We consider a multiple-rule, generalized modus ponens inference scheme, with an interpretation based on compositional rule of inference (CRI) and a residuated implication. We show that such a system is equivalent, as far as CRI is concerned, to a system that satis5es the “basic requirement for fuzzy reasoning”, proposed by Turksen and Tian (Fuzzy Sets and Systems 58 (1993) 3–40). We establish a...

The description of the error dynamics (30) in our paper [1] contains an omission that leads to some bounds used in the conditions of Theorem 8 and Corollary 2 in the paper to be incorrectly defined. In what follows, the correct error dynamics and the corresponding conditions are given. Instead of (30) in [1], the error dynamics are actually given by ė = m ∑ i=1 wi(z)[(Ai − LiC +MiAδi)e +Mi(Āδix̂...

Recently, Carlsson and Fuller [C. Carlsson, R. Fuller, On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems 122 (2001) 315–326] have introduced possibilistic mean, variance and covariance of fuzzy numbers and Fuller and Majlender [R. Fuller, P. Majlender, On weighted possibilistic mean and variance of fuzzy numbers, Fuzzy Sets and Systems 136 (2003) 363–374] have in...

This paper is a brief summary of “M.Takahashi, T.Murofushi, S.Asahina, A new necessary and sufficient condition for the Egoroff theorem in non-additive measure theory, Fuzzy Sets and Systems, to appear.” This paper states that a newly defined condition, called condition (M), is a necessary and sufficient condition for the Egoroff theorem in non-additive measure theory. The existing necessary an...

Matchbox manifolds M are a special class of foliated spaces, which include as special examples the weak solenoids, suspensions of odometer and Toeplitz actions, and tiling spaces associated to aperiodic tilings with finite local complexity. They have many properties analogous to those of a compact manifold, but the additional data inherently encoded in the pseudogroup dynamics of its foliation ...

Semiuniform semigroups provide a natural setting for the convolution of generalized finite measures on semigroups. A semiuniform semigroup is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the semigroup is contained in an ambit. In the convolution algebras constructed over ambitable semigroups, topological centres have a tractable characterization. 1...

We investigate attractors for compact sets by considering a certain quotient space. The following theorem is included. Let /: G -> G, G a closed convex subset of a Banach space, / a mapping satisfying (i) there exists M c G which is an attractor for compact sets under/; (ii) the family {/"}Ü°_i is equicontinuous. Then/has a fixed point. 1. Since the appearance of the celebrated Schauder fixed p...

Theorem 1. Let {Xn}n=1 ⊂ L∞(T ) be a sequence of stochastic processes on T . The followings are equivalent. (1) Xn converge in distribution to a tight stochastic process X ∈ L∞(T ); (2) both of the followings: (a) Finite Dimensional Convergence (FIDI): for every k ∈ N and t1, · · · , tk ∈ T , (Xn(t1), · · · , Xn(tk)) converge in distribution as n→∞; (b) the sequence {Xn} is asymptotically stoch...