Fuzzy Semigroups

Author : John N. Mordeson,Davender S. Malik,Nobuaki Kuroki
Publisher : Springer
Page : 324 pages
File Size : 43,6 Mb
Release : 2012-11-03
Category : Mathematics
ISBN : 9783540371250

Get Book

Fuzzy Semigroups by John N. Mordeson,Davender S. Malik,Nobuaki Kuroki Pdf

Lotfi Zadeh introduced the notion of a fuzzy subset of a set in 1965. Ris seminal paper has opened up new insights and applications in a wide range of scientific fields. Azriel Rosenfeld used the notion of a fuzzy subset to put forth cornerstone papers in several areas of mathematics, among other discplines. Rosenfeld is the father of fuzzy abstract algebra. Kuroki is re sponsible for much of fuzzy ideal theory of semigroups. Others who worked on fuzzy semigroup theory, such as Xie, are mentioned in the bibliogra phy. The purpose of this book is to present an up to date account of fuzzy subsemigroups and fuzzy ideals of a semigroup. We concentrate mainly on theoretical aspects, but we do include applications. The applications are in the areas of fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. An extensive account of fuzzy automata and fuzzy languages is given in [100]. Consequently, we only consider results in these areas that have not appeared in [100] and that pertain to semigroups. In Chapter 1, we review some basic results on fuzzy subsets, semigroups, codes, finite state machines, and languages. The purpose of this chapter is to present basic results that are needed in the remainder of the book. In Chapter 2, we introduce certain fuzzy ideals of a semigroup, namely, fuzzy two-sided ideals, fuzzy bi-ideals, fuzzy interior ideals, fuzzy quasi ideals, and fuzzy generalized bi-ideals.

Author : Young Bae Jun,Madad Khan,Florentin Smarandache,Saima Anis
Publisher : Infinite Study
Page : 96 pages
File Size : 45,6 Mb
Release : 2018-01-01
Category : Mathematics
ISBN : 9781599735481

Get Book

Fuzzy and Neutrosophic Sets in Semigroups by Young Bae Jun,Madad Khan,Florentin Smarandache,Saima Anis Pdf

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.

Author : W. B. Vasantha Kandasamy
Publisher : Infinite Study
Page : 455 pages
File Size : 43,7 Mb
Release : 2003
Category : Mathematics
ISBN : 9781931233743

Get Book

Smarandache Fuzzy Algebra by W. B. Vasantha Kandasamy Pdf

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.

Author : Madad Khan,Florentin Smarandache,Sania Afzal
Publisher : Infinite Study
Page : 16 pages
File Size : 53,7 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 8210379456XXX

Get Book

Neutrosophic Set Approach for Characterizations of Left Almost Semigroups by Madad Khan,Florentin Smarandache,Sania Afzal Pdf

In this paper we have defined neutrosophic ideals, neutrosophic interior ideals, netrosophic quasi-ideals and neutrosophic bi-ideals (neutrosophic generalized bi-ideals) and proved some results related to them.

Author : Broumi, Said
Publisher : IGI Global
Page : 944 pages
File Size : 52,7 Mb
Release : 2022-03-04
Category : Mathematics
ISBN : 9781799879817

Get Book

Handbook of Research on Advances and Applications of Fuzzy Sets and Logic by Broumi, Said Pdf

Fuzzy logic, which is based on the concept of fuzzy set, has enabled scientists to create models under conditions of imprecision, vagueness, or both at once. As a result, it has now found many important applications in almost all sectors of human activity, becoming a complementary feature and supporter of probability theory, which is suitable for modelling situations of uncertainty derived from randomness. Fuzzy mathematics has also significantly developed at the theoretical level, providing important insights into branches of traditional mathematics like algebra, analysis, geometry, topology, and more. With such widespread applications, fuzzy sets and logic are an important area of focus in mathematics. The Handbook of Research on Advances and Applications of Fuzzy Sets and Logic studies recent theoretical advances of fuzzy sets and numbers, fuzzy systems, fuzzy logic and their generalizations, extensions, and more. This book also explores the applications of fuzzy sets and logic applied to science, technology, and everyday life to further provide research on the subject. This book is ideal for mathematicians, physicists, computer specialists, engineers, practitioners, researchers, academicians, and students who are looking to learn more about fuzzy sets, fuzzy logic, and their applications.

