Journal of Algebraic Hyperstructures and Logical Algebras
Volume:2 Issue: 3, Summer 2021

In this paper, state operators on hyper BE-algebras (correspondingly, state hyper BE-algebras) are introduced and studied. State hyper filters are introduced and generated state hyper filters are represented in state hyper BE-algebras. Also, maximal (prime) state hyper filters are characterised and the relations between state maximal hyper filters and state prime hyper filters are discussed. Moreover, some related results of state (compatible) hyper congruence are obtained. Especially, it follows that there is an isotone bijection between all state strong regular $circ$-reflexive hyper filter $mathcal{F}_s(H,xi)$ and all state compatible hyper congruence $mathcal{C}_s(H,xi)$ on state commutative transitive RD-hyper BE-algebra $(H,xi)$.

In this paper, we introduce the new concept of a hyper BZ-algebra which is a generalization of BZ-algebra and hyper BCI-algebra, and give some examples and basic properties. We discuss the relationships among hyper BZ-algebras, hyper BCC-algebras and hyper BCI-algebra. Moreover, we propose the concepts of anti-grouped hyper BZ-algebras and generalized anti-grouped hyper BZ-algebras, and prove that the following important results (1) Every anti-grouped hyper BZ-algebra is an anti-grouped BZ-algebra;(2) Every generalized anti-grouped hyper BZ-algebra corresponds to a semihypergroup. Finally, we present a method to construct a new hyper BZ-algebra by using a hyper BCC-algebra and a standard generalized anti-grouped hyper BZ-algebra.

Molodtsov proposed soft set theory to address uncertainty in a parameter manner, and Atanassov introduced intuitionistic fuzzy set which is very useful in providing a flexible model to elaborate uncertainty and vagueness involved in decision making. Using intuitive fuzzy set and soft set, Jun et al. introduced a new notion, ``soju structure'', as a kind of hybrid structure. The concept of implicative soju ideal in BCK-algebra will be introduced and several properties will be investigated in this article. We will discuss the relationship between soju subalgebra, soju ideal, positive implicative soju ideal, commutative soju ideal and implicative soju ideal. Also, characterizations of implicative soju ideal will be established.

This paper aims at introducing two types of orthopair soft sets, which might serve as novel approaches to granular computing based on parametrization. These generalized soft sets emerge naturally when linguistic parameters are employed to convey uncertainty attached to elements of certain sets. Concepts of uncertainty measures attached to the parameters and the whole orthopair soft sets are presented as well. The proposed uncertainty measures are useful for classifying elements of the set of parameters. Different types of granularity measures associated with parameters are presented and are extended to orthopair soft sets. Collective wisdom is helpful in decision making based on consensus. A numerical example is given to demonstrate how orthopair soft sets can be employed in this regard.

The purpose of this paper is to introduce and explore cubic soft matrix theory. Moreover we apply the notion of cubic soft matrices using the weighted arithmetic means for applications in medical diagnosis by introducing two algorithms.

In this paper, we have studied the notion of nearness $d$-algebras which is a generalization of nearness BCK-algebras (or NBCK-algebra for short). Therefore, it is defined that the notions of nearness d$-subalgebra, nearness d-ideal in nearness $d$-algebras. Afterward, we investigated relations among  them and gave some examples.

In this research article, new fuzzy K-algebras, namely, spherical fuzzy K-algebras and $(in, in vee q)$-spherical fuzzy K-algebras are constructed. Certain properties of these spherical fuzzy K-structures are investigated. The behavior of spherical fuzzy K-algebras under homomorphism is characterized. The spherical fuzzy K-algebra with thresholds is also delineated.

In this paper, the notions of uni-soft p-semisimple ideals and uni-soft strong ideals in BCI-algebras are introduced and related properties are investigated. Some conditions for a uni-soft ideal to be a uni-soft p-semisimple ideal are given. Also, a necessary and sufficient condition for a uni-soft ideal to be a uni-soft strong ideal is given. Finally, the relationships between uni-soft p-semisimple ideals and uni-soft strong ideals are investigated.

In this paper, we define the notion of minimal prime ideals of hoops and investigate some properties of them. Then by using the notion of annihilators, we study the relation between minimal prime ideals and annihilators. Also, we introduce the notion of zero divisors elements of hoops and prove that the set of all zero divisors of hoops is a union of all minimal prime ideals of hoop. Finally, by using the notions of minimal prime ideals and maximal ideals of hoop, we introduce two new ideals as p-ideal and m-ideal. Then we study some properties of them and investigate the relation between them and prove that every p-ideal of semi-simple hoop is an m-ideal of it.