This derivation of (2) is not valid, because this duality applies to inferences and theorems only, not to definitions. In fact, (1) should be treated as an axiom. Accordingly, the duality of Lemma 3.3.1 would not be valid until the dual (2) of (1) is proved independently, as we do below. Our new proof will make use of Proposition 3.3.3, the original proof of which is based on duality. So, we mu...

Answering a recent question posed by Gregori, Morillas and Sapena (“On a class of completable fuzzy metric spaces”, Fuzzy Sets and Systems, 161 (2010), 2193–2205) we present two examples of non strong fuzzy metrics (in the sense of George and Veeramani).

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...

In this state-of-the-art paper, important advances that have been made during the past five years for both general and interval type-2 fuzzy sets and systems are described. Interest in type-2 subjects is worldwide and touches on a broad range of applications and many interesting theoretical topics. The main focus of this paper is on the theoretical topics, with descriptions of what they are, wh...

In reply to Péter Majlender, the connection between the (maximum spread) equidifferent OWA operator weights and the analytical method for the minimum variance OWA operator problem [R. Fullér, P. Majlender, On obtaining minimal variability OWA operator weights, Fuzzy Sets and Systems 136 (2003) 203–215] is pointed out and the differences between them are clarified. 2006 Elsevier Inc. All rights ...

We reformulate Mesiar’s hypothesis [Possibility measures, integration and fuzzy possibility measures, Fuzzy Sets and Systems 92 (1997) 191196], which as such was shown to be untrue by Murofushi [Two-valued possibility measures induced by σ-finite σ-additive measures, Fuzzy Sets and Systems 126 (2002) 265268]. We prove that a two-valued σ-maxitive measure can be induced by a σ-additive measure u...

It is shown that, for any spatial frame L (i.e., L is a complete lattice generated by the set of all prime elements), both the specialization L-preorder of L-topological spaces introduced by Lai and Zhang [Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems 157 (2006) 1865–1885] and that of L-fuzzifying topological spaces introduced by Fang and Qiu [Fuzzy orders and fuzzifying topologies,...

In 2011, Mallozzi et al. [Fuzzy Sets and Systems 165(2011) 98105] introduced a core-like concept (called F-core) and a balanced-like condition for games in which the worth of any coalition is given by means of a fuzzy interval. They proved that a balanced-like condition is necessary but not sufficient enough to guarantee the F-core to be non-empty. In this paper, we study deeply on this problem...

In this paper, we shall give examples to answer that an open problem posed by De Baets et al. in “Triangular norms on product lattices (Fuzzy Sets and Systems 104(1999), 61-75)”.