MBJ-neutrosophic Ideals of KU-algebras

In this paper, the notion of MBJ-neutrosophic ideal for KU-algebra is introduced and its properties are investigated. Also, a condition for an MBJ-neutrosophic subalgebra to be an MBJ-neutrosophic ideal and converse part of a KU-algebra are discussed.

Novel Cubic Fermatean Fuzzy Soft Ideal Structures

The theory of collections is a necessary mathematical tool. It gives mathematical models for the class of problems that explains with exactness, precision and uncertainty. Characteristically, non crisp set theory is extensional. More often than not, the real life problems inherently involve uncertainties, imprecision and not clear. In particular, such classes of problems arise in economics, engineering, environmental sciences, medical sciences, and social sciences etc. They studied basic operations over the fermatean uncertainty sets. Here we shall introduce three new operations, subtraction, division, and fermatean sum of mean operations over fermatean uncertainty sets. Several researchers have considered q-rung orthopair fuzzy sets as fermatean uncertainty sets (FUSs). The Fuzzy Set Theory approach is found most appropriate for dealing with uncertainties. However, it is short of providing a mechanism on how to set the membership function extremely individualistic. The major reason for these difficulties arising with the above theories is due to the inadequacies of their parameterization tools. In order to overcome these difficulties, in 1999 Molodtsov [7] introduced the concept of soft set as a completely new Mathematical tool with adequate parameterization for dealing with uncertainties. In this area, we introduce the concept of cubic fermatean uncertainty soft set and define cubic fermatean uncertainty soft sub algebra of KU-algebras’ which is applicable in various algebraic structures. In addition, we proved every closed cubic fermatean uncertainty soft ideal is a cubic fermatean uncertainty soft KU-algebra and every closed cubic fermatean uncertainty soft ideal is a cubic fermatean uncertainty soft ideal. Also, we discuss the closed cubic fermatean uncertainty ideal structures on fermatean uncertainty soft set. Finally, we prove that every closed cubic fermatean uncertainty soft ideal of a non-empty set is a cubic fermatean uncertainty soft ideal and converse part is not true with suitable example.

Maximum Waiting Times are Asymptotically Independent

For every n consider a subset Hn of the patterns of length n over a fixed finite alphabet. The limit distribution of the waiting time until each element of Hn appears in an infinite sequence of independent, uniformly distributed random letters was determined in an earlier paper. This time we prove that these waiting times are getting independent as n → ∞. Our result is used for applying the converse part of the Borel–Cantelli lemma to problems connected with such waiting times, yielding thus improvements on some known theorems.