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In this paper, we study the notion of derivation on hoop algebras and also the (isotone, contractive, ideal, regular, idempotent and perfect) derivation on hoop algebras. We state and prove some theorems, which determine the relationship between these notions and other types of derivations on hoop algebra. We also find the equivalent condition for isotone derivation. The notion of derivations by introducing the notion of generalized derivation is extended. Also, some results on generalized derivation in hoop algebras are discussed and some equivalent conditions are given. We study some properties of new derivation and investigate some related properties of them and show that the fixed point set of a good generalized ideal derivation is a hoop algebra. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of hesitant fuzzy subsemiring, hesitant fuzzy ideals, hesitant fuzzy (bi, quasi, interior) ideals of (ordered) Γ -semiring. We characterize simple and regular (ordered) Γ -semiring by using hesitant fuzzy ideals. [ABSTRACT FROM AUTHOR]

In this paper, the notion of fuzzy pseudo-CI-filter in a pseudo-CI-algebra is introduced and its elementary properties are investigated. With the upper level set, the relationship between pseudo-CI-filter and fuzzy pseudo-CI-filter is shown and this relationship is illustrated with an example. Some type of fuzzy pseudo-CI-filters and the relationships between them and the fuzzy pseudo-CI-filter are checked. We study generated fuzzy pseudo-CI-filter by a fuzzy set. In addition, the properties of fuzzy pseudo-CI-filter are studied in Noetherian and Artinian pseudo-CI-algebra. We construct a fuzzy pseudo-CI-filter by a strictly ascending sequence of pseudo-CI-filter of pseudo-CI-algebra and any strictly decreasing sequence in (0 , 1). [ABSTRACT FROM AUTHOR]

The main objective of this study is to introduce a neutrosophic N - subalgebra (ideal) of L-algebras and to investigate some properties. It is shown that the level-set of a neutrosophic N - subalgebra (ideal) of an L-algebra is its subalgebra (ideal), and the family of all neutrosophic N - subalgebras of an L-algebra forms a complete distributive modular lattice. Additionally, it is proved that every neutrosophic N - ideal of an L-algebra is the neutrosophic N - subalgebra but the inverse of the statement may not be true in general. As the concluding part, some special cases are provided as ideals which are particular subsets of an L-algebra defined due to N - functions. [ABSTRACT FROM AUTHOR]

Recently, a number of researches studied relationship between codes and BCK-algebras, dealing with the category codes in a BCK-algebra have not been considered in earlier works. This paper investigates a code constructed by a BCK-algebra and also a BCK-algebra constructed based on code. The suggested rendered algorithm constructs the code based on BCK-algebra, the fixed dimension of this code is guaranteed by a BCK-algebra with some condition. We introduce the category of linear codes and denoted by LC. In addition, a subcategory of BCK-algebra is described and denoted by E BCK . Finally, we prove that LC is equivalent to E BCK . [ABSTRACT FROM AUTHOR]

Different extensions of fuzzy sets like intuitionistic, picture, Pythagorean, and spherical have been proposed to model uncertainty. Although these extensions are able to increase the level of accuracy, imposing rigid restrictions on the grades are the main problem of them. In these types of fuzzy sets, the value of grades and also the sum of them must be in the closed unit interval of [0, 1]. The sum condition seriously restricts the eligible values for grades. q-rung orthopair and T-spherical fuzzy sets have been introduced to establish a framework to tackle the mentioned problem for two-grade and three-grade fuzzy sets, respectively. Reducing the value of grades by means of power operator is the backbone idea of the both sets. However, these fuzzy sets are suffering from two drawbacks. The first one arises from the fact that there is no automatic structure to identify a proper power. Also, information loss is the other one which affects the accuracy of the decision-making process. This problem is a damaging consequence of changing the values of the grades. This paper introduces a novel reducing strategy to improve q-rung orthopair and T-spherical fuzzy sets by tackling the mentioned drawbacks. The proposed strategy solves out the former problem by establishing an automatic framework for finding a proper power which guarantee enough reduction of the values. The automatic framework is used for reducing the value of the maximum grade. Besides, the novel strategy reduces the rest of the grades according to their distance with the the maximum grade and its reduction rate. This paper proves mathematically that the ratio between the grades before and after of the reduction process will be intact, which results in solving information loss problem. Moreover, the higher accuracy level of the novel reduction strategy in comparison with the preceding methods, q-rung orthopair and T-sipherical fuzzy sets, is shown via different examples. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of pseudo CI-filter in the pseudo CI-algebra and defined of congruence relation, transitive CI-algebra and pseudo CI-filters generated by a set. The Maximal pseudo-filter, prime pseudo CI-filter and closed pseudo CIfilter are defined, and we show that each Maximal pseudo CI-filter is a prime pseudo CI-filter. With an example, it shows that the inverse is not true. Define of homomorphism on CI-algebras is another aim of this article, and proves that every homomorphic image and preimage of a pseudo CI-filter is also a pseudo CI-filter. Furthermore, there are some relations between prime pseudo CI-filters, Maximal pseudo CI-filters and generated pseudo CI-filters. The notion of congruence relations on pseudo CI-algebras is one of the purposes of this article. There are some relations between pseudo CI-filters and pseudo congruence. Also, the transitive CI-algebra and generated pseudo CI-filter are introduced. [ABSTRACT FROM AUTHOR]

