This article concerns a connection of fuzzy logic and lattice theory. Namely, the fuzzy sets form a Heyting lattice with union and intersection of fuzzy sets as meet and join operations. The lattice of fuzzy sets is defined as the product of interval posets. As the final result, we have characterized the composition of fuzzy relations in terms of lattice theory and proved its associativity.

In this paper we define a correspondence between the set of all fuzzy hideals of a Γ-hemiring S and the set of all fuzzy h-ideals of the operator hemirings of that Γ-hemiring. We deduce that the lattice of all fuzzy hideals of a Γ-hemiring is isomorphic to the lattice of all fuzzy h-ideals of the operator hemirings of that Γ-hemiring. Finally, the cartesian product of corresponding fuzzy h-idea...

The aim of this paper is the study of fuzzy Γ-hyperrings. In this regard the notion of ν-fuzzy hyperideals of Γ-hyperrings are introduced and basic properties of them are investigated. In particular, the representation theorem for ν-fuzzy hyperideals are given and it is shown that the image of a ν-fuzzy hyperideal of a Γ-hyperring under a certain conditions is two-valued. Finally, the product o...

Fuzzy distance is applied on data analysis, classification, and product positioning analysis widely. In this paper, We introduce a fuzzy distance by using graded mean integration representation of generalized fuzzy number and the span of fuzzy number, We also discuss the distance of the linguistic data of “greater or less than x” and “about x”. It is reasonable to say “the fuzzy distance of abo...

In response to fast-growing and rapidly-changing markets, launching new products faster than competitors cannot only assist firms in acquiring larger market share but also reducing development lead time, significantly. However, owing to its intrinsically uncertain properties of managing NPD (new product development), manufacturing companies often struggle with the dilemma of increasing product ...

Fuzzy regression models have commonly been used to correlate engineering characteristics with consumer preferences regarding a new product. Based on the models, product developers can determine optimal engineering characteristics of the new product in order to satisfy consumer preferences. However, they have a common limitation in that they cannot guarantee to include significant regressors wit...

In this paper, we study the concept of generalized differentiability for fuzzy-valued functions on time scales. Usingthe derivative of the product of two functions, we provide solutions to first order linear fuzzy dynamic equations. Wepresent some examples to illustrate our results.

Disassembly is rapidly growing in importance as manufacturers face increasing pressure to deal with obsolete products in an environmentally responsible and economically sound manner. This paper builds upon our previous work to address uncertainty management in disassembly. By taking advantage of fuzzy logic and the formalism of Petri nets, this paper proposes a Fuzzy Disassembly Petri Net (F-DP...