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...make use of the literature in case the reader is not thorough with the basics. The second chapter deals with different types of neutrosophic bilinear algebras and bivector spaces and proves several results analogous to linear bialgebra. In chapter three the authors introduce the notion of n-linear algebras and prove several theorems related to them. Many of the classical t...

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...Dedication 5 Preface 7 Chapter One INTRODUCTION TO BASIC CONCEPTS 9 1.1 Introduction to Bilinear Algebras and their Generalizations 9 1.2 Introduction to Neutrosophic Algebraic Structures 11 Chapter Two NEUTROSOPHIC LINEAR ALGEBRA 15 2.1 Neutrosophic Bivector Spaces 15 2.2 Strong Neutrosophic Bivector Spaces 32 2....

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... W. B. Vasantha Kandasamy Florentin SmarandacheNEUTROSOPHIC BILINEAR ALGEBRAS AND THEIR GENERALIZATIONS Svenska fysikarkivet St... ...ne INTRODUCTION TO BASIC CONCEPTS 91.1 Introduction to Bilinear Algebras and their Generalizations 91.2 Introduction... ...and their Generalizations 91.2 Introduction to Neutrosophic Algebraic Structures 11 Chapter Two NEUTROSOPHIC LINEAR ALGEBRA ... ...aces of Type II 307 Chapter Four APPLICATIONS OF NEUTROSOPHIC n-LINEAR ALGEBRAS 359 Chapter Five SUGGESTED PROBLEMS ... ...concept of neutrosophic bilinearalgebras and their generalizations to n-linear algebras, n>2.This book has five chapters. The reader should be well-ve... ...2). These neutrosophic n-matrices can also be used to modelNeutrosophic Fuzzy Relational maps, when n-experts give theiropinion on any real world pro...

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...This book has four chapters. The first chapter just introduces n-group which is essential for the definition of n-vector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several related results which are analogues of the classical linear algebra theorems. In case of n-vector spaces we can define several types of linear tr...

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...Preface 5 Chapter One BASIC CONCEPTS 7 Chapter Two n-VECTOR SPACES OF TYPE I AND THEIR PROPERTIES 13 Chapter Three APPLICATIONS OF n-LINEAR ALGEBRA OF TYPE I 81 Chapter Four SUGGESTED PROBLEMS 103 FURTHER READING 111 INDEX 116 ABOUT THE AUTHORS 120...

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... 13Chapter ThreeAPPLICATIONS OFn-LINEAR ALGEBRA OF TYPE I 81 3Ch... ...20 4PREFACE With the advent of computers one needs algebraic structuresthat can simultaneously work with bulk data. One suchal... ...taneously work with bulk data. One suchalgebraic structure namely n-linear algebras of type I areintroduced in this book and its applications to n-Mar... ...given. These structures can bethought of as the generalization of bilinear algebras and bivectorspaces. Several interesting n-linear algebra propertie... ...roup which is essential for the definition of n-vector spaces and n-linear algebras of type I. Chapter two givesthe notion of n-vector spaces and seve... ...l world problems which adopts fuzzymodels like Fuzzy Cognitive Maps, Fuzzy Relational Equationsand Bidirectional Associative Memories. The application...

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...The aim of this book is two fold. At the outset the book gives most of the available literature about Fuzzy Relational Equations (FREs) and its properties for there is no book that solely caters to FREs and its applications. Though we have a comprehensive bibliography, we do not promise to give all the possible available literature...

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... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHEFUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATIONAL MAPS HEXIS ... ...SOPHIC RELATIONAL MAPS HEXIS Church Rock 2004FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATIONAL MAPS W. B. Vasant... ...ication 6Preface 7Chapter OneFUZZY RELATIONAL EQUATIONS: BASIC CONCEPTSAND PROPERTIES 1.1 Fuzzy Relationa... ... problems with fuzzy relation equation constraints 57 1.9 Neural fuzzy relational system with a new learning algorithm 63 1.10 U... ...ainable Solution of FRE 67 1.11 Specificity shift in solving fuzzy relational equations 70 1.12 FRE with defuzzification algori... ...a fuzzy relation equation in an arbitrary max-minalgebra. By a max-min fuzzy algebra B we mean any linearly orderedset (B, ≤) with the binary operati... ...ndthe relation X ∈ B (n, p) is unknown. An important special case of max-min algebra is Godelalgebra, in which the underlying set is the closed unit ... ...s the closed unit intervalwith natural ordering of real numbers. This max-min algebra willbe denoted by BG. An implication operator in BG is defined b... ... whichneed not be dense nor bounded. An extension B* is defined as thebounded algebra created from B by adding the least element, orthe greatest eleme...