Nowadays, wireless sensor networks (WSNs) are used to monitor and collect data in various environments. One of the main challenges in WSNs is the energy consumption due to the deployed sensor nodes in WSNs are energy-constrained. Clustering method is a solution for this problem and the cluster head (CH) selection process is a major part of the clustering method. This paper used the firefly algorithm (FA) and hesitant fuzzy to propose a new CH selection protocol. The proposed protocol uses three parameters of sensor nodes to calculate the score of each node to determine the best CHs. In order to describe the performance of the proposed protocol, three scenarios are simulated and evaluated. The simulation results show that the proposed protocol improves the energy saving and increases the network lifetime. [ABSTRACT FROM AUTHOR]

In this paper, some types of fuzzy filters of a strong Sheffer stroke non-associative MV-algebra (for short, strong Sheffer stroke NMV-algebra) are introduced. By presenting new properties of filters, we define a prime filter in this algebraic structure. Then (prime) fuzzy filters of a strong Sheffer stroke NMV-algebra are determined and some features are proved. Finally, we built quotient strong Sheffer stroke NMV-algebra by a fuzzy filter. [ABSTRACT FROM AUTHOR]

In this paper, at first median algebras and the Yang–Baxter equation are studied, some of their properties are presented. After giving some solutions to the set-theoretical Yang–Baxter equation by using these properties, it is found a solution that is not usually a solution to the set-theoretical Yang–Baxter equation in median algebras but it is the solution in Boolean algebras. [ABSTRACT FROM AUTHOR]

A complex Pythagorean fuzzy set, an extension of Pythagorean fuzzy set, is a powerful tool to handle two dimension phenomenon. Dombi operators with operational parameters have outstanding flexibility. This article presents certain aggregation operators under complex Pythagorean fuzzy environment, including complex Pythagorean Dombi fuzzy weighted arithmetic averaging (CPDFWAA) operator, complex Pythagorean Dombi fuzzy weighted geometric averaging (CPDFWGA) operator, complex Pythagorean Dombi fuzzy ordered weighted arithmetic averaging (CPDFOWAA) operator and complex Pythagorean Dombi fuzzy ordered weighted geometric averaging (CPDFOWGA) operator. Moreover, this paper explores some fundamental properties of these operators with appropriate elaboration. A decision‐making numerical example related to the selection of bank to purchase loan is given to demonstrate the significance of our proposed approach. Finally, a comparative analysis with existing operators is given to demonstrate the peculiarity of our proposed operators. [ABSTRACT FROM AUTHOR]

In this paper, we study the notion of M V -modules of fractions with respect to a ⋅-prime ideal P. Also the relation between the ideals of M V -module M and the ideals of M V -module of fractions M P is studied and it is shown that there is a one to one correspondence between Q -prime A -ideals of M V -module M and Q P -prime A P ′ -ideals of M V -module of fractions M P , where A P ′ is the maximal localization of A at a maximal ⋅-ideal P of A and Q is a ⋅-prime ideal of A such that Q ⊆ P. [ABSTRACT FROM AUTHOR]

Hamming codes are of primary concern in information theory and its applications. Despite a number of researches that have been conducted on such codes and their characterizations, dealing with the properties of previously introduced codes in a BCK-algebraic framework has not been considered in earlier works. This paper investigates a code constructed based on BCK-algebraic models and proposes an algorithm corresponding to the presented code. It is noticeable that the suggested rendered algorithm is also established on the basis of the elements of a BCK-algebra. In fact, both the Hamming distance and dimension, associated with the presented code, can be estimated through a BCK-algebra structure due to the mechanism of its algorithm which is heavily dependent on the parity check matrix. In addition, the way in which the codes are designed contributes substantially to classification of them and to extract greater number of their attributes compared to the previous works. The highlight of the proposed method is that the number of atoms of the BCK-algebra plays a key role in calculation of the Hamming distance and dimension of these codes. Moreover, the obtained codes possess specified and recognizable Hamming distance which are essential in performing error-correcting, error-detecting and decoding tasks. [ABSTRACT FROM AUTHOR]