Author : Madad Khan,Florentin Smarandache,Tariq Aziz
Publisher : Infinite Study
Page : 84 pages
File Size : 42,6 Mb
Release : 2015-01-15
Category : Fuzzy sets
ISBN : 9781599733395

Get Book

Fuzzy Abel Grassmann Groupoids by Madad Khan,Florentin Smarandache,Tariq Aziz Pdf

Author : Jana, Chiranjibe,Senapati, Tapan,Pal, Madhumangal
Publisher : IGI Global
Page : 439 pages
File Size : 44,6 Mb
Release : 2019-10-25
Category : Mathematics
ISBN : 9781799801924

Get Book

Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures by Jana, Chiranjibe,Senapati, Tapan,Pal, Madhumangal Pdf

In the world of mathematics, the study of fuzzy relations and its theories are well-documented and a staple in the area of calculative methods. What many researchers and scientists overlook is how fuzzy theory can be applied to industries outside of arithmetic. The framework of fuzzy logic is much broader than professionals realize. There is a lack of research on the full potential this theoretical model can reach. The Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures provides emerging research exploring the theoretical and practical aspects of fuzzy set theory and its real-life applications within the fields of engineering and science. Featuring coverage on a broad range of topics such as complex systems, topological spaces, and linear transformations, this book is ideally designed for academicians, professionals, and students seeking current research on innovations in fuzzy logic in algebra and other matrices.

Author : P G Romeo,John. C Meakin,A R Rajan
Publisher : Springer
Page : 218 pages
File Size : 55,6 Mb
Release : 2015-07-06
Category : Mathematics
ISBN : 9788132224884

Get Book

Semigroups, Algebras and Operator Theory by P G Romeo,John. C Meakin,A R Rajan Pdf

This book discusses recent developments in semigroup theory and its applications in areas such as operator algebras, operator approximations and category theory. All contributing authors are eminent researchers in their respective fields, from across the world. Their papers, presented at the 2014 International Conference on Semigroups, Algebras and Operator Theory in Cochin, India, focus on recent developments in semigroup theory and operator algebras. They highlight current research activities on the structure theory of semigroups as well as the role of semigroup theoretic approaches to other areas such as rings and algebras. The deliberations and discussions at the conference point to future research directions in these areas. This book presents 16 unpublished, high-quality and peer-reviewed research papers on areas such as structure theory of semigroups, decidability vs. undecidability of word problems, regular von Neumann algebras, operator theory and operator approximations. Interested researchers will find several avenues for exploring the connections between semigroup theory and the theory of operator algebras.

Author : Madad Khan,Saima Anis,Florentin Smarandache, Young Bae Jun
Publisher : Infinite Study
Page : 16 pages
File Size : 43,6 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 8210379456XXX

Get Book

Neutrosophic N-structures and their applications in semigroups by Madad Khan,Saima Anis,Florentin Smarandache, Young Bae Jun Pdf

The notion of neutrosophic N-structure is introduced, and applied it to semigroup. The notions of neutrosophic N-subsemigroup, neutrosophic N-product and ε-neutrosophic N-subsemigroup are introduced, and several properties are investigated.

Author : Syed Tariq Rizvi,Asma Ali,Vincenzo De Filippis
Publisher : Springer
Page : 430 pages
File Size : 49,9 Mb
Release : 2016-11-18
Category : Mathematics
ISBN : 9789811016516

Get Book

Algebra and its Applications by Syed Tariq Rizvi,Asma Ali,Vincenzo De Filippis Pdf

This book discusses recent developments and the latest research in algebra and related topics. The book allows aspiring researchers to update their understanding of prime rings, generalized derivations, generalized semiderivations, regular semigroups, completely simple semigroups, module hulls, injective hulls, Baer modules, extending modules, local cohomology modules, orthogonal lattices, Banach algebras, multilinear polynomials, fuzzy ideals, Laurent power series, and Hilbert functions. All the contributing authors are leading international academicians and researchers in their respective fields. Most of the papers were presented at the international conference on Algebra and its Applications (ICAA-2014), held at Aligarh Muslim University, India, from December 15–17, 2014. The book also includes papers from mathematicians who couldn't attend the conference. The conference has emerged as a powerful forum offering researchers a venue to meet and discuss advances in algebra and its applications, inspiring further research directions.

