Pub Date : 2021-03-31DOI: 10.22342/JIMS.27.1.905.9-28
Sudin Mandal, Injamam Ul Karim, S. Raha
In this paper, an attempt is made to study approximate reasoning based on a Type-2 fuzzy set theory. In the process, we have examined the underlying fuzzy logic structure on which the reasoning is formulated. We have seen that the partial/incomplete/imprecise truth-values of elements of a type-2 fuzzy set under consideration forms a lattice. We propose two new lattice operations which ultimately help us to define a residual and thereby making the structure of truth- values a residuated lattice. We have focused upon two typical rules of inference used mostly in ordinary approximate reasoning methodology based on Type-1 fuzzy set theory. Our proposal is illustrated with typical artificial examples.
{"title":"A Theory of Approximate Reasoning with Type-2 Fuzzy Set","authors":"Sudin Mandal, Injamam Ul Karim, S. Raha","doi":"10.22342/JIMS.27.1.905.9-28","DOIUrl":"https://doi.org/10.22342/JIMS.27.1.905.9-28","url":null,"abstract":"In this paper, an attempt is made to study approximate reasoning based on a Type-2 fuzzy set theory. In the process, we have examined the underlying fuzzy logic structure on which the reasoning is formulated. We have seen that the partial/incomplete/imprecise truth-values of elements of a type-2 fuzzy set under consideration forms a lattice. We propose two new lattice operations which ultimately help us to define a residual and thereby making the structure of truth- values a residuated lattice. We have focused upon two typical rules of inference used mostly in ordinary approximate reasoning methodology based on Type-1 fuzzy set theory. Our proposal is illustrated with typical artificial examples.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":"27 1","pages":"9-28"},"PeriodicalIF":0.3,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41570943","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 : 2021-03-31DOI: 10.22342/JIMS.27.1.948.1-8
Akhlak Mansuri, Rohit Mehta, R. Chandel
This article shows the study about the harmonious coloring and to investigate the harmonious chromatic number of the central graph of quadrilateral snake, double quadrilateral snake, triple quadrilateral snake, k-quadrilateral snake, alternate quadrilateral snake, double alternate quadrilateral snake, triple alternate quadrilateral snake and k-alternate quadrilateral snake, denoted by C(Qn), C(DQn), C(TQn), C(kQn), C(AQn), C(D(AQn)), C(T(AQn)), C(k(AQn)) respectively.
{"title":"Central Graph of Quadrilateral Snakes with Chromatic Number","authors":"Akhlak Mansuri, Rohit Mehta, R. Chandel","doi":"10.22342/JIMS.27.1.948.1-8","DOIUrl":"https://doi.org/10.22342/JIMS.27.1.948.1-8","url":null,"abstract":"This article shows the study about the harmonious coloring and to investigate the harmonious chromatic number of the central graph of quadrilateral snake, double quadrilateral snake, triple quadrilateral snake, k-quadrilateral snake, alternate quadrilateral snake, double alternate quadrilateral snake, triple alternate quadrilateral snake and k-alternate quadrilateral snake, denoted by C(Qn), C(DQn), C(TQn), C(kQn), C(AQn), C(D(AQn)), C(T(AQn)), C(k(AQn)) respectively.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":"27 1","pages":"1-8"},"PeriodicalIF":0.3,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42740395","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 : 2021-03-31DOI: 10.22342/JIMS.27.1.881.103-114
B. Sooryanarayana, Suma A.S., Chandrakala S.B.
Let G=(V,E) be a simple connected graph. For each ordered subset S={s_1,s_2,...,s_k} of V and a vertex u in V, we associate a vector Gamma(u/S)=(d(u,s_1),d(u,s_2),...,d(u,s_k)) with respect to S, where d(u,v) denote the distance between u and v in G. A subset S is said to be resolving set of G if Gamma(u/S) not equal to Gamma(v/S) for all u, v in V-S. The purpose of this paper is to introduce various types of r-sets and compute minimum cardinality of each set, in possible cases, particulary for paths, cycles, complete graphs and wheels.