In this paper, congruences and (order, prime and compatible) filters are introduced in Sheffer stroke basic algebras. They are interrelated with each other. Also some relationships between filters and congruences by focusing on their properties in these structures are given. In addition to these, a basic algebra is constructed by the help of compatible filter and A/Θ(F). Moreover, a representation theorem for Sheffer stroke basic algebra by using prime filters and A/Θ(F) is stated and proved. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of implication filter as a generalization of Boolean filter of first kind in Hilbert algebra and study it in detail. Also, we prove that F is an implication filter of a Hilbert algebra H if and only if every implicative filter of quotient algebra H / F is an implication filter. Finally, we generalized Boolean algebra and introduced a weak implication algebra, we prove that F is an implication filter of a Hilbert algebra H if and only if the quotient algebra H / F is a weak implication algebra. By suitable diagrams, we summarize the results of this paper and the previous results in these fields. [ABSTRACT FROM AUTHOR]

This paper introduces and applies the notion of fuzzy hyper EQ-subalgebras as a generalization of the notation of fuzzy EQ-subalgebras and constructs extendable fuzzy EQ-subalgebras via these concepts. Moreover, by using the fuzzy hyper EQ-filters, it defines a congruence relation on hyper EQ-algebras that under some conditions is strongly regular and the quotient of any hyper EQ-algebra via this relation is an EQ-algebra. [ABSTRACT FROM AUTHOR]

This study introduces the notion of n-valued refined neutrosophic (EQ-subalgebras)EQ–(pre)filters and investigates some of their properties. We show how to construct n-valued refined neutrosophic EQ-(pre)filters and determine the relationship between n-valued refined neutrosophic EQ-(pre)filters and EQ–(pre)filters with respect to (α, β, γ)-level set. Finally, the extension of n–valued refined neutrosophic EQ–(pre)filters are considered via homomorphisms and some applications of n–valued refined neutrosophic EQ–(pre)filters are presented. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of pseudo-CI algebras and investigate some of their properties. It is a generalization of the notion of pseudo-BE algebras, pseudo-BCK algebras and pseudo-MV algebras. We give and provide some conditions for a pseudo-CI algebra to be a pseudo-BE algebra. Also, we define the class of singular pseudo-CI algebras and show that any singular pseudo-CI algebra is a pseudo-BCI algebra. The adjoint group of a pseudo-CI algebra is defined and studied. Furthermore, distributive pseudo-CI algebras are discussed and showed that these coincide with distributive pseudo-BE algebras. [ABSTRACT FROM AUTHOR]

Graph operations produce new classes of graphs from initial ones which in turn may be useful for the modeling and recognition of computer network designs. A Pythagorean fuzzy set-based model offers more flexibility to cope with human evaluation information as compared to intuitionistic fuzzy model. The main objective of this research study is to expand the area of discussion on Pythagorean fuzzy graphs by establishing fruitful results and notions related to an operation on Pythagorean fuzzy graphs called strong product. Certain concepts, including connectedness, completeness, regularity and partially regularity of strong product Pythagorean fuzzy graphs are discussed. It is shown that the strong product of two regular Pythagorean fuzzy graphs may not be regular. Moreover, some necessary and sufficient conditions for the strong product of two regular Pythagorean fuzzy graphs to be regular are established. Finally, an algorithm for Pythagorean fuzzy multi-criteria decision making is presented and problem concerning to evaluation of domestic airlines in Japan is solved to demonstrate the applicability of PFGs in realistic scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we intend to introduce the notion of the radical of a filter in a pseudo BL-algebra and express its characteristics and properties. We define dense, infinitesimal, nilpotent, and unity elements in a pseudo BL-algebra, and then, investigate the relationship between these elements and the radical in a pseudo BL-algebra. Our study revealed significant results in this regard. [ABSTRACT FROM AUTHOR]

