Smarandache Fuzzy Algebra

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Smarandache Fuzzy Algebra

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233748
Total Pages : 455 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Smarandache Fuzzy Algebra by : W. B. Vasantha Kandasamy

Download or read book Smarandache Fuzzy Algebra written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2003 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author studies the Smarandache Fuzzy Algebra, which, like its predecessor Fuzzy Algebra, arose from the need to define structures that were more compatible with the real world where the grey areas mattered, not only black or white.In any human field, a Smarandache n-structure on a set S means a weak structure {w(0)} on S such that there exists a chain of proper subsets P(n-1) in P(n-2) in?in P(2) in P(1) in S whose corresponding structures verify the chain {w(n-1)} includes {w(n-2)} includes? includes {w(2)} includes {w(1)} includes {w(0)}, where 'includes' signifies 'strictly stronger' (i.e., structure satisfying more axioms).This book is referring to a Smarandache 2-algebraic structure (two levels only of structures in algebra) on a set S, i.e. a weak structure {w(0)} on S such that there exists a proper subset P of S, which is embedded with a stronger structure {w(1)}. Properties of Smarandache fuzzy semigroups, groupoids, loops, bigroupoids, biloops, non-associative rings, birings, vector spaces, semirings, semivector spaces, non-associative semirings, bisemirings, near-rings, non-associative near-ring, and binear-rings are presented in the second part of this book together with examples, solved and unsolved problems, and theorems. Also, applications of Smarandache groupoids, near-rings, and semirings in automaton theory, in error correcting codes, and in the construction of S-sub-biautomaton can be found in the last chapter.

Q-Smarandache Fuzzy Implicative Ideal of QSmarandache BH-Algebra

Author : Husein Hadi Abbass
Publisher : Infinite Study
ISBN 13 :
Total Pages : 15 pages
Book Rating : 4./5 ( download)

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Book Synopsis Q-Smarandache Fuzzy Implicative Ideal of QSmarandache BH-Algebra by : Husein Hadi Abbass

Download or read book Q-Smarandache Fuzzy Implicative Ideal of QSmarandache BH-Algebra written by Husein Hadi Abbass and published by Infinite Study. This book was released on with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, The notions of Q-Smarandache fuzzy implicative ideal and Q- Smarandache fuzzy sub implicative ideal of a Q-Smarandache BH-Algebra introduced, examples are given, and related properties investigated the relationships among these notions and other types of Q-Smarandache fuzzy ideal of a Q-Smarandache BH-Algebra are studied.

Linear Algebra and Smarandache Linear Algebra

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233756
Total Pages : 175 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Linear Algebra and Smarandache Linear Algebra by : W. B. Vasantha Kandasamy

Download or read book Linear Algebra and Smarandache Linear Algebra written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2003 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author analyzes the Smarandache linear algebra, and introduces several other concepts like the Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra. We indicate that Smarandache vector spaces of type II will be used in the study of neutrosophic logic and its applications to Markov chains and Leontief Economic models ? both of these research topics have intense industrial applications. The Smarandache linear algebra, is defined to be a Smarandache vector space of type II, on which there is an additional operation called product, such that for all a, b in V, ab is in V.The Smarandache vector space of type II is defined to be a module V defined over a Smarandache ring R such that V is a vector space over a proper subset k of R, where k is a field.

Algebraic Structures on Fuzzy Unit Square and Neutrosophic Unit Square

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1599732726
Total Pages : pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Algebraic Structures on Fuzzy Unit Square and Neutrosophic Unit Square by : W. B. Vasantha Kandasamy

Download or read book Algebraic Structures on Fuzzy Unit Square and Neutrosophic Unit Square written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book authors build algebraic structures on fuzzy unit semi-open square UF = {(a,b), with a, b in [0, 1)} and on neutrosophic unit semi-open square UN = {a+bI, with a, b in [0, 1)}. As distributive laws are not true, we are not in a position to develop several properties of rings, semirigs and linear algebras. Seven open conjectures are proposed.

On a Q-Smarandache Fuzzy Commutative Ideal of a Q-Smarandache BH-algebra

Author : Husein Hadi Abbass
Publisher : Infinite Study
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4./5 ( download)

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Book Synopsis On a Q-Smarandache Fuzzy Commutative Ideal of a Q-Smarandache BH-algebra by : Husein Hadi Abbass

Download or read book On a Q-Smarandache Fuzzy Commutative Ideal of a Q-Smarandache BH-algebra written by Husein Hadi Abbass and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the notions of Q-Smarandache fuzzy commutative ideal and Q-Smarandache fuzzy sub-commutative ideal of a Q-Smarandache BH-Algebra are introduced, examples and related properties are investigated. Also, the relationships among these notions and other types of Q-Smarandache fuzzy ideal of a Q-Smarandache BH-Algebra are studied.

