The aim of this paper is to point out and correct some errors of two theorems for IFSs in Atanassov (Two theorems for intuitionistic fuzzy sets, Fuzzy Sets and Systems, 2000) and bring forward a new theorem for IFSs. In the end, some elementary, but non-standard equalities between IFSs were formulated.

We provide an extension of the notion of chain-valued frame introduced by Pultr and Rodabaugh in [Category theoretic aspects of chain-valued frames: parts I and II, Fuzzy Sets and Systems 159 (2008) 501–528 and 529–558] by relaxing the assumption that L be a complete chain. As a result of this investigation we formulate the category L-Frm of L-frames under the weaker assumption that L is a comp...

<p>We elaborate in this paper a new structure Pythagorean fuzzy<br />$N$-soft groups which is the generalization of intuitionistic />soft group initiated by Karaaslan 2013. In />N-soft sets concepts fuzzy sets, soft N-soft soft<br />sets, are<br />generalized. We also talk about some elementary basic and<br />operations on with assistance of<br />illusi...

‎in this paper, a new class of fuzzy sets called fuzzy strongly ${{g}^{*}}$-closed sets is introduced and its properties are investigated. moreover, we study some more properties of this type of closed spaces.

T is my great pleasure to welcome you to the inaugural I issue of the IEEE TRANSACTIONS ON FUZZY SYSTEMS. Many of you are probably quite familiar with the basic ideas underlying fuzzy sets and systems that utilize fuzzy models. However, there will also be readers who are looking at the contents of this issue, wondering what it’s all about. For this latter group, the papers in this first issue m...

in this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.