Fuzzy logic and zadeh algebra paavo kukkurainen school of engineering science, lappeenranta university of technology, lappeenranta, finland abstract in this work we create a connection between afs axiomatic fuzzy sets fuzzy logic systems and zadeh algebra. 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. The extension of algebraic and analytical concepts to the theory of fuzzy sets appears to play a central role in the investigation of nondeterministic techniques. In this book, we study the subject of smarandache fuzzy algebra. In 1991, xi 25 applied the concept of fuzzy sets to bci, bck, mv algebras. Vasantha kandasamy, florentin smarandache comments. Since an exact description of any real physical situation is virtually impossbile, it is necessary to develop schemes which. We observe, that the smarandache linear algebra can be constructed only using the smarandache vector space of type ii. In its trajectory of stupendous growth, it has also come to include the theory of fuzzy algebra and for the past five decades, several researchers have been working on concepts like fuzzy semigroup, fuzzy groups, fuzzy rings, fuzzy ideals, fuzzy semirings, fuzzy. Finally we construct quotient of smarandache blalgebras via mv algebra and prove some.
The paper also provides an overview of the present state of the art of ftt. This is an extension of the book set linear algebra and set fuzzy linear algebra. This site is like a library, use search box in the widget to get ebook that you want. It is also proved that the set of all s\\alpha \ fuzzy cosets will form a semigroup under a suitable binary operation and its structure properties are determined. In this paper we introduce the notion of q smarandache fuzzy commutative ideal and q smarandache fuzzy subcommutative ideal of a q smarandache bh algebra. Fuzzy sets, fuzzy algebra, and fuzzy statistics ieee. For more about these concepts, please refer 48, 60. Smarandache fuzzy strong ideal and smarandache fuzzy n.
In this paper we define the smarandache bl algebra, q smarandache ideal and q smarandache implicative ideal, we obtain some related results. Click download or read online button to get some topics in fuzzy algebra book now. Set linear algebra and set fuzzy linear algebra download. The notions of the neutrosophic hesitant fuzzy subalgebra and neutrosophic hesitant fuzzy filter in pseudobci algebras are introduced, and some properties and equivalent conditions are investigated. Pdf neutrosophic hesitant fuzzy subalgebras and filters. Use of fuzzy neutrosophic models in the study of social problem or technical problem has become a demand for the day due to the involvement of indeterminacy. Home package smarandache fuzzy algebra w b vasantha kandasamy pdf. Vasantha kandasamy 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. Fuzzy sets, fuzzy algebra, and fuzzy statistics abstract.
In 16, the authors applied the concept of fuzzy sets to closed ideals in b. These algebraic structures basically exploit only the set theoretic property, hence in applications one. Smarandache fuzzy algebra w b vasantha kandasamy pdf al. In this paper, we introduce the notion of bi smarandache bl algebra, biweak smarandache bl algebra, biq smarandache ideal and biq smarandache implicative filter, we obtain some related results and construct quotient of bi smarandache blalgebras via mvalgebras or briefly bi smarandache quotient bl algebra and prove some theorems.
The reader is expected to be wellversed with a strong background in algebra, fuzzy algebra and smarandache algebraic notions. Finally, the notion of bistrong smarandache bl algebra. Fuzzy dot bckbcialgebras 1 introduction and preliminaries. We have used fuzzy cognitive maps and neutrosophic cognitive maps to analyze the views of the revolutionary periyar e. After that by considering the notions of these ideals we determine relationships between ideals in bl algebra and q smarandache implicative ideals of bl algebra. Beginning with simple concepts we construct fuzzy logic concepts. In these six chapters, we have succeeded in introducing around 664 concepts related to smarandache fuzzy algebra. Section two gives the basic notions in bilinear algebra and the final section gives the definition of fuzzy vector spaces. Smarandache fuzzy strong ideal and smarandache fuzzy nfold strong ideal of a bh algebra. 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. Pdf set linear algebra and set fuzzy linear algebra.
Eqalgebrabased fuzzy type theory and its extensions irafm. Namdar, introduced the notion of a smarandache bch algebra and q smarandache ideal of a smarandache bch algebra 1. Algebra coding theory fuzzy models applications of algebra smarandache algebra. A necessary and sufficient condition for an s\\alpha. Several researchers explored on the generalization of the notion of fuzzy sets in classes of algebras such as bccbckbcikualgebras, see 1. Since its inception, the theory of fuzzy sets, ideal theory and its fuzzification has. This book for the first time introduces the notion of special set linear algebra and special set fuzzy linear algebra. We will be providing unlimited waivers of publication charges for accepted articles related to covid19.
Fuzzy algebra book pdf download ebook pdf, epub, tuebl, mobi. This book has seven chapters, which are divided into two parts. We are committed to sharing findings related to covid19 as quickly and safely as possible. X, the algebra of the power set px of x, that is, of the set of crisp subsets of x, is usually.
In its trajectory of stupendous growth, it has also come to include the theory of fuzzy algebra and for the past five decades, several researchers have been working on concepts like fuzzy semigroup, fuzzy groups, fuzzy rings, fuzzy ideals, fuzzy semirings, fuzzy nearrings and so on. F 2d of all idempotent fuzzy subsets of a cancellative semigroup d forms a complete lattice results concerning the set f d of all fuzzy subsets of and its substructures f 1d and f. Then we study their connection of p fuzzy subalgebras with fuzzy. Fuzzy and neutrosophic analysis of periyars views on. Abbass introduced the notion of a q smarandache fuzzy closed ideal with respect to an element of a smarandache bch. The reader is expected to have a good background both in algebra and in nearrings.
For always one is not in the position to say true or false, or assign a fuzzy value to any problem. For the first time, the social problem of untouchability, which is peculiar to india, is being studied mathematically. Smarandache fuzzy bcialgebras sun shin ahn1 and young joo seo. Some topics in fuzzy algebra download ebook pdf, epub. Smarandache fuzzy algebra w b vasantha kandasamy pdf. In any human field, a smarandache nstructure on a set s means a weak structure w0 on s such that there exists a chain of proper subsets pn1 in pn2 in. Theorems and applications by hassan abid yasser ed. It includes a range of theorems and applications in different branches of linear algebra, such as linear systems, matrices, operators, etc. Search for library items search for lists search for contacts search for a library. Click download or read online button to get fuzzy algebra book pdf book now. If you couldnt download the book then contact us on our email email protected. Fuzzy bsubalgebras of balgebra with respect to tnorm core. The notions of a smarandache fuzzy subalgebra ideal of a smarandache bci algebra, a smarandache. Vasantha kandasamy, title smarandache fuzzy algebra, year 2003 share.
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