Smarandache Near-Rings

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1931233667
Total Pages : 201 pages
Book Rating : 4.9/5 (312 download)

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Book Synopsis Smarandache Near-Rings by : W. B. Vasantha Kandasamy

Download or read book Smarandache Near-Rings written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B in A which is embedded with a stronger structure S. These types of structures occur in our everyday life, that's why we study them in this book. Thus, as a particular case: A Near-Ring is a non-empty set N together with two binary operations '+' and '.' such that (N, +) is a group (not necessarily abelian), (N, .) is a semigroup. For all a, b, c in N we have (a + b) . c = a . c + b . c. A Near-Field is a non-empty set P together with two binary operations '+' and '.' such that (P, +) is a group (not necessarily abelian), (P \ {0}, .) is a group. For all a, b, c I P we have (a + b) . c = a . c + b . c. A Smarandache Near-ring is a near-ring N which has a proper subset P in N, where P is a near-field (with respect to the same binary operations on N).

Smarandache pseudo-CI algebras

Author : L. C. Ciungu
Publisher : Infinite Study
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4./5 ( download)

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Book Synopsis Smarandache pseudo-CI algebras by : L. C. Ciungu

Download or read book Smarandache pseudo-CI algebras written by L. C. Ciungu and published by Infinite Study. This book was released on with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we define the notion of Smarandache pseudo-CI algebras and we investigate their properties. We also define and study the notions of Smarandache filters, pseudo-CI Smarandache homomorphisms and modal Smarandache operators on pseudo-CI algebras.

Set Linear Algebra and Set Fuzzy Linear Algebra

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1599730294
Total Pages : 346 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Set Linear Algebra and Set Fuzzy Linear Algebra by : W. B. Vasantha Kandasamy

Download or read book Set Linear Algebra and Set Fuzzy Linear Algebra written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2008 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set linear algebras, introduced by the authors in this book, are the most generalized form of linear algebras.These structures make use of very few algebraic operations and are easily accessible to non-mathematicians as well.The dominance of computers in everyday life calls for a paradigm shift in the concepts of linear algebra. The authors believe that set linear algebra will cater to that need.

n-Linear Algebra of Type 1 and Its Applications

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 159973074X
Total Pages : 122 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis n-Linear Algebra of Type 1 and Its Applications by : W. B. Vasantha Kandasamy

Download or read book n-Linear Algebra of Type 1 and Its Applications written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2008 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: n-Linear Algebra of type I introduced in this book find applications in Markov chains and Leontief economic models.Innovative scientists and engineers can adopt this concept in Fuzzy Finite Element analysis of mechanical structures with uncertain parameters.

On the structure of general algebras and its applications

Author : Young Joo Seo
Publisher : Infinite Study
ISBN 13 :
Total Pages : 79 pages
Book Rating : 4./5 ( download)

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Book Synopsis On the structure of general algebras and its applications by : Young Joo Seo

Download or read book On the structure of general algebras and its applications written by Young Joo Seo and published by Infinite Study. This book was released on with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we discuss some structural theory of a d-algebra which is a generalization of a BCK-algebra, and wedis uss analytic real algebras. We investigate several conditions for analytic real algebras to be d-algebras. Moreover, we introduce the notion of a Smarandacheness to BCI-algebras, and obtain several properties on Smarandache fuzzy BCI-algebras.

Smarandache BE-Algebras

Author : Arsham Borumand Saeid
Publisher : Infinite Study
ISBN 13 : 1599732416
Total Pages : 65 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Smarandache BE-Algebras by : Arsham Borumand Saeid

Download or read book Smarandache BE-Algebras written by Arsham Borumand Saeid and published by Infinite Study. This book was released on with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);} w\:* {behavior:url(#default#VML);} .shape {behavior:url(#default#VML);} Normal 0 false false false EN-US X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin-top:0in; mso-para-margin-right:0in; mso-para-margin-bottom:8.0pt; mso-para-margin-left:0in; line-height:107%; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin;} There are three types of Smarandache Algebraic Structures: 1. A Smarandache Strong Structure on a set S means a structure on S that has a proper subset P with a stronger structure. A Smarandache Weak Structure on a set S means a structure on S that has a proper subset P with a weaker structure. A Smarandache Strong-Weak Structure on a set S means a structure on S that has two proper subsets: P with a stronger structure, and Q with a weaker structure. By proper subset of a set S, one understands a subset P of S, different from the empty set, from the original set S, and from the idempotent elements if any. Having two structures {u} and {v} defined by the same operations, one says that structure {u} is stronger than structure {v}, i.e. {u} > {v}, if the operations of {u} satisfy more axioms than the operations of {v}. Each one of the first two structure types is then generalized from a 2-level (the sets P ⊂ S and their corresponding strong structure {w1}>{w0}, respectively their weak structure {w1}<{w0}) to an n-level (the sets Pn-1 ⊂ Pn-2 ⊂ … ⊂ P2 ⊂ P1 ⊂ S and their corresponding strong structure {wn-1} > {wn-2} > … > {w2} > {w1} > {w0}, or respectively their weak structure {wn-1} < {wn-2} < … < {w2} < {w1} < {w0}). Similarly for the third structure type, whose generalization is a combination of the previous two structures at the n-level. A Smarandache Weak BE-Algebra X is a BE-algebra in which there exists a proper subset Q such that 1 Q, |Q| ≥ 2, and Q is a CI-algebra. And a Smarandache Strong CI-Algebra X is a CI-algebra X in which there exists a proper subset Q such that 1 Q, |Q| ≥ 2, and Q is a BE-algebra. The book elaborates a recollection of the BE/CI-algebras, then introduces these last two particular structures and studies their properties.

