambiguousness of Human Perception","authors":"Pritpal Singh","doi":"10.54216/jnfs.050106","DOIUrl":"https://doi.org/10.54216/jnfs.050106","url":null,"abstract":"Recently, precise measurement of uncertainty of data with fuzzy attributes is considered as one of the main problems. For this purpose, fuzzy sets, intuitionistic fuzzy sets, and neutrosophic set theory are extensively introduced. The problem arises in computing the complement of true or false membership values in the case of indeterminacy. Instead of indeterminacy as discussed in neutrosophic set theory, it can be completely true, partially true, or partially false. To deal with this, the theory of ambiguous sets has recently been introduced. A real-time example of dealing with unconsciousness and ambiguousness in relation to human perception is discussed, illustrating the motivation of the ambiguous set theory. Finally, this study focuses on the definition of the ambiguous set, its mathematical representation, and the associated concepts.","PeriodicalId":438286,"journal":{"name":"Journal of Neutrosophic and Fuzzy Systems","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131442368","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}
Choice of materials is difficult since it requires considering several factors, assigning relative importance to those criteria, and ultimately choosing the most relevant criterion. Finally, it is important to set the criteria in a way that takes into account both the known material attributes and the needs of the application. Therefore, MCDM techniques may be used to the process of selecting materials. A possibility of incomplete dilemmas arises due to the decision maker's language inputs. Therefore, the inputs might be supplied as fuzzy numbers in order to circumvent the issue. Considering that a neutrosophic set is a metaphor to overcome uncertainty of human perceptions. To assess this recruitment process in a neutrosophic setting, this paper employs a neutrosophic-based version of the MCDM tool TOPSIS to determine which alternative materials should be used for the center console of an electric car.
{"title":"An Integrated Neutrosophic MCDM Methodology for Material Selection","authors":"A. Abdelmonem, Mahmoud M M.Ismail","doi":"10.54216/jnfs.010108","DOIUrl":"https://doi.org/10.54216/jnfs.010108","url":null,"abstract":"Choice of materials is difficult since it requires considering several factors, assigning relative importance to those criteria, and ultimately choosing the most relevant criterion. Finally, it is important to set the criteria in a way that takes into account both the known material attributes and the needs of the application. Therefore, MCDM techniques may be used to the process of selecting materials. A possibility of incomplete dilemmas arises due to the decision maker's language inputs. Therefore, the inputs might be supplied as fuzzy numbers in order to circumvent the issue. Considering that a neutrosophic set is a metaphor to overcome uncertainty of human perceptions. To assess this recruitment process in a neutrosophic setting, this paper employs a neutrosophic-based version of the MCDM tool TOPSIS to determine which alternative materials should be used for the center console of an electric car.","PeriodicalId":438286,"journal":{"name":"Journal of Neutrosophic and Fuzzy Systems","volume":"166 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115552599","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 paper the concepts of somewhat neutrosophic δ-continuous functions, somewhat neutrosophic δ-open functions between neutrosophic topological spaces are introduced and studied. Besides giving characterizations of these functions, several interesting properties of these functions are studied. The concepts of neutrosophic δ-resolvable spaces and neutrosophic δ-irresolvable spaces are also introduced and studied in this paper. These functions can be extended to a somewhat neutrosophic δ-irresolute continuous functions in neutrosophic topological spaces.
{"title":"Somewhat Neutrosopic δ-Continuous Functions in Neutrosophic Topological Spaces","authors":"C. John Sundar, A. Vadivel","doi":"10.54216/jnfs.060204","DOIUrl":"https://doi.org/10.54216/jnfs.060204","url":null,"abstract":"In this paper the concepts of somewhat neutrosophic δ-continuous functions, somewhat neutrosophic δ-open functions between neutrosophic topological spaces are introduced and studied. Besides giving characterizations of these functions, several interesting properties of these functions are studied. The concepts of neutrosophic δ-resolvable spaces and neutrosophic δ-irresolvable spaces are also introduced and studied in this paper. These functions can be extended to a somewhat neutrosophic δ-irresolute continuous functions in neutrosophic topological spaces.","PeriodicalId":438286,"journal":{"name":"Journal of Neutrosophic and Fuzzy Systems","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128454153","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}
This paper is dedicated to present a wide review study on the recent advantages of neutrosophic linear diophantine equations and number theory. We revise the neutrosophic linear diophantine equations, refined neutrosophic Diophantine equations, and n-refined neutrosophic linear Diophantine equations.