In this paper, the notions of orthogonal, dense, regular, zero-divisor, strong and complemented elements in a pseudo BL-algebra are introduced and relation between the orthogonal and zero-divisor elements for perfect (good) pseudo BL-algebras is investigated. In particular, we get some results when a pseudo BL- algebra is good or perfect. Finally, a new characterization of these elements in a pseudo BL-algebra by a diagram is given. [ABSTRACT FROM AUTHOR]

In this paper, we investigate related properties of some particular derivations and give some characterizations of regular derivations in commutative multiplicative semilattices. Also we give some characterizations of zero derivations in prime commutative multiplicative semilattices. Then we prove that the set of all prefect derivations ideals on commutative multiplicative semilattices with prefect derivations can form a complete Heyting algebra and obtain that there exists a one to one correspondence between the set of all prefect derivations ideals on commutative multiplicative semilattices with prefect derivations and its quotient structure. Finally, we show that the structure of an idempotent commutative quantale is completely determined by its set of all principal derivations. [ABSTRACT FROM AUTHOR]

In the paper, we introduce some stabilizers and investigate related properties of them in MTL-algebras. Then, we also characterize some special classes of MTL-algebras, for example, IMTL-algebras, integral MTL-algebras, Gödel algebras and MV-algebras, in terms of these stabilizers. Moreover, we discuss the relation between stabilizers and several special filters (ideals) in MTL-algebras. Finally, we discuss the relation between these stabilizers and prove that the right implicative stabilizer and right multiplicative stabilizer are order isomorphic. This results also give answers to some open problems, which were proposed by Motamed and Torkzadeh in [Soft Comput, 21 (2017) 686-693]. [ABSTRACT FROM AUTHOR]

This paper considers wireless sensor (hyper) networks by single-valued neutrosophic (hyper)graphs. It tries to extend the notion of single-valued neutrosophic graphs to single-valued neutrosophic hypergraphs and it is derived single-valued neutrosophic graphs from single-valued neutrosophic hypergraphs via positive equivalence relation. We use single-valued neutrosophic hypergraphs and positive equivalence relation to create the sensor clusters and access to cluster heads. Finally, the concept of (extended) derivable single-valued neutrosophic graph is considered as the energy clustering of wireless sensor networks and is applied this concept as a tool in wireless sensor (hyper) networks. [ABSTRACT FROM AUTHOR]

In recent years, there has been a marked increase in the use of wireless sensor networks in various environments such as crisis areas, military operations, and monitoring systems. These networks do not use a fixed network infrastructure and therefore they are a popular choice for highly dynamic environments. One of the main concerns in these networks is the topology management issue, which the clustering method is a subfield for that. The main objective of clustering methods is optimizing the energy consumption. This paper proposes a new clustering protocol, which uses many parameters such as the activity history of each node, local and general state of nodes and their resources condition to determine the best cluster heads and members of each cluster that can increase the network lifetime, fair resource consumption and network coverage. [ABSTRACT FROM AUTHOR]

This paper extends the notion of fuzzy BCK-subalgebras to fuzzy hyper BCK-subalgebras and defines an extended fuzzy BCK-subalgebras. This study considers a type of fuzzy hyper BCK-ideals in this hyperstructure and describes the relationship between hyper BCK-ideals and fuzzy hyper BCK-ideals. In fact, it tries to introduce a strongly regular relation on hyper BCK-algebras. Moreover, by using the fuzzy hyper BCK-ideals, it defines a congruence relation on (weak commutative) hyper BCK-algebras that under some conditions is strongly regular and the quotient of any hyper BCK-algebra via this relation is a (hyper BCK-algebra) BCK-algebra. [ABSTRACT FROM AUTHOR]

In this paper, we introduce commutative hyper BE-algebra and study it in detail. We show that every commutative (row diagonal, column row, very thin) hyper BE-algebra is a BE-algebra. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of nodes and nodal filters in BL-algebras. Then we study the relationships between nodal filters and some other types of filters, likeness prime filter and special filter in BL-algebras. Also, we study inverse image of a nodal filter under a BL-homomorphism. Finally, we obtain a characterization of the nodal filters in terms of congruences. [ABSTRACT FROM AUTHOR]