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...Algebraic structures on linguistic sets associated with a linguistic variable are introduced. The linguistics with single closed binary operations are only semigroups and monoids. We describe the new notion of linguistic semi...

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...MIGROUPS AND THEIR PROPERTIES 62Chapter ThreeLINGUISTIC SEMILINEAR ALGEBRAS AND LINGUISTICSEMIVECTOR SPACES 128 ... ... 191ABOUT THE AUTHORS 196 4PREFACE Algebraic structures on linguistic sets associated with alinguistic variab... ...inguistic semifields, linguistic semivector spaces and linguisticsemilinear algebras defined over linguistic semifields. We alsodefine algebraic struc... ...as over linguistic semifields. Clearly, linguistic semifieldsare linguistic algebraic structures with two binary operations. 5We define... .... This study is very vital for we develop the notion of linguistic relational equations which is one of the important linguistic models tha... ...ions which is one of the important linguistic models that uses linguistic relational equations. To this effect we briefly describe some speci... ...he following are very basic for us to introduce the concept of linguistic relational equations and applications to real world problems and in comp... ...m heights d Figure 1.7 The map or the relational edges / lines are markedas {best growth, good growth, very good... ...age}. Now the expert connects the linguistic sets S and R by thefollowing relational linguistic maps with linguistic values /terms{very hard working...

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...In this book authors for the first time construct a MOD Relational Maps model analogous to Fuzzy Relational Maps (FRMs) model or Neutrosophic Relational Maps (NRMs) model using the MOD rectangular or relational matrices. The advantage of using these models is that we are sure to g...

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... MOD Relational MapsModels and MOD NaturalNeutrosophic Relational Maps Models W. B. Vasantha Kandasamy Ila... ... 4Chapter OneINTRODUCTION 9Chapter TwoMOD RELATIONAL MAPS MODELS 13Chapter ThreeMOD-NATURAL NEUTR... ...TIONAL MAPS MODELS 13Chapter ThreeMOD-NATURAL NEUTROSOPHIC RELATIONALMAPS MODEL AND THEIR PROPERTIES 9... ...ND THEIR PROPERTIES 99Chapter FourMOD INTERVAL RELATIONAL MAPS 175Chapter FiveSUGGESTED PR... ...numbers (a+bI, where I =indeterminacy).2003 – Introduction of I-neutrosophic algebraic structures.2003 – introduction to neutrosophic cognitive maps.h... ...for the first time construct a MODRelational Maps model analogous to Fuzzy Relational Maps(FRMs) model or Neutrosophic Relational Maps (NRMs) modelu... ...04.23. Vasantha Kandasamy, W.B., and Smarandache, F., Basic Neutrosophic algebraic structures and their applications to fuzzy and Neutrosophic ... ...ntha Kandasamy, W.B., Neelakantan, N.R., and Kannan, S.R., Replacement of Algebraic Linear Equations by Fuzzy Relation Equations in Chemical Eng... ... W. B. and Smarandache, F., Neutrosophic algebraic structures and neutrosophic N-algebraic structures, Hexis...

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...ion sequence which is a new concept, related sequences, conjectures, properties, and problems. This study was conducted by using (Maple 8){a computer Algebra System. Keywords Smarandache inversion, Smarandache reverse sequence. Introduction In [1], C.Ashbacher, studied the Smarandache reverse sequence: 1; 21; 321; 4321; 54321; 654321; 7654321; 87654321; 987654321; 10...

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...the Smarandache-type function 31 P. Zhang : An equation involving the function ±k(n) 35 Y. B. Jun : Smarandache fantastic ideals of Smarandache BCI-algebras 40 T. Jayeo. la : On the Universality of some Smarandache loops of Bol-Moufang type 45 W. Kandasamy, M. Khoshnevisan and K. Ilanthenral : Smarandache representation and its applications 59 Y. Wang, X. Ren and S. M...

