Trillas et al. (1999, Soft computing, 3 (4), 197-199) and Trillas and Cubillo (1999, On non-contradictory input/output couples in Zadeh's CRI proceeding, 28-32) introduced the study of contradiction in the framework of fuzzy logic because of the significance of avoiding contradictory outputs in inference processes. Later, the study of contradiction in the framework of Atanassov' s intuitionisti...

Department of Industrial and Business Management, College of Management, Chang Gung University, 259, Wen-Hwa 1st Road, Kwei-Shan, Taoyuan 333, Taiwan. Graduate Institute of Business Administration, College of Management, Chang Gung University, 259, Wen-Hwa 1st Road, Kwei-Shan, Taoyuan 333, Taiwan. Department of Information Management, College of Management, Chang Gung University, 259, Wen-Hwa 1...

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,...

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).

The formulation of strong and weak laws of large numbers for fuzzy random variables based on variance is given. The concept of the variance of fuzzy random variables, introduced by K1 orner (Fuzzy Sets and Systems 92 (1997) 83) and by Feng (Fuzzy Sets and Systems 120 (2001) 487) demonstrates its e2ciency. c © 2002 Elsevier Science B.V. All rights reserved.

The theory of fuzzy sets [1] proposed by Zadeh has achieved a great success in various fields. Out of several higher order fuzzy sets, the concept of an intuitionistic fuzzy set (IFS) introduced by Atanassov has been found to be highly useful to deal with vagueness/imprecision. IFS theory has been extensively applied to areas like Artificial Intelligence, networking, Soft decision making, Progr...

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...