In the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to avoid this shortcoming, a new multiplicative operation of product type is introduced, the so-called cross-product of fuzzy numbers. Th...

L-bonds represent relationships between formal contexts. We study properties of these intercontextual structures w.r.t. isotone conceptforming operators in fuzzy setting. We also focus on the direct product of two formal fuzzy contexts and show conditions under which a bond can be obtained as an intent of the product. In addition, we show that the previously studied properties of their antitone...

In this paper the notion of idempotent fuzzy subquasigroups with respect to a s-norm is introduced and some related properties are investigated. Then properties of homomorphic image and inverse image of fuzzy subquasigroups respect to a s-norm are discussed. Next some properties of direct product of fuzzy subquasigroups with respect to a s-norm are presented. Finally abnormalization of fuzzy su...

at early stages of new product development, the effort tooptimize is low and effects on the whole innovation process are high.therefore, a deeper understanding of fuzzy front end and its successcan help firms to be more successful in developing new products. wepresented and tested a conceptual model of relationships among keyvariable sre lated to the fuzzy front end,execution phase of new produ...

in this paper, rstly, it is proved that, for a fuzzy vector space, the set of its fuzzy bases de ned by shi and huang, is equivalent to the family of its bases de ned by p. lubczonok. secondly, for two fuzzy vector spaces, it is proved that they are isomorphic if and only if they have the same fuzzy dimension, and if their fuzzy dimensions are equal, then their dimensions are the same, however,...

let $r$ be a commutative ring. we write $mbox{hom}(mu_a, nu_b)$ for the set of all fuzzy $r$-morphisms from $mu_a$ to $nu_b$, where $mu_a$ and $nu_b$ are two fuzzy $r$-modules. we make$mbox{hom}(mu_a, nu_b)$ into fuzzy $r$-module by redefining a function $alpha:mbox{hom}(mu_a, nu_b)longrightarrow [0,1]$. we study the properties of the functor $mbox{hom}(mu_a,-):frmbox{-mod}rightarrow frmbox{-mo...

In the present paper, we investigate a connection between two fuzzy inner product one of which arises from Felbin's fuzzy norm and the other is based on Bag and Samanta's fuzzy norm. Also we show that, considering a fuzzy inner product space, how one can construct another kind of fuzzy inner product on this space.

the aim of this paper is the study of the sequence of join spacesand fuzzy subsets associated with a hypergroupoid. in thispaper we give some properties of the membership function$widetildemu_{otimes}$ corresponding to the direct pro-duct oftwo hypergroupoids and we determine the fuzzy grade of thehypergroupoid $langle htimes h, otimesrangle$ in a particularcase.

we introduce and  study  fuzzy (co-)inner product and fuzzy(co-)norm of hyperspaces. in this regard by considering  the notionof hyperspaces, as a generalization of vector spaces, first we willintroduce the notion of fuzzy (co-)inner product in hyperspaces and will apply it to formulate the notions offuzzy (co-)norm and fuzzy (co-)orthogonality  in hyperspaces. inparticular, we will prove that ...

We introduce and  study  fuzzy (co-)inner product and fuzzy(co-)norm of hyperspaces. In this regard by considering  the notionof hyperspaces, as a generalization of vector spaces, first we willintroduce the notion of fuzzy (co-)inner product in hyperspaces and will apply it to formulate the notions offuzzy (co-)norm and fuzzy (co-)orthogonality  in hyperspaces. Inparticular, we will prove that ...