{"title":"Certain Varieties of Resolving Sets of A Graph","authors":"B. Sooryanarayana, Suma A.S., Chandrakala S.B.","doi":"10.22342/JIMS.27.1.881.103-114","DOIUrl":"https://doi.org/10.22342/JIMS.27.1.881.103-114","url":null,"abstract":"Let G=(V,E) be a simple connected graph. For each ordered subset S={s_1,s_2,...,s_k} of V and a vertex u in V, we associate a vector Gamma(u/S)=(d(u,s_1),d(u,s_2),...,d(u,s_k)) with respect to S, where d(u,v) denote the distance between u and v in G. A subset S is said to be resolving set of G if Gamma(u/S) not equal to Gamma(v/S) for all u, v in V-S. The purpose of this paper is to introduce various types of r-sets and compute minimum cardinality of each set, in possible cases, particulary for paths, cycles, complete graphs and wheels.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45857208","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 : 2021-03-31DOI: 10.22342/JIMS.27.1.955.90-102
S. Rathee, Monika Swami
The motivation behind this paper is to use hybrid method for searching a typical component of the set of fixed point of an infinite family of non expansive mapping and the set of monotone, Lipschtiz continuous variational inequality problem. The contemplated method is combination of two method one is extragradient method and the other one is DQ method. Also, we demonstrate the strong convergence of the designed iterative technique, under some warm conditions.
{"title":"Strong Convergence of A Hybrid Method for Infinite Family of Nonexpansive Mapping and Variational Inequality","authors":"S. Rathee, Monika Swami","doi":"10.22342/JIMS.27.1.955.90-102","DOIUrl":"https://doi.org/10.22342/JIMS.27.1.955.90-102","url":null,"abstract":"The motivation behind this paper is to use hybrid method for searching a typical component of the set of fixed point of an infinite family of non expansive mapping and the set of monotone, Lipschtiz continuous variational inequality problem. The contemplated method is combination of two method one is extragradient method and the other one is DQ method. Also, we demonstrate the strong convergence of the designed iterative technique, under some warm conditions.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":"27 1","pages":"90-102"},"PeriodicalIF":0.3,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48023445","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 : 2021-03-31DOI: 10.22342/JIMS.27.1.939.123-129
C. Granados
In this paper, we used the notion of soft w-open sets to introduce and study the concepts of soft b-w-open sets. Moreover, some of their properties are shown. Furthermore, the concepts of soft b-T1 and soft b-T2 spaces are defined.
{"title":"On Soft b-w-Open Sets","authors":"C. Granados","doi":"10.22342/JIMS.27.1.939.123-129","DOIUrl":"https://doi.org/10.22342/JIMS.27.1.939.123-129","url":null,"abstract":"In this paper, we used the notion of soft w-open sets to introduce and study the concepts of soft b-w-open sets. Moreover, some of their properties are shown. Furthermore, the concepts of soft b-T1 and soft b-T2 spaces are defined.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43841036","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 : 2021-03-31DOI: 10.22342/JIMS.27.1.869.75-89
M. Ghadiri
A larger class of algebraic hyperstructures satisfying the ring (field)-likeaxioms is the class of Hv-rings (Hv-fields). In this paper, we define the Hv-integraldomain and introduce the Hv-field of fractions of an Hv-integral domain. Also, theHv-quotient ring and some relative theorems are presented. Finally, some interestingresults about the Hv-rings of fractions, Hv-quotient rings and the relations betweenthem are proved.
{"title":"Hv-Field of Fractions and Hv-Quotient Rings","authors":"M. Ghadiri","doi":"10.22342/JIMS.27.1.869.75-89","DOIUrl":"https://doi.org/10.22342/JIMS.27.1.869.75-89","url":null,"abstract":"A larger class of algebraic hyperstructures satisfying the ring (field)-likeaxioms is the class of Hv-rings (Hv-fields). In this paper, we define the Hv-integraldomain and introduce the Hv-field of fractions of an Hv-integral domain. Also, theHv-quotient ring and some relative theorems are presented. Finally, some interestingresults about the Hv-rings of fractions, Hv-quotient rings and the relations betweenthem are proved.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41662503","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 : 2021-03-31DOI: 10.22342/JIMS.27.1.968.48-63
H. Bordbar, M. M. Zahedi, Y. Jun
A characterization of cubic subalgebra is established. The notion of internal and external cubic subalgebra in BCK/BCI -algebra and several properties are investigated. The R-union, R-intersection, P-union, and P-intersection of internal and external cubic subalgebras in BCK/BCI -algebra are discussed.
