(m,n)-Semirings and a Generalized Fault Tolerance Algebra of Systems

We propose a new class of mathematical structures called (m,n)-semirings} (which generalize the usual semirings), and describe their basic properties. We also define partial ordering, and generalize the concepts of congruence, homomorphism, ideals, etc., for (m,n)-semirings. Following earlier work by Rao, we consider a system as made up of several components whose failures may cause it to fail, and represent the set of systems algebraically as an (m,n)-semiring. Based on the characteristics of these components we present a formalism to compare the fault tolerance behaviour of two systems using our framework of a partially ordered (m,n)-semiring.Comment: 26 pages; extension of arXiv:0907.3194v1 [math.GM

On intuitionistic fuzzy sub-hyperquasigroups of hyperquasigroups

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. In this paper, we consider the intuitionistic fuzzification of the concept of sub-hyperquasigroups in a hyperquasigroup and investigate some properties of such sub-hyperquasigroups. In particular, we investigate some natural equivalence relations on the set of all intuitionistic fuzzy sub-hyperquasigroups of a hyperquasigroup.Comment: 13 page

FUZZY SUBSETS OF THE PHENOTYPES OF F2-OFFSPRING

This paper presents a connection between fuzzy sets, biological inheritance and hyperstructures in which we consider the set of phenotypes of the second generation $F_{2}$ in different types of inheritance, define fuzzy subsets of it and construct a sequence of join spaces associated to each of its types