Pub Date : 2023-11-01DOI: 10.7546/nifs.2023.29.3.318-324
R. Buvaneswari, K. Umamaheswari
The concept of strong edges in domination set and its properties are discussed. The increasing or reducing domination numbers using cardinality are also studied. Bondage $(alpha(G))$ and non-bondage $(alpha_K(G))$ sets are defined in regular intuitionistic fuzzy graph. The properties of bondage and non-bondage number of intuitionistic fuzzy graph analyzed. A minimum $2$-bondage set $X$ of an intuitionistic fuzzy graph (IFG) $G$ is a bondage set of regular intuitionistic fuzzy graph in $G$.
{"title":"Bondage and non-bondage sets in regular intuitionistic fuzzy graphs","authors":"R. Buvaneswari, K. Umamaheswari","doi":"10.7546/nifs.2023.29.3.318-324","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.3.318-324","url":null,"abstract":"The concept of strong edges in domination set and its properties are discussed. The increasing or reducing domination numbers using cardinality are also studied. Bondage $(alpha(G))$ and non-bondage $(alpha_K(G))$ sets are defined in regular intuitionistic fuzzy graph. The properties of bondage and non-bondage number of intuitionistic fuzzy graph analyzed. A minimum $2$-bondage set $X$ of an intuitionistic fuzzy graph (IFG) $G$ is a bondage set of regular intuitionistic fuzzy graph in $G$.","PeriodicalId":489404,"journal":{"name":"Notes on IFS","volume":"47 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135515738","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 : 2023-10-01DOI: 10.7546/nifs.2023.29.3.292-297
Lilija Atanassova
Circular Intuitionistic Fuzzy Sets (CIFS) are one of the newest extensions of the intuitionistic fuzzy sets. In the present paper, three procedures for de-intuitionistic fuzzification of CIFS are discussed.
{"title":"Three de-intuitionistic fuzzification procedures over circular intuitionistic fuzzy sets","authors":"Lilija Atanassova","doi":"10.7546/nifs.2023.29.3.292-297","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.3.292-297","url":null,"abstract":"Circular Intuitionistic Fuzzy Sets (CIFS) are one of the newest extensions of the intuitionistic fuzzy sets. In the present paper, three procedures for de-intuitionistic fuzzification of CIFS are discussed.","PeriodicalId":489404,"journal":{"name":"Notes on IFS","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136059679","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 : 2023-10-01DOI: 10.7546/nifs.2023.29.3.298-317
Anjali Sonkariya, Shiv Prasad Yadav
Data envelopment analysis (DEA) is a non-parametric linear programming (LP) based technique to measure the relative efficiencies of decision-making units (DMUs). The conventional DEA models assume that input-output data is crisp, which may not always be feasible in practical situations due to the presence of ambiguity and imprecision. Therefore, to handle uncertain and imprecise data, the concept of intuitionistic fuzzy sets (IFS) has been introduced. In this study, the relative efficiencies of DMUs with uncertain data will be determined. For this reason, the conventional cost efficiency (CE) model of DEA is extended to IF environment. Also, the lower and upper-cost efficiency models are developed using α-cut and β-cut approach. The data for inputs, outputs and input prices are considered intuitionistic fuzzy numbers (IFNs), in particular triangular intuitionistic fuzzy numbers (TIFNs). To demonstrate the practical application of the proposed intuitionistic fuzzy cost efficiency models (IFCEMs), a numerical example is presented.