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... 35 Y. B. Jun : Smarandache fantastic ideals of Smarandache BCI-algebras 40 T. Ja´ıy´eo.l´a : On the Universality of some Sm... ...ies, and problems. This study was conducted by using (Maple 8)–a computer Algebra System. Keywords Smarandache inversion, Smarandache reverse sequen... ...eferences [1] El-Qallali A., L∗-unipotent semigroups, J. Pure and Applied Algebra, 62 (1989), 19-33.30 X.M. Ren and H.Y. Zhou ... ...4, 40-44 Smarandache fantastic ideals of Smarandache BCI-algebras Y. B. Jun Department of Mathematic... ...-Smarandache fantastic ideals is established. Keywords Smarandache BCI-algebra, Smarandache fresh ideal, Smarandache clean ideal, Smarandache fan... ...matrices. The notion of these matrices have beenused to define neutrosophic relational equations and fuzzy neutrosophic relational equations. Here we ...

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...The algebraic structure, linear algebra happens to be one of the subjects which yields itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief eco...

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...In this section we give the definition of linear algebra and just state the few important theorems like Cayley Hamilton theorem, Cyclic Decomposition Theorem, Generalized Cayley Hamilton Theorem and give some properties about linear algebra....

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... 2CONTENTSPreface 5Chapter OneINTRODUCTION TO LINEAR ALGEBRA AND S-LINEAR ALGEBRA 1.1 Basic properties of linear algebra ... ... 1.1 Basic properties of linear algebra 7 1.2 Introduction to s-linear algebra 15 1.3 Some aapplications of S-linear algebra 30Chap... ...NEUTROSOPHIC LINEAR BIALGEBRA AND ITSAPPLICATION 4.1 Some basic neutrosophic algebraic structures 131 4.2 Smarandache neutros... ... 229ABOUT THE AUTHORS 238 4PrefaceThe algebraic structure, linear algebra happens to be one ofthe subjects wh... ...ic matrices for NCMs and use rectangularneutrosophic matrices for Neutrosophic Relational Maps 137(NRMs). We need the notion of neutrosop... ...ic matrices. The notion of these matriceshave been used to define neutrosophic relational equationsand fuzzy neutrosophic relational equations. ... ...hoenix, 2003.45. VASANTHA KANDASAMY, W.B., and FLORENTIN Smarandache, Fuzzy Relational Equations and Neutrosophic Relational Equations, Hexis, Chu... ... integral neutrosophic matrices, 193Fuzzy neutrosophic matrices, 194, 195Fuzzy Relational Maps, 138GGeneralized Cayley Hamilton Theorem, 7, 9Generator... ... 141-2Neutrosophic polynomial, 150Neutrosophic quotient group, 133Neutrosophic relational maps, 137Neutrosophic rectangular bimatrix, 192Neutrosophic ...

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...This ninth volume of Collected Papers includes 87 papers comprising 982 pages on Neutrosophic Theory and its applications in Algebra, written between 2014-2022 by the author alone or in collaboration with the following 81 co-authors (alphabetically ordered) from 19 countries: E.O. Adeleke, A.A.A. Agboola, Ahmed B. Al-Nafee, Ahmed Mostafa Khalil, Ak...

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... apers (on Neutrosophic Theory and Its Applications in Algebra) lobal ... ...r) Collected Papers(on Neutrosophic Theory and Its Applications in Algebra) Volume IXPeer-Reviewers: Muhammad Saeed ... ...nd editor) Collected Papers(on Neutrosophic Theory and Its Applications in Algebra) Volume IX GLOBAL KNOWLEDGE Publish... ...rs comprising 982 pages on Neutrosophic Theory and its applications in Algebra, written between 2014-2022 by the author alone or in collaboration ... ...lorentin bus, Ohio, USA, 76 p., 2014. Smarandache, Fuzzy Relational Equations & 55. Florentin Smarandache & Mumtaz Ali - ... ... 55. Florentin Smarandache & Mumtaz Ali - edi- Neutrosophic Relational Equations, Hexis, tors, Neutrosophic Sets and Syste... ... imprecise environment. Kandasamy and Smarandache [7] introduced fuzzy relational maps and neutrosophic relational maps. Thomason [8], introd... ...stems, Vol. 3, 2014 4. W. B. V. Kandasamy and F. Smarandache,” Fuzzy Relational Maps and Neutrosophic Relational Maps” , HEXIS Church Roc... ... (2013) pp 511-517. 8. W. B. V. Kandasamy and F. Smarandache,” Fuzzy Relational Maps and Neutrosophic Relational Maps” , HEXIS Church Roc...