Author : Etienne E. Kerre,John Mordeson
Publisher : MDPI
Page : 287 pages
File Size : 51,5 Mb
Release : 2018-11-28
Category : Electronic books
ISBN : 9783038973225

Get Book

Fuzzy Mathematics by Etienne E. Kerre,John Mordeson Pdf

This book is a printed edition of the Special Issue "Fuzzy Mathematics" that was published in Mathematics

Author : Bing-Yuan Cao,Hadi Nasseri
Publisher : Springer Science & Business Media
Page : 558 pages
File Size : 48,9 Mb
Release : 2013-11-26
Category : Technology & Engineering
ISBN : 9783642386671

Get Book

Fuzzy Information & Engineering and Operations Research & Management by Bing-Yuan Cao,Hadi Nasseri Pdf

Fuzzy Information & Engineering and Operations Research & Management is the monograph from submissions by the 6th International Conference on Fuzzy Information and Engineering (ICFIE2012, Iran) and by the 6th academic conference from Fuzzy Information Engineering Branch of Operation Research Society of China (FIEBORSC2012, Shenzhen,China). It is published by Advances in Intelligent and Soft Computing (AISC). We have received more than 300 submissions. Each paper of it has undergone a rigorous review process. Only high-quality papers are included in it containing papers as follows: I Programming and Optimization. II Lattice and Measures. III Algebras and Equation. IV Forecasting, Clustering and Recognition. V Systems and Algorithm. VI Graph and Network. VII Others.

Author : K. PORSELVI ,B. ELAVARASAN,FLORENTIN SMARANDACHE,Y. B. JUN
Publisher : Infinite Study
Page : 14 pages
File Size : 42,5 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 8210379456XXX

Get Book

NEUTROSOPHIC N -BI-IDEALS IN SEMIGROUPS by K. PORSELVI ,B. ELAVARASAN,FLORENTIN SMARANDACHE,Y. B. JUN Pdf

In this paper, we introduce the notion of neutrosophic N -bi-ideal structure over a semigroup. We characterize semigroups, regular semigroups and intra-regular semigroups in terms of neutrosophic N -bi-ideal structures. We also show that the intersection of neutrosophic N -ideals and the neutrosophic N -product of ideals will coincide for a regular semigroup.

Author : Florentin Smarandache,Mohamed Abdel-Basset,Said Broumi
Publisher : Infinite Study
Page : 970 pages
File Size : 51,6 Mb
Release : 2022-09-01
Category : Mathematics
ISBN : 8210379456XXX

Get Book

Neutrosophic Sets and Systems, vol. 51/2022 by Florentin Smarandache,Mohamed Abdel-Basset,Said Broumi Pdf

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation and with their spectrum of neutralities in between them (i.e. notions or ideas supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic).

Author : Sunil Mathew,John N. Mordeson,M. Binu
Publisher : Springer Nature
Page : 226 pages
File Size : 49,8 Mb
Release : 2023-08-20
Category : Technology & Engineering
ISBN : 9783031397561

Get Book

Weighted and Fuzzy Graph Theory by Sunil Mathew,John N. Mordeson,M. Binu Pdf

One of the most preeminent ways of applying mathematics in real-world scenario modeling involves graph theory. A graph can be undirected or directed depending on whether the pairwise relationships among objects are symmetric or not. Nevertheless, in many real-world situations, representing a set of complex relational objects as directed or undirected is not su¢ cient. Weighted graphs o§er a framework that helps to over come certain conceptual limitations. We show using the concept of an isomorphism that weighted graphs have a natural connection to fuzzy graphs. As we show in the book, this allows results to be carried back and forth between weighted graphs and fuzzy graphs. This idea is in keeping with the important paper by Klement and Mesiar that shows that many families of fuzzy sets are lattice isomorphic to each other. We also outline the important work of Head and Weinberger that show how results from ordinary mathematics can be carried over to fuzzy mathematics. We focus on the concepts connectivity, degree sequences and saturation, and intervals and gates in weighted graphs.