{"title":"Development of intuitionistic fuzzy cost efficiency model in data envelopment analysis","authors":"Anjali Sonkariya, Shiv Prasad Yadav","doi":"10.7546/nifs.2023.29.3.298-317","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.3.298-317","url":null,"abstract":"Data envelopment analysis (DEA) is a non-parametric linear programming (LP) based technique to measure the relative efficiencies of decision-making units (DMUs). The conventional DEA models assume that input-output data is crisp, which may not always be feasible in practical situations due to the presence of ambiguity and imprecision. Therefore, to handle uncertain and imprecise data, the concept of intuitionistic fuzzy sets (IFS) has been introduced. In this study, the relative efficiencies of DMUs with uncertain data will be determined. For this reason, the conventional cost efficiency (CE) model of DEA is extended to IF environment. Also, the lower and upper-cost efficiency models are developed using α-cut and β-cut approach. The data for inputs, outputs and input prices are considered intuitionistic fuzzy numbers (IFNs), in particular triangular intuitionistic fuzzy numbers (TIFNs). To demonstrate the practical application of the proposed intuitionistic fuzzy cost efficiency models (IFCEMs), a numerical example is presented.","PeriodicalId":489404,"journal":{"name":"Notes on IFS","volume":"132 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136094727","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 : 2023-09-27DOI: 10.7546/nifs.2023.29.3.239-246
Krassimir Atanassov
Two intuitionistic fuzzy modal operators from a second type are used for introducing of new intuitionistic fuzzy modal topological structures. After this, these structures, extended with the two standard intuitionistic fuzzy modal operators, generate four new intuitionistic fuzzy bimodal topological structures. They are illustrated with examples.
{"title":"Four new intuitionistic fuzzy bimodal topological structures","authors":"Krassimir Atanassov","doi":"10.7546/nifs.2023.29.3.239-246","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.3.239-246","url":null,"abstract":"Two intuitionistic fuzzy modal operators from a second type are used for introducing of new intuitionistic fuzzy modal topological structures. After this, these structures, extended with the two standard intuitionistic fuzzy modal operators, generate four new intuitionistic fuzzy bimodal topological structures. They are illustrated with examples.","PeriodicalId":489404,"journal":{"name":"Notes on IFS","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135537336","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 : 2023-09-27DOI: 10.7546/nifs.2023.29.3.277-291
Rasul Rasuli
In this paper, we introduced intuitionistic fuzzy G-modules on M under norms (t-norm T and s-conorm S) and some related results like intersection, sum and direct sum of them has also been discussed. Also some of their properties have been investigated under G-module homomorphisms.
{"title":"Intuitionistic fuzzy G-modules with respect to norms (T and S)","authors":"Rasul Rasuli","doi":"10.7546/nifs.2023.29.3.277-291","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.3.277-291","url":null,"abstract":"In this paper, we introduced intuitionistic fuzzy G-modules on M under norms (t-norm T and s-conorm S) and some related results like intersection, sum and direct sum of them has also been discussed. Also some of their properties have been investigated under G-module homomorphisms.","PeriodicalId":489404,"journal":{"name":"Notes on IFS","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135537566","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 : 2023-09-27DOI: 10.7546/nifs.2023.29.3.261-276
P. K. Sharma
The aim of this paper is to present some characterizations of almost prime ideals and almost prime submodules in the intuitionistic fuzzy environment. We investigate various properties of these concepts and achieve many results.
{"title":"On intuitionistic fuzzy almost prime ideals and intuitionistic fuzzy almost prime submodules","authors":"P. K. Sharma","doi":"10.7546/nifs.2023.29.3.261-276","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.3.261-276","url":null,"abstract":"The aim of this paper is to present some characterizations of almost prime ideals and almost prime submodules in the intuitionistic fuzzy environment. We investigate various properties of these concepts and achieve many results.","PeriodicalId":489404,"journal":{"name":"Notes on IFS","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135536739","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 : 2023-09-27DOI: 10.7546/nifs.2023.29.3.247-260
Jaydip Bhattacharya
The concept of intuitionistic fuzzy sets is becoming very popular day by day among mathematicians and researchers from other areas of science. It has been noticed that some operators have very interesting properties in Intuitionistic fuzzy sets. That is why these properties are investigated in this study. New findings on equality are obtained and proved.
{"title":"Some new results on intuitionistic fuzzy operators","authors":"Jaydip Bhattacharya","doi":"10.7546/nifs.2023.29.3.247-260","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.3.247-260","url":null,"abstract":"The concept of intuitionistic fuzzy sets is becoming very popular day by day among mathematicians and researchers from other areas of science. It has been noticed that some operators have very interesting properties in Intuitionistic fuzzy sets. That is why these properties are investigated in this study. New findings on equality are obtained and proved.","PeriodicalId":489404,"journal":{"name":"Notes on IFS","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135537375","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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