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...The notion of a neutrosophic quadruple BCK/BCI-number is considered, and a neutrosophic quadruple BCK/BCI-algebra, which consists of neutrosophic quadruple BCK/BCI-numbers, is constructed. Several properties are investigated, and a (positive implicative) ideal in a neutrosophic quadruple BCK-algebra and a closed ideal in a neutro...

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...eok-Zun Song, Florentin Smarandache and Hashem BordbarNeutrosophic Quadruple BCK/BCI-AlgebrasReprinted from: Axioms 2018, 7, 41, doi: 10.3390/axioms70... ...Kim and Florentin SmarandacheInterval Neutrosophic Sets with Applications in BCK/BCI-AlgebraReprinted from: Axioms 2018, 7, 23, doi: 10.3390/axioms702... ...dache, Seok-Zun Song andMadad KhanNeutrosophic Positive Implicative N -Ideals in BCK-AlgebrasReprinted from: Axioms 2018, 7, 3, doi: 10.3390/axioms701... ...le BCK/BCI-number is considered in the first article(“Neutrosophic Quadruple BCK/BCI-Algebras”, by Young Bae Jun, Seok-Zun Song, FlorentinSmarandache,... ...28, 1163–1176. [CrossRef]31. Biswas, P.; Pramanik, S.; Giri, B.C. Entropy based grey relational analysis method for multi-attribute decision making ... ...onment. Appl. Intell. 2017, 1–15. [CrossRef]95. Pramanik, S.; Mukhopadhyaya, D. Grey relational analysis-based intuitionistic fuzzy multi-criteria gro... ...i-criteria group decision making in intuitionistic fuzzy environment based on grey relational analysis for weaver selection in Khadi institution. J.... ...Methods 2015, 10, 1–14.98. Dey, P.P.; Pramanik, S.; Giri, B.C. An extended grey relational analysis based interval neutrosophic multi-attribute... ...v. Res. Sci. Eng. Technol. 2015, 4, 158–164.14. Pramanik, S.; Mukhopadhyaya, D. Grey relational analysis based intuitionistic fuzzy multi-criteria gro...

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...ophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc....

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...tics that started in 1995 and their applications in any field,such as the neutrosophic structures developed in algebra, geometry, topology, etc. The ... ...ail: kulhur@wonkwang.ac.kr. Bucaramanga, Colombia,Kemale Veliyeva & Sadi Bayramov, Department of Algebra Email: rafael2188797@corre... ....... 17H. Bordbar1 M. Mohseni Takallo, R.A. Borzooei and Young Bae Jun, BMBJ-neutrosophic subalgebrain BCI/BCK-algebras………………………………………………………………………...…... ...………………………………………………..... 120Mohsin Khalid, Neha Andaleeb Khalid and Said Broumi, T-Neutrosophic Cubic Set on BF-Algebra……………………………………………………………………………………... ... of entropy weights, findingpositive ideal solution(PIS),and negative ideal solution(NIS), calculation of grey relational coefficient,calculation of d... ...nt,calculation of degree of weighted grey relational coefficient of each alternative, determination ofrelative relational degree of each alternative f... ... ), max(Iij ), max(Fij )), max(μij ), min(Iij ), min(Fij ))), j = 1,2, . . . , m. (13)Step 7. Find the grey relational coefficient of each evaluati... ... 1,2, . . . , m, where τ ∈ [0,1]. Generally, τ = 0.5 is used.Step 8. Find out the degree of weighted grey relational coefficient of each alternat... ...∑j=1 wξij , where 𝑖 = 1,2, . . . , n. (15) jStep 9. Find out the relative relational degree of each alternative f...

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...ophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc....

