r. a. borzooei

In this paper, by using the notion of ordinal sum of equality algebras which is defined in [4], weinvestigate some related properties and different kinds of filters of it such as prime and maximal. Inaddition, by focusing on chain equality algebra, we define the concept of a cut of an equality algebraand use it to introduce a new ordinal sum of them. By defining a relation relative to a cut, we showthat the family of classes is made a cone algebra. Finally, we prove that every chain equality algebracan be represented as an ordinal sum of chain cone algebras.

L-algebras, connected to algebraic logic and quantum structures, were first introduced by Rump [13]. In [5], the number of some finite L-algebras is counted. But classifying and finding examples of L-algebras is not always an easy task and is very important. So, in this paper, we classify the set of all non-isomorphic L-algebras up to order 4. For this, we define the notion of partial and total conditions and by using them, we characterize all of the L-algebras of orders 2, 3 and 4. We prove that that there are 5 L-algebras of order 3 and 44 L-algebras of order 4, up to isomorphism.

In this paper, by using the notion of prime filter, we show representation theorem of hoops and we prove that every nontrivial ∨-hoop is a subdirect product of hoop-chains. In the following, by using the concept of maximal filter of hoops, we introduce radical of hoops. Then some equivalence definitions of it and some related properties are investigated. Then by using this notion, we introduce the concepts of r-filters and p-filters on hoops and the relation between them and other filters of hoops are investigated. Finally, by using p-filters on hoops, we define new open sets on hoop that could be used to construct a Zarisky topology.

After introducing the concept of single valued neutrosophic ideal in a pseudo MV-algebra, its properties are examined. The various conditions under which a single valued neutrosophic set can be a single valued neutrosophic ideal are examined. Characterizations of a single valued neutrosophic ideal of a pseudo MV-algebra are considered.

The notion of commutative falling intuitionistic fuzzy ideal of a BCK-algebra is introduced and related properties are investigated. We verify that every commutative intuitionistic fuzzy ideal is a commutative falling intuitionistic fuzzy ideal, and provide example to show that a commutative falling intuitionistic fuzzy ideal is not a commutative intuitionistic fuzzy ideal. Relations between a falling intuitionistic fuzzy ideal and a commutative falling intuitionistic fuzzy ideal are considered, and a condition for a falling intuitionistic fuzzy ideal to be a commutative falling intuitionistic fuzzy ideal is provided.

In this paper, first we define the concept of nilpotent element on a hoop H, study some properties of them and investigate the relation with ultra deductive systems. Then by using this notion, we introduce cyclic hoops and prove that every cyclic hoop has a unique generator and is a local MV-algebra. In the follows, we introduce the notion of Boolean elements on hoops and investigate some of their properties and relation among Boolean elements with ultra deductive systems and nilpotent elements. Finally, we introduce a functor between the category of hoops and category of Boolean elements of them.

In this paper, we defined the notions of (∈, ∈)-fuzzy implicative deductive systems and (∈, ∈ ∨ q)-fuzzy implicative deductive systems of hoops and studied some traits and tried to define some definitions that are equivalent to them. Thus by using the notion of (∈, ∈)- fuzzy deductive system of hoop, we defined a new congruence relation on hoop and show that the algebraic structure that is made by it is a Brouwerian semilattice, Heyting algebra and Wajesberg hoop.

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.

In the paper [J. Ghosh and T.K. Samanta, Hyperfuzzy sets and hyperfuzzy group, Int. J. Advanced Sci Tech. 41 (2012), 27–37], Ghosh and Samanta introduced the concept of hyperfuzzy sets as a generalization of fuzzy sets and interval-valued fuzzy sets, and applied it to group theory. The aim of this manuscript is to study N -structures in BCK/BCI-algebras induced from hyperfuzzy structures.

The present paper aims to introduce the concepts of adding a strong arc, cobondage set, cobondage number, t-cobondage set, and t-cobondage number in the vague graphs, as well as expressing some of the new segmentation of the additions of arc and reduce the effect of adding a strong arc on domination parameters in vague graphs. Finally, some of their applications are pinpointed.

