Mumtaz Ali, F. Smarandache, L. Vlădăreanu, M. Shabir
In this paper we extend soft neutrosophic rings and soft neutrosophic fields to soft neutrosophic birings, soft neutrosophic N-rings and soft neutrosophic bifields and soft neutrosophic N-fields. We also extend soft neu- trosophic ideal theory to form soft neutrosophic biideal and soft neutrosophic N-ideals over a neutrosophic biring and soft neutrosophic N-ring . We have given examples to illustrate the theory of soft neutrosophic birings, soft neutrosophic N-rings and soft neutrosophic fields and soft neutrosophic N-fields and display many properties of these.
{"title":"Generalization of Soft Neutrosophic Rings and Soft Neutrosophic Fields","authors":"Mumtaz Ali, F. Smarandache, L. Vlădăreanu, M. Shabir","doi":"10.5281/ZENODO.30173","DOIUrl":"https://doi.org/10.5281/ZENODO.30173","url":null,"abstract":"In this paper we extend soft neutrosophic rings and soft neutrosophic fields to soft neutrosophic birings, soft neutrosophic N-rings and soft neutrosophic bifields and soft neutrosophic N-fields. We also extend soft neu- trosophic ideal theory to form soft neutrosophic biideal and soft neutrosophic N-ideals over a neutrosophic biring and soft neutrosophic N-ring . We have given examples to illustrate the theory of soft neutrosophic birings, soft neutrosophic N-rings and soft neutrosophic fields and soft neutrosophic N-fields and display many properties of these.","PeriodicalId":46897,"journal":{"name":"Neutrosophic Sets and Systems","volume":"6 1","pages":"34-40"},"PeriodicalIF":0.0,"publicationDate":"2014-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71067649","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, we introduce and study the concept of "neutrosophic closed set "and "neutrosophic continuous function". Possible application to GIS topology rules are touched upon.
本文引入并研究了“嗜中性闭集”和“嗜中性连续函数”的概念。讨论了GIS拓扑规则的可能应用。
{"title":"Neutrosophic Closed Set and Neutrosophic Continuous Functions","authors":"A. Salama, F. Smarandache, Valeri Kromov","doi":"10.5281/ZENODO.30213","DOIUrl":"https://doi.org/10.5281/ZENODO.30213","url":null,"abstract":"In this paper, we introduce and study the concept of \"neutrosophic closed set \"and \"neutrosophic continuous function\". Possible application to GIS topology rules are touched upon.","PeriodicalId":46897,"journal":{"name":"Neutrosophic Sets and Systems","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71067991","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}
Mumtaz Ali, F. Smarandache, M. Shabir, Munazza Naz
In this paper, we extend the theory of neutrosophic rings and neutrosophic fields to soft sets and construct soft neutrosophic rings and soft neutrosophic fields. We also extend neutrosophic ideal theory to form soft neutrosophic ideal over a neutrosophic ring and soft neutrosophic ideal of a soft neutrosophic ring . We have given many examples to illustrate the theory of soft neutrosophic rings and soft neutrosophic fields and display many properties of of these. At the end of this paper, we gave soft neutrosophic ring homomorphism
{"title":"Soft Nuetrosophic Ring and Soft Neutrosophic Field","authors":"Mumtaz Ali, F. Smarandache, M. Shabir, Munazza Naz","doi":"10.5281/ZENODO.30325","DOIUrl":"https://doi.org/10.5281/ZENODO.30325","url":null,"abstract":"In this paper, we extend the theory of neutrosophic rings and neutrosophic fields to soft sets and construct soft neutrosophic rings and soft neutrosophic fields. We also extend neutrosophic ideal theory to form soft neutrosophic ideal over a neutrosophic ring and soft neutrosophic ideal of a soft neutrosophic ring . We have given many examples to illustrate the theory of soft neutrosophic rings and soft neutrosophic fields and display many properties of of these. At the end of this paper, we gave soft neutrosophic ring homomorphism","PeriodicalId":46897,"journal":{"name":"Neutrosophic Sets and Systems","volume":"3 1","pages":"53-59"},"PeriodicalIF":0.0,"publicationDate":"2014-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71067821","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 : 2014-03-02DOI: 10.6084/M9.FIGSHARE.1502551.V1
A. A. Salama, Haitham A. El-Ghareeb, Ayman M. Manie, F. Smarandache
In this paper, we have developed an Excel package to be utilized for calculating neutrosophic data and analyze them. The use of object oriented programming techniques and concepts as they may apply to the design and development a new framework to implement neutrosophic data operations, the c# programming language, NET Framework and Microsoft Visual Studio are used to implement the neutrosophic classes. We have used Excel as it is a powerful tool that is widely accepted and used for statistical analysis. Figure 1 shows Class Diagram of the implemented package. Figure 2 presents a working example of the package interface calculating the complement. Our implemented Neutrosophic package can calculate Intersection, Union, and Complement of the nuetrosophic set. Figure 3 presents our neutrosphic package capability to draw figures of presented neutrosphic set. Figure 4 presents charting of Union operation calculation, and figure 5 Intersection Operation. nuetrosophic set are characterized by its efficiency as it takes into consideration the three data items: True, Intermediate, and False.
