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This paper considers the notion of nonbinary (linear) codes and the notion of hypergraphs and makes a relation between two mathematical tools for real-world applications. We consider a nonbinary (linear) code as an underline set and construct a type of hypergraphs called N.C-hypergraph (N.L.C-hypergraph) and establish any given hypergraph is isomorphic to an N.C-hypergraph (N.L.C-hypergraph). This study introduces an equivalence relation on any given code as a positive equivalence relation based on the weight of codewords, generates quotient N.C-hypergraph, and computes the cardinal of its hyperedges and Hamming distance of any given two code words of quotient N.C-hypergraphs. Also, we introduce a binary relation on quotient N.C-hypergraphs, convert them to simple graphs as code-based graphs, and prove that all graphs are positive code-based graphs. We characterize the minimum distance and maximum distance of codewords in hyperedges of code-based (hyper)graphs concerning linear codes. Finally, we design real problems (such as wireless sensor (hyper)networks and American standard code for information interchange) as complex hypernetworks (such that are based on the code words) as a quotient N.C-hypergraph (N.L.C-hypergraph) and convert them to the code-based graphs (such as wireless sensor networks). [ABSTRACT FROM AUTHOR]

A hypertree is a special type of connected hypergraph that removes any, its hyperedge then results in a disconnected hypergraph. Relation between hypertrees (hypergraphs) and trees (graphs) can be helpful to solve real problems in hypernetworks and networks and it is the main tool in this regard. The purpose of this paper is to introduce a positive relation (as α-relation) on hypertrees that makes a connection between hypertrees and trees. This relation is dependent on some parameters such as path, length of a path, and the intersection of hyperedges. For any q ∈ N, we introduce the concepts of a derivable tree, (α, q)-hypergraph, and fundamental (α, q)-hypertree for the first time in this study and analyze the structures of derivable trees from hypertrees via given positive relation. In the final, we apply the notions of derivable trees, (α, q)-trees in real optimization problems by modeling hypernetworks and networks based on hypertrees and trees, respectively. [ABSTRACT FROM AUTHOR]

As concerning the views of T norms and T conorms, the intent of article is to define and probe the fuzzy semigroups, fuzzy ideals, fuzzy bi-ideals, bifuzzy subsemigroups, bifuzzy ideals, bifuzzy bi-ideals, fuzzy (1; 2)-ideals and bifuzzy (1; 2)-ideals in any given semigroup. Also, we indicate and study their basic properties of them in completely regular semigroups. Finally, we extend these concepts and so characterise (pre)image of them in semigroup homomorphisms. [ABSTRACT FROM AUTHOR]

The purpose of this paper is the study of non-weak commutative hypergroups associated with hypergraphs. In this regards, we construct a hyperoperation on the set of vertices of hypergraph and obtain some results and characterizations of them. Moreover, according to this hyperoperation, we investigate conditions under which the hypergroupoid is a join space hypergroup. Finally, we present an application to marketing social network. [ABSTRACT FROM AUTHOR]

This paper explores the defects in fuzzy (hyper) graphs (as complex (hyper) networks) and extends the fuzzy (hyper) graphs to fuzzy (quasi) superhypergraphs as a new concept. We have modeled the fuzzy superhypergraphs as complex superhypernetworks in order to make a relation between labeled objects in the form of details and generalities. Indeed, the structure of fuzzy (quasi) superhypergraphs collects groups of labeled objects and analyzes them in the form of the part to part of objects, the part of objects to the whole group of objects, and the whole to the whole group of objects at the same time. We have investigated the properties of fuzzy (quasi) superhypergraphs based on any positive real number as valued fuzzy (quasi) superhypergraphs, considering the complement of valued fuzzy (quasi) superhypergraphs, the notation of isomorphism of valued fuzzy (quasi) superhypergraphs based on the permutations, and we have presented the isomorphic conditions of (self complemented) valued fuzzy (quasi) superhypergraphs. The concept of impact membership value of fuzzy (quasi) superhypergraphs is introduced in this study and it is applied in designing the real problem in the real world. Finally, the problem of business superhypernetworks is presented as an application of fuzzy valued quasi superhypergraphs in the real world. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce and study the concept of a hyperideal-based zero-divisor graph associated with a general hyperring. This is a generalized version of the zero-divisor graph associated with a commutative ring. For any general hyperring R having a hyperideal I, the I-based zero-divisor graph Γ(I)(R) associated with R is the simple graph whose vertices are the elements of R∖I having their hyperproduct in I, and two distinct vertices are joined by an edge when their hyperproduct has a non-empty intersection with I. In the first part of the paper, we concentrate on some general properties of this graph related to absorbing elements, while the second part is dedicated to the study of the I-based zero-divisor graph associated to the general hyperring Zn of the integers modulo n, when n=2pmq, with p and q two different odd primes, and fixing the hyperideal I. [ABSTRACT FROM AUTHOR]