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In this paper, we are going to introduce a fundamental relation on \(H_{v}BE\)-algebra and investigate some of properties, also construct new \((H_{v})BE\)-algebras via this relation. We show that quotient of any \(H_{v}BE\)-algebra via a regular regulation is an \(H_{v}BE\)-algebra and this quotient, via any strongly relation is a \(BE\)-algebra. Furthermore, we investigate that under what conditions some relations on \(H_{v}BE\)-algebra are transitive relations.

In this paper‎, ‎as a further generalization of fuzzy ideals‎, ‎we introduce the notion of a fuzzy (soft) quasi-interior ideals of semirings and characterize regular semiring in terms of fuzzy (soft) quasi-interior ideals of semirings‎. ‎We prove that $(\mu‎, ‎A)$ is a fuzzy soft left quasi-interior ideal‎ ‎over a regular semiring $M,$ if and only if $(\mu‎, ‎A)$ is a fuzzy soft quasi-ideal over a semiring $M,$‎ ‎and study some of the properties‎.

The Markov Weighted Fuzzy Time Series (MWFTS) is a method for making predictions based on developing a fuzzy time series (FTS) algorithm. The MWTS has overcome certain limitations of FTS, such as repetition of fuzzy logic relationships and weight considerations of fuzzy logic relationships. The main challenge of the MWFTS method is the absence of standardized rules for determining partition intervals. This study compares the MWFTS model to the partition methods Genetic Algorithm-Fuzzy K-Medoids clustering (GA-FKM) and Fuzzy K-Medoids clustering-Particle Swarm Optimization (FKM-PSO) to solve the problem of determining the partition interval and develop an algorithm. Optimal partition optimization. The GA optimization algorithm’s performance on GA-FKM depends on optimizing the clustering of FKM to obtain the most significant partition interval. Implementing the PSO optimization algorithm on FKM-PSO involves maximizing the interval length following the FKM procedure. The proposed method was applied to Anand Vihar, India’s air quality data. The MWFTS method combined with the GA-FKM partitioning method reduced the mean absolute square error (MAPE) from 17.440 to 16.85%. While the results of forecasting using the MWFTS method in conjunction with the FKM-PSO partition method were able to reduce the MAPE percentage from 9.78% to 7.58%, the MAPE percentage was still 9.78%. Initially, the root mean square error (RMSE) score for the GA-FKM partitioning technique was 48,179 to 47,01. After applying the FKM-PSO method, the initial RMSE score of 30,638 was reduced to 24,863. Doi: 10.28991/ESJ-2022-06-06-010 Full Text: PDF

We introduce Engel elements in a BCI-algebra by using left and right normed commutators, and some properties of these elements are studied. The notion of $n$-Engel BCI-algebra as a natural generalization of commutative BCI-algebras is introduced, and we discuss Engel BCI-algebra, which is defined by left and right normed commutators. In particular, we prove that any nilpotent BCI-algebra of type $2$ is an Engel BCI-algebra, but solvable BCI-algebras are not Engel, generally. Also, it is proved that $1$-Engel BCI-algebras are exactly the commutative BCI-algebras.

Hilbert algebras are important tools for certain investigations in intuitionistic logic and other non-classical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GE-algebra (generalized exchange algebra), is introduced and studied its properties. We consider filters, upper sets and congruence kernels in a GE-algebra. We also characterize congruence kernels of transitive GE-algebras.

In this paper, we introduce a Sheffer stroke Hilbert algebra by giving definitions of Sheffer stroke and a Hilbert algebra. After it is shown that the axioms of Sheffer stroke Hilbert algebra are independent, it is given some properties of this algebraic structure. Then it is stated the relationship between Sheffer stroke Hilbert algebra and Hilbert algebra by defining a unary operation on Sheffer stroke Hilbert algebra. Also, it is presented deductive system and ideal of this algebraic structure. It is defined an ideal generated by a subset of a Sheffer stroke Hilbert algebra, and it is constructed a new ideal of this algebra by adding an element of this algebra to its ideal.

The present study aimed to introduce $n$-fold interval valued residuated lattice (IVRL for short) filters in triangle algebras. Initially, the notions of $n$-fold (positive) implicative IVRL-extended filters and $n$-fold (positive) implicative triangle algebras were defined. Afterwards, several characterizations of the algebras were presented, and the correlations between the $n$-fold IVRL-extended filters, $n$-fold (positive) implicative algebras, and the Gödel triangle algebra were discussed.