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...ophic sets ………....................................................… 86 Algebras Based on Neutrosophic Points ……………..… 26 S. Pram... ...onment....…………………….. 95 subalgebras and ideals in BCK/BCI-algebras ……...…… 36 Surapati Pramanik, Rama Mallick, Anindi... ...als in BCK- Attribute Decision Making in Neutrosophic Environ- algebras …………………………………….....………… 44 ment: An Overv... ... C. Giri. Entropy based grey Recognition Letters, 34(14), 1609–1622. relational analysis method for multi-attribute decision- [30] P. Biswas,... ... 11[41] S, Ye and J. Ye. Dice similarity measure between single grey relational analysis. Neutrosophic Sets and Systems, 9 valued neutrosophic... ...ed grey [61] S. Pramanik, P. P. Dey, and B. C. Giri. TOPSIS for single relational analysis method for multi-attribute decision- valued neutro... ...ems, 2 (2014), 102–110. [62] S. Pramanik, and D. Mukhopadhyaya. Grey relational[48] J. Ye and Q. S. Zhang. Single valued neutrosophic similarity... ... based [65] Abdel-Basset, M., Gunasekaran, M., Mohamed, M., & on grey relational analysis for weaver selection in khadi Smarandache, F. A no... ...rsity of New Mexico Generalizations of Neutrosophic Subalgebras in BCK/BCI-Algebras Based on Neutrosophic Points ...

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... applications in any field, such asthe neutrosophic structures developed in algebra, geometry, topology, etc. The submitted papers should be professi... ... Bucaramanga, Colombia,Kemale Veliyeva & Sadi Bayramov, Department of Algebra Email: rafael2188797@correo.uis.edu.co.and Geometry, Baku Sta... ... ContentsAtena Tahmasbpour Meikola, Eight Kinds of Graphs of BCK-algebras Based on Ideal and DualIdeal…………………………………………………………………………………………………... ...ah and Abd Ghafur Ahmad, Structures on Doubt Neutrosophic Ideals of BCK/BCI-Algebras under (S, T)-Norms…………………………………………………………………….....276 ... ...…298 Akbar Rezaei and Florentin Smarandache, The Neutrosophic Triplet of BI-algebras ……………..315 Mohamed Grida, Rehab Mohamed and Abdelnaser H. Zaid, A... ...c hypergraph. Let us consider a decision making situation to find inter relational impacts of the factorscontributing towards the sales promotion ... ...9020037.27. Biswas, P, Pramanik, S. & Giri, B.C. (2014). Entropy based grey relational analysis method for multi- attribute decision making under sin...

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...ophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc....

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...applications in any field,such as the neutrosophic structures developed in algebra, geometry, topology, etc. The submitted papers should be professio... ...ramov, Department of University of Antwerp, Antwerp, Belgium, Email:Algebra and Geometry, Baku State University, 23 Z. willem.brauers@ua.a... ...hammad Akram, Hina Gulzar, F. Smarandache. Neutrosophic Soft Topological K-Algebras…………………………………...………………………………………………………….…….. 104Mohana K, Christy V,... ..., Young Bae Jun Neutrosophic Quadruple Ideals in NeutrosophicQuadruple BCI-Algebras ……………………………………………………………….…...…. 161P. Arulpandy, M. Trinita Pricil... ...168, (2013).[23] P. Biswas, S. Pramanik and B. C. Giri, Entropy based grey relational analysis method for multi-attribute decision making under singl... ...ri, Neutrosophic soft multi-attribute group decision making based on grey relational analysis method. Journal of New Results in Science, 10, 25-37, (... ...d systems, , 20,87-96.[3] P. Bosc, O. Pivert (2013), On a fuzzy bipolar relational algebra, Information Sciences, 219,1–16.[4] Florentin Smaran... ...odel for Clay-Brick Selection in Construction Field Based on Grey Relational Analysis, Neutrosophic Sets and Systems,9,64-71. doi.o... ...rtha Pratim Dey, Surapati Pramanik, Bibhas C. Giri(2016), An extended grey relational analysis based multiple attribute decision making in interva...

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...ophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc....

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...rted in 1995 and their applications in any field,such as the neutrosophic structures developed in algebra, geometry, topology, etc. The submitted pap... ...kallo, R.A. Borzooei, Young Bae Jun. MBJ-neutrosophic structures and its applica-tions in BCK/BCI-algebras ……………………………………………………………………..………... ... ...………..………... 72Vasantha W.B., Ilanthenral Kandasamy, Florentin Smarandache. Algebraic. Structure of Neutrosoph-ic Duplets in Neu... ...akallo, Florentin Smarandache, Young Bae Jun. Positive implicativeBMBJ-neutrosophic ideals in BCK-algebras …………………………………………………..……... ... ...erp, Belgium, Email:Kemale Veliyeva & Sadi Bayramov, Department of willem.brauers@ua.ac.be.Algebra and Geometry, Baku State University, 23 Z. ... ....[55] K. Mondal and S. Pramanik. Rough neutrosophic multi-attribute decision-making based on grey relational anal -ysis., Neutrosophic Sets and Syste... ...5281/zenodo.570884.[42] Partha Pratim Dey, Surapati Pramanik, Bibhas C. Giri: An extended grey relational analysis based multiple attribute deci- ... ...ls: Pons Editions, 2018.[45] P. Biswas, S. Pramanik, and B. C. Giri. Entropy based grey relational analysis method for multi-attribute decis...