{"title":"Introduction to Develop Some Software Programs for Dealing with Neutrosophic Sets","authors":"A. A. Salama, Haitham A. El-Ghareeb, Ayman M. Manie, F. Smarandache","doi":"10.6084/M9.FIGSHARE.1502551.V1","DOIUrl":"https://doi.org/10.6084/M9.FIGSHARE.1502551.V1","url":null,"abstract":"In this paper, we have developed an Excel package to be utilized for calculating neutrosophic data and analyze them. The use of object oriented programming techniques and concepts as they may apply to the design and development a new framework to implement neutrosophic data operations, the c# programming language, NET Framework and Microsoft Visual Studio are used to implement the neutrosophic classes. We have used Excel as it is a powerful tool that is widely accepted and used for statistical analysis. Figure 1 shows Class Diagram of the implemented package. Figure 2 presents a working example of the package interface calculating the complement. Our implemented Neutrosophic package can calculate Intersection, Union, and Complement of the nuetrosophic set. Figure 3 presents our neutrosphic package capability to draw figures of presented neutrosphic set. Figure 4 presents charting of Union operation calculation, and figure 5 Intersection Operation. nuetrosophic set are characterized by its efficiency as it takes into consideration the three data items: True, Intermediate, and False.","PeriodicalId":46897,"journal":{"name":"Neutrosophic Sets and Systems","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71206907","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}
P. Biswas, Surapati Pramanik, B. Giri, Nandalal Ghosh
In this paper we investigate multi-attribute decision making problem with single-valued neutrosophic attribute values. Crisp values are inadequate to model real life situation due to imprecise information frequently used in decision making process. Neutrosophic set is one such tool that can handle these situations. The rating of all alternatives is expressed with single-valued neutrosophic set which is characterised by truth-membership degree, indeterminacy-membership degree, and falsity-membership degree. Weight of each attribute is completely unknown to decision maker. We extend the grey relational analysis method to neutrosophic environment and apply it to multi-attribute decision making problem. Information entropy method is used to determine the unknown attribute weights. Neutrosophic grey relational coefficient is determined by using Hamming distance between each alternative to ideal neutrosophic estimates reliability solution and the ideal neutrosophic estimates un-reliability solution. Then neutrosophic relational degree is defined to determine the ranking order of all alternatives. Finally, an example is provided to illustrate the application of the proposed method.
{"title":"Entropy Based Grey Relational Analysis Method for Multi- Attribute Decision Making under Single Valued Neutrosophic Assessments","authors":"P. Biswas, Surapati Pramanik, B. Giri, Nandalal Ghosh","doi":"10.5281/ZENODO.22459","DOIUrl":"https://doi.org/10.5281/ZENODO.22459","url":null,"abstract":"In this paper we investigate multi-attribute decision making problem with single-valued neutrosophic attribute values. Crisp values are inadequate to model real life situation due to imprecise information frequently used in decision making process. Neutrosophic set is one such tool that can handle these situations. The rating of all alternatives is expressed with single-valued neutrosophic set which is characterised by truth-membership degree, indeterminacy-membership degree, and falsity-membership degree. Weight of each attribute is completely unknown to decision maker. We extend the grey relational analysis method to neutrosophic environment and apply it to multi-attribute decision making problem. Information entropy method is used to determine the unknown attribute weights. Neutrosophic grey relational coefficient is determined by using Hamming distance between each alternative to ideal neutrosophic estimates reliability solution and the ideal neutrosophic estimates un-reliability solution. Then neutrosophic relational degree is defined to determine the ranking order of all alternatives. Finally, an example is provided to illustrate the application of the proposed method.","PeriodicalId":46897,"journal":{"name":"Neutrosophic Sets and Systems","volume":"2 1","pages":"102-110"},"PeriodicalIF":0.0,"publicationDate":"2014-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71048234","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 neutrosophic hypercompositional structures ( ) H I arising from the hypercompositions derived from the binary relations τ on a neutrosophic set ( ) H I . We give the characterizations of τ that make ( ) H I hypergroupoids,quasihypergroups, semihypergroups, neutrosophic hypergroupoids, neutrosophic quasihypergroups, neutrosophic semihypergroups and neutrosophic hypergroups.
{"title":"Neutrosophic Hypercompositional Structures defined by Binary Relations","authors":"A. Agboola, S. Akinleye","doi":"10.5281/ZENODO.22589","DOIUrl":"https://doi.org/10.5281/ZENODO.22589","url":null,"abstract":"The objective of this paper is to study neutrosophic hypercompositional structures ( ) H I arising from the hypercompositions derived from the binary relations τ on a neutrosophic set ( ) H I . We give the characterizations of τ that make ( ) H I hypergroupoids,quasihypergroups, semihypergroups, neutrosophic hypergroupoids, neutrosophic quasihypergroups, neutrosophic semihypergroups and neutrosophic hypergroups.","PeriodicalId":46897,"journal":{"name":"Neutrosophic Sets and Systems","volume":"3 1","pages":"29-36"},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71048673","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 aim of this paper is to introduce the concept of re- lation on neutrosophic parameterized soft set (NP- soft sets) theo- ry. We have studied some related properties and also put forward some propositions on neutrosophic parameterized soft relation with proofs and examples. Finally the notions of symmetric, transitive, reflexive, and equivalence neutrosophic parameterized soft set relations have been established in our work. Finally a de- cision making method on NP-soft sets is presented.
