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The goal of this paper is to introduce a novel soft hyperstructure called multi-fuzzy hyperstructure. We investigate the notion hypermodules and some their structural properties are discussed. discuss behavior image inverse set under function. According Zadeh’s extension principle, we prove that further hypermodule.

In earlier work, we conducted an exploratory investigation of concerns in two existing Java packages: jFTPd and gnu.regexp. Two separate developers marked concerns in the source for each package: these concerns were then compared and analyzed. In this paper, we describe the next step of our investigations: the use of the IBM Hyper/J tool to separate and configure the identified concerns. We des...

1. In Definition 2.4, ‘‘(iv) {0} = g(r i−1 1 , 0, r n−1 i+1 , x)’’. 2. In Definition 2.5, ‘‘g(R(n−1),N) ∈ P (N)’’. 3. Page 5, line 1, ‘‘0 ∈ g(0, 1 R ,m) ⊆ g(R, 1 (n−2) R ,m)’’. 4. Page 6, line 4, ‘‘f (x1 ) = h(x m 1 ) = m i=1 xi = m i=1 xi =’’. 5. Page 7, Lemma 3.7 is not true (is removed) and XP(M) is not a subhypermodule ofM . Hence, we define the set XP(M) accompany with XP(M) and consider...

To solve complicated problems in economics, engineering, and environment, we cannot successfully use classical methods because of various uncertainties typical for those problems. There are three theories: theory of probability, theory of fuzzy sets, and the interval mathematics which we can consider as mathematical tools for dealing with uncertainties. Uncertainties cannot be handled using tra...

Background: A prerequisite for successful embryo implantation is adequate preparation of receptive endometrium and the establishment and maintenance of a viable embryo. The success of implantation further relies upon a two-way dialogue between the embryo and uterus. However, molecular bases of these preimplantation and implantation processes in humans are not well known. Materials and Methods: ...

Let $G$ be a monoid with identity $e$. In this paper, first we introduce the notions of $G$-graded hyperrings, graded hyperideals and graded hyperfields in the sense of Krasner hyperring $R$. Also, we define the notion of a greded $R$-hypermodules and some examples are presented. Then we investigate graded maximal, graded prime and graded primary hyperideals of a graded hyperring $R$. Finally, ...