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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.

This paper defines the concept of partitioned hypergraphs‎, ‎and enumerates the number of these hypergraphs and discrete complete hypergraphs‎. ‎A positive equivalence relation is defined on hypergraphs‎, ‎this relation establishes a connection between hypergraphs and graphs‎. ‎Moreover‎, ‎we define the concept of (extended) derivable graph‎. ‎Then a connection between hypergraphs and (extended) derivable graphs was investigated‎. ‎Via the positive equivalence relation on hypergraphs‎, ‎we show that some special trees are derivable graph and complete graphs are self derivable graphs‎.

In this paper, we propose a new intuitionistic entropy measurement for multi-criteria decision-making (MCDM) problems. The entropy of an intuitionistic fuzzy set (IFS) measures uncertainty related to the data modelling as IFS. The entropy of fuzzy sets is widely used in decision support methods, where dealing with uncertain data grows in importance. The Complex Proportional Assessment (COPRAS) method identifies the preferences and ranking of decisional variants. It also allows for a more comprehensive analysis of complex decision-making problems, where many opposite criteria are observed. This approach allows us to minimize cost and maximize profit in the finally chosen decision (alternative). This paper presents a new entropy measurement for fuzzy intuitionistic sets and an application example using the IFS COPRAS method. The new entropy method was used in the decision-making process to calculate the objective weights. In addition, other entropy methods determining objective weights were also compared with the proposed approach. The presented results allow us to conclude that the new entropy measure can be applied to decision problems in uncertain data environments since the proposed entropy measure is stable and unambiguous.

In this paper, we show the relationship between (skew) deductive system and (skew) filter in residuated skew lattices. It is shown that if a residuated skew lattice is conormal, then any skew deductive system is a skew filter under a condition and deductive system and skew deductive system are equivalent under some conditions too. It is investigated that in branchwise residuated skew lattice, filter, deductive system and skew deductive system are equivalent. We define some types of prime (skew) filters in residuated skew lattices and show the relationship between prime (skew) filters and residuated skew chaines. It is proved that in prelinear residuated skew lattice any proper filter can be extended to a maximal, prime filter of type (I). The notion of the radical of a filter is defined and several characterizations of the radical of a filter are given. We show that in non conormal prelinear residuated skew lattice with element 0, infinitesimal elements are equal to intersection of all the maximal filters.

The notions of a dual pseudo-Q algebra and a dual pseudo-QC algebra are introduced. The properties and characterizations of them are investigated. Conditions for a dual pseudo-Q algebra to be a dual pseudo-QC algebra are given. Commutative dual pseudo-QC algebras are considered. The interrelationships between dual pseudo-Q/QC algebras and other pseudo algebras are visualized in a diagram.

In this paper, we introduce the notions of multiplier, ⊙-closure operator and modal operator on hoop-algebras. After that, we investigate some algebraic properties of multiplier, ⊙-closure operator and modal operator on hoop-algebras. Then we study relationships between multiplier and closure operator on hoop-algebras showing that, any monotone modal operator on hoop-algebra serves as a closure operator. Finally we represent image of hoop-algebra under the closure operator can be a hoop-algebra.

Inthispaper, weintroducethenotionof(implicative)neutrosophicfilters in BE-algebras. The relation between implicative neutrosophic filters and neutrosophic filters is investigated and we show that in self distributive BE-algebras these notions are equivalent.

Soft set theory plays a vital role in solving many complicated problems with inherited uncertainty. An n-ary algebraic systems is a generalization of algebraic structures and it is the most natural way for the further development, deeper understanding of their properties. In this paper, we apply soft set theory to an n-ary algebraic systems and introduce the notions of soft n-ary groups and soft n-ary subgroups. Further, some operations on soft sets are extended to the former. Finally, we provide the characterization of soft n-ary subgroups over an n-ary group (G,f) and study their related properties.

In this article we introduce the notion of e-group as a new generalization of a group. The condition for a group to be an e-group is given. The characterization of some properties is established and some results follow.

In this paper, we investigate the relationship between dual (Weak) Subtraction algebras, Heyting algebras and BE-algebras. In fact, the purpose of this paper is to show that BE-algebra is a generalization of Heyting algebra and dual (Weak) Subtraction algebras. Also, we show that a bounded commutative self distributive BE-algebra is equivalent to the Heyting algebra.

The aime of this paper is the study of residual mappings and convexity in hyperlattices. To get this point, we study principal down set in hyperlattices and we give some conditions for a mapping between two hyperlattices to be equivalent with a residual maping. Also, we investigate convex subsets in ∧-hyperlattices.

Fuzzy graphs (FGs) and their generalizations have played an essential role in dealing with real-life problems involving uncertainties. The goal of this article is to show some serious flaws in the existing definitions of several root-level generalized FG structures with the help of some counterexamples. To achieve this, first, we aim to improve the existing definition for interval-valued FG, interval-valued intuitionistic FG and their complements, as these existing definitions are not well-defined; i.e., one can obtain some senseless intervals using the existing definitions. The limitations of the existing definitions and the validity of the new definitions are supported with some examples. It is also observed that the notion of a single-valued neutrosophic graph (SVNG) is not well-defined either. The consequences of the existing definition of SVNG are discussed with the help of examples. A new definition of SVNG is developed, and its improvement is demonstrated with some examples. The definition of an interval-valued neutrosophic graph is also modified due to the shortcomings in the current definition, and the validity of the new definition is proved. An application of proposed work is illustrated through a decision-making problem under the framework of SVNG, and its performance is compared with existing work.

By using vague sets we generalize the notion of convex sets and introduce the notion of (α, β ,T )-convex vague sets and study their properties, where T is a triangular norm on [0, 1].

In this paper, we introduce the notion of hesitant fuzzy (implicative) filters and get some results on BE-algebras and show that every hesitant fuzzy implicative filter is a hesitant fuzzy filter but not the converse. Finally, we state and prove the relationship between hesitant fuzzy (implicative) filters and γ-inclusive sets.

In this note, by using the concept of vague sets, the notion of vague \(BCK/BCI\)-algebra is introduced. And the notions of \(\alpha\)-cut and vague-cut are introduced and the relationships between these notions and crisp subalgebras are studied.

This paper focuses on the investigation of fuzzy filters of -algebras, an important and popular generic logical algebra. By studying the equivalent conditions of fuzzy fantastic filter and fuzzy normal filter of -algebras, the relation between these two filters are revealed. Two open problems of -algebras, i.e.,”Under what suitable condition a normal filter becomes a fantastic filter? ” and ” Under what suitable condition extension property for normal filter holds? (Extension property for a normal filter)”, are solved accordingly.

In this paper, we introduce the notion of dual Q-algebras and we show that the CI-algebras are equivalent to the dual Q-algebras.