Special Set Linear Algebra and Special Set Fuzzy Linear Algebra

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1599731061
Total Pages : 469 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Special Set Linear Algebra and Special Set Fuzzy Linear Algebra by : W. B. Vasantha Kandasamy

Download or read book Special Set Linear Algebra and Special Set Fuzzy Linear Algebra written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2009-01-01 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special Set Linear Algebras introduced by the authors in this book is an extension of Set Linear Algebras, which are the most generalized form of linear algebras. These structures can be applied to multi-expert models. The dominance of computers in everyday life calls for a paradigm shift in the concepts of linear algebras. The authors belief that special set linear algebra will cater to that need.

Algebraic Structures on MOD Planes

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1599733676
Total Pages : 215 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Algebraic Structures on MOD Planes by : W. B. Vasantha Kandasamy

Download or read book Algebraic Structures on MOD Planes written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2015-11-01 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Study of MOD planes happens to a very recent one. In this book, systematically algebraic structures on MOD planes like, MOD semigroups, MOD groups and MOD rings of different types are defined and studied. Such study is innovative for a large four quadrant planes are made into a small MOD planes. Several distinct features enjoyed by these MOD planes are defined, developed and described.

A Q- Smarandache Implicative Ideal of Q-Smarandache BH-algebra

Author : Husein Hadi Abbass
Publisher :
ISBN 13 : 9783659839238
Total Pages : 188 pages
Book Rating : 4.8/5 (392 download)

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Book Synopsis A Q- Smarandache Implicative Ideal of Q-Smarandache BH-algebra by : Husein Hadi Abbass

Download or read book A Q- Smarandache Implicative Ideal of Q-Smarandache BH-algebra written by Husein Hadi Abbass and published by . This book was released on 2016-06-23 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fuzzy and Neutrosophic Sets in Semigroups

Author : Young Bae Jun
Publisher : Infinite Study
ISBN 13 : 1599735482
Total Pages : 96 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Fuzzy and Neutrosophic Sets in Semigroups by : Young Bae Jun

Download or read book Fuzzy and Neutrosophic Sets in Semigroups written by Young Bae Jun and published by Infinite Study. This book was released on 2018-01-01 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topics discussed in this book are Int-soft semigroup, Int-soft left (right) ideal, Int-soft (generalized) bi-ideal, Int-soft quasi-ideal, Int-soft interior ideal, Int-soft left (right) duo semigroup, starshaped (∈, ∈∨ qk)-fuzzy set, quasi-starshaped (∈, ∈∨ qk)-fuzzy set, semidetached mapping, semidetached semigroup, (∈, ∈ ∨qk)-fuzzy subsemi-group, (qk, ∈ ∨qk)-fuzzy subsemigroup, (∈, ∈ ∨ qk)-fuzzy subsemigroup, (qk, ∈ ∨ qk)-fuzzy subsemigroup, (∈ ∨ qk, ∈ ∨ qk)-fuzzy subsemigroup, (∈, ∈∨ qkδ)-fuzzy subsemigroup, ∈∨ qkδ -level subsemigroup/bi-ideal, (∈, ∈∨ qkδ )-fuzzy (generalized) bi-ideal, δ-lower (δ-upper) approximation of fuzzy set, δ-lower (δ-upper) rough fuzzy subsemigroup, δ-rough fuzzy subsemigroup, Neutrosophic N -structure, neutrosophic N -subsemigroup, ε-neutrosophic N -subsemigroup, and neutrosophic N -product.

Smarandache Special Elements in Multiset Semigroups

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
ISBN 13 : 1599735644
Total Pages : 244 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Smarandache Special Elements in Multiset Semigroups by : W. B. Vasantha Kandasamy

Download or read book Smarandache Special Elements in Multiset Semigroups written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authors in this book study the notion of Smarandache element in multiset semigroups. It is important to keep on record that we define four operations on multisets viz. +, X, union and intersection in a free way. Thus all sets finite or infinite order contribute to infinite order multisets and the semigroup under any of these operations is of infinite order.

Interval Linear Algebra

Author : W. B. Vasantha Kandasamy, Florentin Smarandache
Publisher : Infinite Study
ISBN 13 : 1599731266
Total Pages : 249 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Interval Linear Algebra by : W. B. Vasantha Kandasamy, Florentin Smarandache

Download or read book Interval Linear Algebra written by W. B. Vasantha Kandasamy, Florentin Smarandache and published by Infinite Study. This book was released on 2010 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interval Arithmetic, or Interval Mathematics, was developed in the 1950s and 1960s as an approach to rounding errors in mathematical computations. However, there was no methodical development of interval algebraic structures to this date.This book provides a systematic analysis of interval algebraic structures, viz. interval linear algebra, using intervals of the form [0, a].