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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]

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]

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 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]

Nowadays, the most important aspects of wireless sensor networks (WSNs) are to make optimal use of and direct the limited energy of sensor nodes towards the desired application and prolong the network lifetime for that application. Although a few studies exist that have addressed these special goals, they have been mostly focused on the process of selecting cluster heads (CHs) and forwarders. No studies have been conducted so far on the selection of fuzzy input parameters in clustering and routing processes as well as the application-based parameter selection process. Generally, a fixed number of parameters have always been selected by designers. Hence, the shuffled frog leaping algorithm (SFLA) was employed in this paper to propose a technique for selecting fuzzy input parameters in a fuzzy multi-hop clustering protocol named the PS-SFLA. This technique includes three main phases, introduced in three versions for the sake of stepwise evaluation. Based on the literature review, the most frequent and diverse parameters were extracted and formulated in the first version. The proposed technique used the SFLA in the second version to select the appropriate parameters fitting the application specifics and scenario and determine the coefficients of parameters simultaneously so that they could be used as the inputs of the fuzzy inference system. It was also utilized in the final version for the automated, accurate, application-based tuning of fuzzy rules before the network was set up. By design, different versions of the PS-SFLA act as the starting points of the next version in addition to the fact that they can be evaluated separately. The PS-SFLA was compared with the LEACH, ASLPR, SIF, ERA, and FSFLA in different scenarios and two applications from the perspective of the alive nodes, the number of packets received by the BS, lifetime, and other factors. According to the simulation results, the PS-SFLA outperformed all of the other methods greatly in all scenarios and applications and PS-SFLA increases the lifetime due to the appropriate selection of fuzzy input parameters based on application and purpose. • Proposing an application-based parameter selection technique in WSNs for 1st time. • Extracting the best parameters and formulated them for clustering and routing. • Automated fuzzy rules tuning by SFLA based on program and application specifics. • Determining of the application-based impact factors of fuzzy rules tables. • The simulation results show the proposed technique outperforms other protocols. [ABSTRACT FROM AUTHOR]