Abstract In this paper, our aim is to consider the new class of log-convex fuzzy-interval-valued function known as log- s -convex functions (log- fuzzy-IVFs). By concept, we have introduced Hermite–Hadamard inequalities (HH-inequalities) by means fuzzy order relation. This relation defined level-wise through Kulisch–Miranker on interval space. Moreover, some Hermite–Hadamard–Fejér (HH–Fejér-ine...

It is shown that every fuzzy n-normed space naturally induces a locally convex topology, and that every finite dimensional fuzzy n-normed space is complete.

Two classes of fuzzy mappings, called pseudolinear and g-pseudolinear fuzzy mappings are introduced by relaxing the definitions of pseudo-convex and pseudo-invex fuzzy mappings. First, some characterizations of pseudolinear and g-pseudolinear fuzzy mappings are obtained. Then, characterizations of the solution sets of pseudolinear and g-pseudolinear fuzzy programs are derived.

In this paper we present a general framework to face the problem of evaluate fuzzy quantities. A fuzzy quantity is a fuzzy set that may be non normal and/or non convex. This new formulation contains as particular cases the ones proposed by Fortemps and Roubens [7], Yager and Filev [12, 13] and follows a completely different approach. It starts with idea of “interval approximation of a fuzzy num...

This paper comments on the recently published work dealing with support vector machine for classification based on fuzzy data [Ji, A.-B., Pang, J.-H., & Qiu, H.-J. (2010). Support vector machine for classification based on fuzzy training data. Expert Systems with Applications 37(4), 3495–3498]. The authors have claimed that their proposed program is a classical convex quadratic program. But, we...

Let X be a locally convex space, m : Σ → X be a vector measure defined on a σ-algebra Σ, and L1(m) be the associated (locally convex) space of m-integrable functions. Let Σ(m) denote {χ E ;E ∈ Σ}, equipped with the relative topology from L1(m). For a subalgebra A ⊆ Σ, let Aσ denote the generated σ-algebra and As denote the sequential closure of χ(A) = {χ E ;E ∈ A} in L1(m). Sets of the form As ...