{"title":"Neutrosophic Parameterized Soft Relations and Their Applications","authors":"I. Deli, Yunus toktas, S. Broumi","doi":"10.5281/ZENODO.22593","DOIUrl":"https://doi.org/10.5281/ZENODO.22593","url":null,"abstract":"The aim of this paper is to introduce the concept of re- lation on neutrosophic parameterized soft set (NP- soft sets) theo- ry. We have studied some related properties and also put forward some propositions on neutrosophic parameterized soft relation with proofs and examples. Finally the notions of symmetric, transitive, reflexive, and equivalence neutrosophic parameterized soft set relations have been established in our work. Finally a de- cision making method on NP-soft sets is presented.","PeriodicalId":46897,"journal":{"name":"Neutrosophic Sets and Systems","volume":"4 1","pages":"25-34"},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71048618","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 : 2013-10-01DOI: 10.6084/M9.FIGSHARE.1502626.V1
A. A. Salama, F. Smarandache, S. A. Alblowi
The purpose of this paper is to introduce and study the characteristic function of a neutrosophic set. After given the fundamental definitions of neutrosophic set operations generated by the characteristic function of a neutrosophic set ( for short), we obtain several properties, and discussed the relationship between neutrosophic sets generated by
{"title":"The Characteristic Function of a Neutrosophic Set","authors":"A. A. Salama, F. Smarandache, S. A. Alblowi","doi":"10.6084/M9.FIGSHARE.1502626.V1","DOIUrl":"https://doi.org/10.6084/M9.FIGSHARE.1502626.V1","url":null,"abstract":"The purpose of this paper is to introduce and study the characteristic function of a neutrosophic set. After given the fundamental definitions of neutrosophic set operations generated by the characteristic function of a neutrosophic set ( for short), we obtain several properties, and discussed the relationship between neutrosophic sets generated by","PeriodicalId":46897,"journal":{"name":"Neutrosophic Sets and Systems","volume":"3 1","pages":"14-17"},"PeriodicalIF":0.0,"publicationDate":"2013-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71207155","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 : 2013-10-01DOI: 10.6084/M9.FIGSHARE.1502610.V1
S. Broumi, F. Smarandache
Smarandache (1995) defined the notion of neutrosophic sets, which is a generalization of Zadeh's fuzzy set and Atanassov's intuitionistic fuzzy set. In this paper, we first develop some similarity measures of neutrosophic sets. We will present a method to calculate the distance between neutrosophic sets (NS) on the basis of the Hausdorff distance. Then we will use this distance to generate a new similarity measure to calculate the degree of similarity between NS. Finally we will prove some properties of the proposed similarity measures.
{"title":"Several Similarity Measures of Neutrosophic Sets","authors":"S. Broumi, F. Smarandache","doi":"10.6084/M9.FIGSHARE.1502610.V1","DOIUrl":"https://doi.org/10.6084/M9.FIGSHARE.1502610.V1","url":null,"abstract":"Smarandache (1995) defined the notion of neutrosophic sets, which is a generalization of Zadeh's fuzzy set and Atanassov's intuitionistic fuzzy set. In this paper, we first develop some similarity measures of neutrosophic sets. We will present a method to calculate the distance between neutrosophic sets (NS) on the basis of the Hausdorff distance. Then we will use this distance to generate a new similarity measure to calculate the degree of similarity between NS. Finally we will prove some properties of the proposed similarity measures.","PeriodicalId":46897,"journal":{"name":"Neutrosophic Sets and Systems","volume":"1 1","pages":"10"},"PeriodicalIF":0.0,"publicationDate":"2013-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71207091","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 we introduce the notion of filter on the neutrosophic crisp set, then we consider a generalization of the filter’s studies. Afterwards, we present the important neutrosophic crisp filters. We also study several relations between different neutrosophic crisp filters and neutrosophic topologies. Possible applications to database systems are touched upon.
{"title":"Filters via Neutrosophic Crisp Sets","authors":"A. A. Salama, F. Smarandache","doi":"10.5281/ZENODO.30168","DOIUrl":"https://doi.org/10.5281/ZENODO.30168","url":null,"abstract":"In this paper we introduce the notion of filter on the neutrosophic crisp set, then we consider a generalization of the filter’s studies. Afterwards, we present the important neutrosophic crisp filters. We also study several relations between different neutrosophic crisp filters and neutrosophic topologies. Possible applications to database systems are touched upon.","PeriodicalId":46897,"journal":{"name":"Neutrosophic Sets and Systems","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71067638","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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