{"title":"Internal and External Cubic Subalgebras of BCK/BCI-Algebras","authors":"H. Bordbar, M. M. Zahedi, Y. Jun","doi":"10.22342/JIMS.27.1.968.48-63","DOIUrl":"https://doi.org/10.22342/JIMS.27.1.968.48-63","url":null,"abstract":"A characterization of cubic subalgebra is established. The notion of internal and external cubic subalgebra in BCK/BCI -algebra and several properties are investigated. The R-union, R-intersection, P-union, and P-intersection of internal and external cubic subalgebras in BCK/BCI -algebra are discussed.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":"27 1","pages":"48-63"},"PeriodicalIF":0.3,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49312693","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 : 2021-03-31DOI: 10.22342/JIMS.27.1.899.29-47
S. Dashputre, C. Padmavati, Kavita Sakure
In this paper, we propose the modified proximal point algorithm with the process for three nearly Lipschitzian asymptotically nonexpansive mappings and multivalued mappings in CAT(0) space under certain conditions. We prove some convergence theorems for the algorithm which was introduced by Shamshad Hussain et al. [18]. A numerical example is given to illustrate the efficiency of proximal point algorithm for supporting our result.
{"title":"Convergence Results for Proximal Point Algorithm in Complete Cat(0) Space for Multivalued Mappings","authors":"S. Dashputre, C. Padmavati, Kavita Sakure","doi":"10.22342/JIMS.27.1.899.29-47","DOIUrl":"https://doi.org/10.22342/JIMS.27.1.899.29-47","url":null,"abstract":"In this paper, we propose the modified proximal point algorithm with the process for three nearly Lipschitzian asymptotically nonexpansive mappings and multivalued mappings in CAT(0) space under certain conditions. We prove some convergence theorems for the algorithm which was introduced by Shamshad Hussain et al. [18]. A numerical example is given to illustrate the efficiency of proximal point algorithm for supporting our result.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":"27 1","pages":"29-47"},"PeriodicalIF":0.3,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41549415","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 : 2021-03-31DOI: 10.22342/JIMS.27.1.931.64-74
Jeetendra Gurjar, S. Jog
The degree sum exponent distance matrix M(G) of a graph G is a square matrix whose (i,j)-th entry is (di+dj)^ d(ij) whenever i not equal to j, otherwise it is zero, where di is the degree of i-th vertex of G and d(ij)=d(vi,vj) is distance between vi and vj. In this paper, we define degree sum exponent distance energy E(G) as sum of absolute eigenvalues of M(G). Also, we obtain some bounds on the degree sum exponent distance energy of some graphs and deduce direct expressions for some graphs.
{"title":"Degree Sum Exponent Distance Energy of Some Graphs","authors":"Jeetendra Gurjar, S. Jog","doi":"10.22342/JIMS.27.1.931.64-74","DOIUrl":"https://doi.org/10.22342/JIMS.27.1.931.64-74","url":null,"abstract":"The degree sum exponent distance matrix M(G) of a graph G is a square matrix whose (i,j)-th entry is (di+dj)^ d(ij) whenever i not equal to j, otherwise it is zero, where di is the degree of i-th vertex of G and d(ij)=d(vi,vj) is distance between vi and vj. In this paper, we define degree sum exponent distance energy E(G) as sum of absolute eigenvalues of M(G). Also, we obtain some bounds on the degree sum exponent distance energy of some graphs and deduce direct expressions for some graphs.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":"27 1","pages":"64-74"},"PeriodicalIF":0.3,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43852937","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 : 2021-03-31DOI: 10.22342/JIMS.27.1.829.115-122
R. Ghorbel, H. Kthiri
Let Fq be a finite field and Fq((X−1 )) the field of formal power series with coefficients in Fq. The purpose of this paper is to exhibit a family of transcendental continued fractions of formal power series over a finite field through some specific irregularities of its partial quotients
{"title":"A Transcendental Unbounded Continued Fraction Expansions over A Finite Field","authors":"R. Ghorbel, H. Kthiri","doi":"10.22342/JIMS.27.1.829.115-122","DOIUrl":"https://doi.org/10.22342/JIMS.27.1.829.115-122","url":null,"abstract":"Let Fq be a finite field and Fq((X−1 )) the field of formal power series with coefficients in Fq. The purpose of this paper is to exhibit a family of transcendental continued fractions of formal power series over a finite field through some specific irregularities of its partial quotients","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":"27 1","pages":"115-122"},"PeriodicalIF":0.3,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48010972","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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