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...ophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc....

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...s of ] 0, 1+[. -developed in algebra, geometry, topology, etc. Neutrosophic Probabil... ... Pinaki Majumdar. On New Measures of UncertaintyPseudo-BCI Algebras…………………………………. 10 for Neutroso... ...Md(u)} and ∀u ∈ U, sup{A(v)|v ∈ ∪Md(u)} = [4] Y.Y. Yao. (1998). Relational interpretations of neighbor-sup{A(v)|v ∈ ∩Md(u)} ... ...ar Filters and Fuzzy Regular Filters in Pseudo-BCI Algebras Xiaohong Zhang1, 2, Yingcang Ma3, and Florentin Smar... ...eutrosophic set is a new mathematical tool filter in pseudo-BCI algebras are introduced, and for handling problems involving imprecise... ...ies are discussed. Moreover, the nacy and inconsistent data. Pseudo-BCI algebra is a relationships among neutrosophic regular filter, fuz... ...d based on grey developed a new MADM method based on the proposed relational analysis. Mondal and Pramanik [25] defined variational ... ...Entropy based [19] Y. Guo, A. Sengur, and J. Ye. A novel image grey relational analysis method for multi-attribute deci- thresholding algorit... ...tion to multiple attribute ti-attribute decision-making based on grey relational group decision making problems. Mathematical and anal...

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...ophical Principles Based on Uniqueness of Truth and Neutrosophy Deriving Newton's Second Law and the like; On Neutrosophic Ideals of Neutrosophic BCI-Algebras....

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...ewton's Second Law and the like 93 A.A.A. Agboola, B. Davvaz On Neutrosophic Ideals of Neutrosophic BCI-Algebras ... ...near Regression, Neutrosophic Sets and Systems, 5 (2014) 3-8. [2] M. Arora, R. Biswas, U. S. Pandy, Neutrosophic Relational Database Decomposit... ...olume X, 2015 93 On Neutrosophic Ideals of Neutrosophic BCI-Algebras 1... ...avvaz@yazd.ac.irAbstractThe objective of this paper is to introduce and study neutrosophic ideals ofneutrosophic BCI-algebras. Elementary properties o... ...BCI-algebras. Elementary properties of neutrosophic ideals ofneutrosophic BCI-algebras are presented.KeywordsBCI/BCK-algebra, Neutrosophic set, Neutro... ...KeywordsBCI/BCK-algebra, Neutrosophic set, Neutrosophic BCI/BCK- algebra, Neutrosophicideal.1 IntroductionBCI/BCK-algebras are generalizations of t...

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...ophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc....

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...tics that started in 1995 and their applications in any field,such as the neutrosophic structures developed in algebra, geometry, topology, etc. The ... ...Economics,Kemale Veliyeva & Sadi Bayramov, Department of University of Antwerp, Antwerp, Belgium, Email:Algebra and Geometry, Baku State Univer... ...................... 69Phattharaphon Rangsuk, Pattarin Huana, Aiyared Iampan. Neutrosophic N-structures over UP-algebras …………………………………………………………........... ............................……245Mohsin Khalid, Rakib Iqbal, Said Broumi Neutrosophic soft cubic Subalgebras of G-algebras…………………….......................... ...al trigonometric Hamming similarity measures ofrough neutrosophic sets. Mondal and Pramanik [17] proposed grey relational analysis among roughneutroso... ... 2016, 1, 93-103.17. Mondal, K.; Pramanik, S. Rough neutrosophic multi-attribute decision-making based on grey relational analysis, Neutrosophic Sets... ...urnal of Pure and Applied Mathematics, 24 (2005), 287-297.7. M. Arora, R. Biswas and U.S. Pandy, Neutrosophic Relational Database Decomposition, Inte... ... 140[41], authors solved intuitionistic fuzzy relational rational calculus problems u... ...eedings, Vol. 1184, No. 1, 2009, pp. 341-34840. Peeva, K.; Kyosev, Y. Solving problems in intuitionistic fuzzy relational calculus with fuzzy relation...