A big shortcoming of the simple genetic algorithm is that whenever it converges to a local optimum, its performance is continuously deteriorating, especially in the highly nonlinear problems such as traveling salesman problem (TSP). Therefore, some heuristics such as local search are needed to help genetic algorithm (GA) loops escaping such situations. The critical point in such hybridization is the determining a suitable time for applying local search to the GA population. In this study, a new hybridization of GA and local search based on a new similarity-based control mechanism is proposed, and its behavior on different TSP instances is compared with simple GA. The experimental results show that the proposed hybrid algorithm yields the optimal tour length in most of the cases, especially in the TSP instances with higher complexity. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of anti fuzzy filter and study the $$\mathcal{N }$$ -subalgebra(filter) of $$CI$$ -algebra $$X$$ . We prove that every anti fuzzy filter of $$BE$$ -algebra is an anti fuzzy subalgebra, but it is not valid in $$CI$$ -algebra. Finally, the notion of fuzzy translations and fuzzy extension of anti fuzzy filter in $$CI$$ -algebras are introduced. We show that every anti fuzzy filter can be as an anti fuzzy extension, but converse may not be true in general. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of upper (down) set in BL-algebras and extended upper sets of BL-algebras. Also, the notions of Krull dimension and regular sequence in BL-algebras are introduced and studied in detail. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two different stabilizers of X with respect to Y for subsets X and Y of an MV-algebra A. We show that stabilizers are ideals and we investigate the relation between stabilizers and some other ideals in MV-algebras. We also show that if I and J are ideals in an MV-algebra A, then the stabilizer of I with respect to J is the relative pseudo-complement of I with respect to J in the lattice of ideals of A. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of coatom and comolecule of BL-algebras, also we state and prove some theorems which determines their properties. Finally we investigate some results in co-annihilators and verify the relationship between comolecules with prime filters, coatoms with hyperarchimedean and investigate $^{\perp}F$ for some types of filters. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the notion of implication filters in BL-algebras and then state and prove some theorems which determine the relationships of these filters and other filters in BL-algebras. We also introduce the notion of implication BL-algebras and investigate its properties, as well as the relationship of implication BL-algebras and other algebraic structures. [ABSTRACT FROM AUTHOR]

Hilbert algebras are introduced for investigations in intuitionistic and other non - classical logics and BE-algebra is a generalization of dual BCK-algebra. In this paper, we investigate the relationship between Hilbert algebras and BE-algebras. In fact, we show that a commutative implicative BE-algebra is equivalent to the commutative self distributive BE-algebra, therefore Hilbert algebras and commutative self distributive BE-algebras are equivalent. [ABSTRACT FROM AUTHOR]

In this paper, we introduce some types of filters in BE-algebras and state some theorems which determine the relationship between these filters and other filters of a BE-algebra and by some examples we show that these notions are different. [ABSTRACT FROM AUTHOR]

In this article, we introduced the notions fuzzy soft subalgebras and fuzzy soft ideal of subtraction algebras. We showed that fuzzy soft image and fuzzy soft inverse image of fuzzy soft ideal are both fuzzy soft ideal under certain conditions. We have studied their related properties in details. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of fuzzy filters(ideals) in CI-algebras. We study fuzzy congruence relation in detail and construct quotient of $$(X/\bar{\theta}; {\circ}, 1/\bar{\theta})$$ via a fuzzy congruence relation on CI-algebra X. [ABSTRACT FROM AUTHOR]

By two relations belonging to $${(\in)}$$ and quasi-coincidence ( q) between fuzzy points and fuzzy sets, we define the concept of ( α, β)-fuzzy subalgebras where α, β are any two of $${\{\in, q, \in\vee q, \in\wedge q\}}$$ with $${\alpha\neq \in\wedge q}$$ . We state and prove some theorems in ( α, β)-fuzzy B-algebras. [ABSTRACT FROM AUTHOR]

In this paper we introduce some types of filters in a BL algebra A, and we state and prove some theorems which determine the relationship between these notions and other filters of a BL algebra, and by some examples we show that these notions are different. Also we consider some relations between these filters and quotient algebras that are constructed via these filters. [ABSTRACT FROM AUTHOR]

In this paper we introduce some types of filters in a BL algebra A, and we state and prove some theorems which determine the relationship between these notions and other filters of a BL algebra, and by some examples we show that these notions are different. Also we consider some relations between these filters and quotient algebras that are constructed via these filters. [ABSTRACT FROM AUTHOR]

Abstract In this note we first define the notions of (weak, strong) implicative hyper K-algebras. Then we show by examples that these notions are different. After that we state and prove some theorems which determine the relationship between these notions and (weak) hyper K-ideals. Also we obtain some relations between these notions and (weak) implicative hyper K-ideals. Finally, we study the implicative hyper K-algebras of order 3, in particular we obtain a relationship between the positive implicative hyper K-algebras and (weak, strong) implicative hyper K-algebras under a simple condition. [ABSTRACT FROM AUTHOR]