{"title":"A Review On Recent Developments In Neutrosophic Linear Diophantine Equations","authors":"Mikail Bal, Katy D. Ahmad, Rozina Ali","doi":"10.54216/jnfs.020106","DOIUrl":"https://doi.org/10.54216/jnfs.020106","url":null,"abstract":"This paper is dedicated to present a wide review study on the recent advantages of neutrosophic linear diophantine equations and number theory. We revise the neutrosophic linear diophantine equations, refined neutrosophic Diophantine equations, and n-refined neutrosophic linear Diophantine equations.","PeriodicalId":438286,"journal":{"name":"Journal of Neutrosophic and Fuzzy Systems","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116846847","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}
The purpose of a failure mode and effect analysis (FMEA) is to improve the safety and dependability of a system, product, procedure, or facility by identifying potential points of failure and determining the consequences of such failures. The assessment of failure modes, the weighting of risk factors, and the ranking of failure modes are all areas where the conventional FMEA falls short when put to use in the real world. To assess the hazard of failure modes in a trapezoidal neutrosophic sets environment, this research proposes a model that combines the neutrosophic sets and MCDM technique such as WASPAS. The WASPAS MCDM method is used to calculate the weights of standards and order the alternatives. Advantages of trapezoidal neutrosophic numbers in dealing with uncertainty, ambiguity, and incompleteness are combined with the benefits of WASPAS to create the suggested risk prioritization strategy.
{"title":"Integrated Multi-Criteria Decision Making Via Trapezoidal Neutrosophic Sets to Evaluate the Risks of Failure Mode","authors":"Mahmoud A. Zaher, N. M. Eldakhly","doi":"10.54216/jnfs.050103","DOIUrl":"https://doi.org/10.54216/jnfs.050103","url":null,"abstract":"The purpose of a failure mode and effect analysis (FMEA) is to improve the safety and dependability of a system, product, procedure, or facility by identifying potential points of failure and determining the consequences of such failures. The assessment of failure modes, the weighting of risk factors, and the ranking of failure modes are all areas where the conventional FMEA falls short when put to use in the real world. To assess the hazard of failure modes in a trapezoidal neutrosophic sets environment, this research proposes a model that combines the neutrosophic sets and MCDM technique such as WASPAS. The WASPAS MCDM method is used to calculate the weights of standards and order the alternatives. Advantages of trapezoidal neutrosophic numbers in dealing with uncertainty, ambiguity, and incompleteness are combined with the benefits of WASPAS to create the suggested risk prioritization strategy.","PeriodicalId":438286,"journal":{"name":"Journal of Neutrosophic and Fuzzy Systems","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127702909","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}
The objective of this paper is to study and define the neutrosophic real functions with one neutrosophic variable depending on the geometric isometry (AH-Isometry), with a lot of concepts from real analysis including continuality, differentiability, derivativility, integrability. We have presented the formal forms of different popular functions in neutrosophic environment like logarithmic function, exponential function, trigonometric functions. Rising neutrosophic derivative, indefinite integral, and definite integral well defined including rising to neutrosophic functions.
{"title":"A Study of Derivative and Integration a Neutrosophic Functions","authors":"A. A. Salama, M. Alaswad, Rasha Dallah","doi":"10.54216/jnfs.050203","DOIUrl":"https://doi.org/10.54216/jnfs.050203","url":null,"abstract":"The objective of this paper is to study and define the neutrosophic real functions with one neutrosophic variable depending on the geometric isometry (AH-Isometry), with a lot of concepts from real analysis including continuality, differentiability, derivativility, integrability. We have presented the formal forms of different popular functions in neutrosophic environment like logarithmic function, exponential function, trigonometric functions. Rising neutrosophic derivative, indefinite integral, and definite integral well defined including rising to neutrosophic functions.","PeriodicalId":438286,"journal":{"name":"Journal of Neutrosophic and Fuzzy Systems","volume":"164 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133907632","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 paper, the neutrosophic crisp minimal structure which is a more general structure than the neutrosophic minimal structure is built on neutrosophic crisp sets. The necessary arguments which are neutrosophic minimal crisp open set, neutrosophic minimal crisp closed set, neutrosophic crisp minimal closure, and neutrosophic crisp minimal interior are defined and their basic properties are presented. Also, the neutrosophic crisp minimal structure subspace of neutrosophic crisp minimal structure is defined and studied some of its properties. Finally, many examples are presented.
{"title":"Neutrosophic Crisp minimal Structure","authors":"R. K. Al-Hamido","doi":"10.54216/jnfs.030103","DOIUrl":"https://doi.org/10.54216/jnfs.030103","url":null,"abstract":"In this paper, the neutrosophic crisp minimal structure which is a more general structure than the neutrosophic minimal structure is built on neutrosophic crisp sets. The necessary arguments which are neutrosophic minimal crisp open set, neutrosophic minimal crisp closed set, neutrosophic crisp minimal closure, and neutrosophic crisp minimal interior are defined and their basic properties are presented. Also, the neutrosophic crisp minimal structure subspace of neutrosophic crisp minimal structure is defined and studied some of its properties. Finally, many examples are presented.","PeriodicalId":438286,"journal":{"name":"Journal of Neutrosophic and Fuzzy Systems","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132197662","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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