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...ophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc....

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...valuation Model Based on the Single Valued bic Closed Ideals of B-algebras …….....……………….Neutrosophic Set …………………………………......... ... ...n any field, such statistics.as the neutrosophic structures developed in algebra, geometry, What distinguishes the neutrosophics from other fi... ...a complete Heytinglogical if and only if it is cotopological. algebra if it satisfies the following conditions:Result 2.3 ([12], Theorem 1... ...gs: In particular, if H is a complete Heyting algebra with the least element 0 then ... ...quation based on closeness coefficient applied to search-neutrosophic grey relational analysis. The weights of at- ing algorithm to obtain attribut... ...tion and ideal neutrosophic estimatesunreliable solution then neutrosophic relational degree Tian et al (2015) [41] put forward the concept of mul... ...ables. Neutrosophic Sets 42. P. Bosc, O. Pivert, More on a fuzzy bipolar relational alge- and Systems, Vol. 8, 2015. bra, Inf... ...5), Interval Neutrosophic Multi- Attribute Decision-Making Based on Grey Relational Anal- ysis. Neutrosophic Sets and Systems, Vol. 9, 2015.34. Rı... ...ing Model for Clay-Brick Selection in Construction Field Based on Grey Relational Analysis. Neutrosophic Sets and Sys- tems, Vol. 9, 2015. ...

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...ophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc....

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...tics that started in 1995 and their applications in any field,such as the neutrosophic structures developed in algebra, geometry, topology, etc. The ... ... and Kemale Veliyeva & Sadi Bayramov, Department ofInformatics, Zagazig University, Egypt, Email: Algebra and Geometry, Baku State Univer... ...………………………………….…………..….214M. Kaviyarasu, K. Indhira and V.M. Chandrasekaran, Direct product of Neutrosophic INK-Algebras…………………………………………………………………………………... ...……………………………………………………...544P. B. Remya and A. Francina Shalini, Neutrosophic Vague Binary G – subalgebra of G – algebra……….576Minna Xu, Rui Yong , and ... ...20 241 4. Biswas, P, Pramanik, S. & Giri, B.C. (2014a). Entropy based grey relational analysis method for mult... ...Pramanik, S., & Giri, B. C. (2016a). Neutrosophic soft multi-attribute group decision making based on grey relational analysis method. Journal of ... .... P., Pramanik, S., & Giri, B. C. (2016b). Neutrosophic soft multi-attribute decision making based on grey relational projection method. Neutrosop... ...ts. Fuzzy Sets and Systems, 20(1), 87-96. 3. Biswas, P, Pramanik, S. & Giri, B.C. (2014). Entropy based grey relational analysis method for mult... ...S. (2015). Neutrosophic decision making model for clay-brick selection in construction field based on grey relational analysis. Neutrosophic Sets ...

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...ophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc....

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...applications in any field,such as the neutrosophic structures developed in algebra, geometry, topology, etc. The submitted papers should be professio... ...ramov, Department of University of Antwerp, Antwerp, Belgium, Email:Algebra and Geometry, Baku State University, 23 Z. willem.brauers@ua.a... ... Bordbar, R.A. Borzooei, Young Bae Jun. BMBJ-neutrosophic ideals inBCK/BCI-algebras ……… …………………………………………………………………..……… 1J. Kavikumar, D. Nagarajan, Sa... ... University of New Mexico BMBJ-neutrosophic ideals in BCK/BCI-algebras M. Mohseni Takallo1, Hashem Bordbar1, R.A. Borzooei1, Young Ba... ...s for an MBJ-neutrosophic set to be a BMBJ-neutrosophic ideal in BCK/BCI-algebras are provided. Characterizations of BMBJ-neutrosophic ideal are dis... ... membership function (MF) designs a structure of practical relationship to relational structurenumerically where the elements lies between 0 and 1. By... ...ups, beganto analyze their properties, and applied them to groups and relational algebraic functions (See [17]).Since then, many papers and s...