Iranian Journal of Fuzzy Systems (IJFS) is an international journal, based on the WoS core collection, this paper uses bibliometric methods and tools (VOSviewer and Bibliometrix) to analyze the publications of IJFS from 2007 to 2020. A total of 716 publications are analyzed. Firstly, according to the basic information of the publications, including the type of publications, the number of publications, the number of citations, the average number of citations and the h-index, we conduct a general statistical analysis to explore the basic characteristics and internal structure of the publications. Afterwards, by studying the citation structure of publications, this paper analyzes which groups and fields the journal is more concerned about. For the journal itself, we combine the number of citations and the number of publications to identify the most popular publications, the most productive and influential authors/institutes/countries/regions. In the collaboration network analysis, we map the collaboration network of countries/regions, institutes and authors to explore the different levels of collaboration. The co-citation network of the journal is studied to explore the relationship between IJFS and other international academic journals. In the analysis of keywords, we discuss the development trend and hot topics of keywords over time through co-occurrence analysis, word growth graph and thematic evolution analysis. Finally, based on the above analysis, we discuss the problems and challenges that the journal may face, and some main conclusions are drawn. This study has certain reference value for the further development of the related researchers  scientific research and the journal.

Based on subalgebras and filters in hoops, the notions of S-quasi-valuation maps and F-quasi-valuation maps are introduced, and related properties are investigated. Relations between S-quasi-valuation maps and F-quasi-valuation maps are introduced. Using F-quasi-valuation map, a (pseudo) metric space is indued, and we show that the operations “⊙”, “→” and “∧” in a hoop are uniformly continuous.

In this paper, the notions of Bosbach states and state-morphisms on implication basic algebra are introduced, along with their properties and related results. It is proved that Bosbach states coincide with Riecan states on bounded implication basic algebras. Accordingly, the relations between Bosbach states and state-morphisms are discussed. It is proved that  sm  is a state-morphism on IB if and only if  sm  is a Bosbach state and  sm(x V y)=sm(x)V sm(y) . In addition, the concept of internal states on implication basic algebras is defined, and accordingly, the notions of IS-prefilters, IS-filters, and IS-congruence relations on implication basic algebras are introduced. Then, it is proved that one-to-one correspondence is available between the set of all IS-filters and IS-congruence relations on implication basic algebras.Finally, the new notion of generalized state maps from an implication basic algebra  IB1  to an arbitrary implication basic algebra  IB2  is defined and generalized state-morphisms and generalized internal states as two types of individual generalized state maps are introduced. This confirmed that the generalized internal states are a generalization of internal states, and the generalized state-morphisms are a generalization of state-morphisms on implication basic algebras. Finally, it is shown that a generalized internal state  gs  is an internal state on implication basic algebra IB if  gs2=g.

Hyper logical algebras were first studied in 2000 by Borzooei et al. They applied the concept of hyperstructures to one of the logical algebraic structures known as the BCK-algebra, and introduced two generalizations of them called the hyper BCK-algebra and hyper K-algebra. Then many researchers in this field continued their research and used hyperstructures on other logical algebras and introduced the concepts of hyper residuated lattices, hyper BL-algebras, hyper MV-algebras, hyper EQ-algebras, hyper BE-algebras, hyper equality algebras, hyper hoops and etc. Moreover, they defined some new notions such as different kinds of hyper ideals, hyper filters and hyper congruence relations on these structures and studied some properties, the relation among them and the quotient structure. Now, in this paper, we review the definitions of all those hyper logical algebras and investigate relations among them.

In the present paper, by considering the notion of ideals in MV -algebras, we study some kinds of ideals in MV -algebras and obtain some results on them. For example, we present definition of ultra ideal in MV -algebras, and we get some results on it. In fact, by definition of ultra ideals, we present new conditions to have prime ideals, positive implicative ideals and maximal ideals in MV -algebras. Also, we state some properties on contracted or extended ideals as useful examples of ideals in MV -algebras. Finally, we try to prove the Chines reminder theorem in MV -algebras.

In this paper, we introduce the concepts of n-fold obstinate pseudo-hoop and n-fold obstinate filter in pseudo-hoops. Then we investigated these notions and proved some properties of them. Also, we discussed the relationship between n-fold obstinate pseudo-hoop and n-fold obstinate filter and other types of n-fold pseudo-hoops and n-fold filters such as n-fold(positive) implicative filter and n-fold fantastic filter in pseudo-hoops. For example, we proved that any $n$-fold obstinate filter is a maximal filter. Finally, we obtain a characterization of n-fold obstinate filters in terms of congruences and we show that any n-fold obstinate pseudo-hoop is an n-fold fantastic, n-fold positive implicative, n-fold implicative pseudo-hoop and simple pseudo-‎hoop.‎