Reduction of a nilpotent intuitionistic fuzzy matrix using implication operator

A problem of reducing intuitionistic fuzzy matrices is examined and some useful properties are obtained with respect to nilpotent intutionistic fuzzy matrices. First, reduction of irreflexive and transitive intuitionistic fuzzy matrices are considered, and then the properties are applied to nilpotent intutionistic fuzzy matrices. Nilpotent intuitionistic fuzzy matrices are intuitionistic fuzzy matrices which signify acyclic graphs, and the graphs are used to characterize consistent systems. The properties are handy for generalization of various systems with intuitionistic fuzzy transitivity

On the asymptotic period of powers of a fuzzy matrix

AbstractIn our prior study, we have examined in depth the notion of an asymptotic period of the power sequence of an n×n fuzzy matrix with max-Archimedean-t-norms, and established a characterization for the power sequence of an n×n fuzzy matrix with an asymptotic period using analytical-decomposition methods. In this paper, by using graph-theoretical tools, we further give an alternative proof for this characterization. With the notion of an asymptotic period using graph-theoretical tools, we additionally show a new characterization for the limit behaviour, and then derive some results for the power sequence of an n×n fuzzy matrix with an asymptotic period

Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value

Nahm's equations, N=1∗N=1^* domain walls, and D-strings in AdS5xS5AdS_5 x S_5

We consider the following two problems: classical domain walls in the $N=1^*$ mass deformation of the maximally supersymmetric Yang Mills theory, and D-strings as external magnetic sources in the context of the AdS/CFT correspondence. We show that they are both described by Nahm's equations with unconventional boundary conditions, and analyze the relevant moduli space of solutions. We argue that general `fuzzy sphere' configurations of D-strings in AdS$_5$ correspond to Wilson-'t Hooft lines in higher representations of the dual SU(n) gauge theory.Comment: Latex, 26 pages, 3 figures, uses JHEP.cls; v4: discussion of holographic interpretation of `fuzzy D-string' configurations modified. Minor esthetic changes otherwis

Groupoids of Type I and II using [0, n)

Study of algebraic structures built using [0, n) happens to be one of an interesting and innovative research. Here in this book authors define non associative algebraic structures using the interval [0, n). Here we define two types of groupoids using [0, n) both of them are of infinite order. It is an open conjecture to find whether these new class of groupoids satisfy any of the special identities like Moufang identity or Bol identity or Bruck identity or so on. We know on [0, n) we cannot build rings only pseudo rings, however in this book we use these type I and type II groupoids to build non associative rings and semirings. Several interesting results are derived and some open problems are suggested

International Journal of Mathematical Combinatorics, Vol.2A

The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 460 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences

Maximum order-index of matrices over commutative inclines: an answer to an open problem

AbstractThis paper proves that the maximum order-index of n×n matrices over an arbitrary commutative incline equals (n−1)2+1. This is an answer to an open problem “Compute the maximum order-index of a member of Mn(L)”, proposed by Cao, Kim and Roush in a monograph Incline Algebra and Applications, 1984, where Mn(L) is the set of all n×n matrices over an incline L