The Human Variation Model views disability as simply "an extension of the natural physical, social, and cultural variability of mankind." Given this human variation, it can be difficult to distinguish between a prosthetic device such as a pair of glasses (which extends limited visual abilities into the "normal" range) and a visual enhancement device such as a pair of binoculars (which extends v...

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 work, several extended approximately invex vector-valued functions of higher order involving a generalized Jacobian are introduced, and some examples are presented to illustrate their existences. The notions of higher-order (weak) quasi-efficiency with respect to a function are proposed for a multi-objective programming. Under the introduced generalization of higher-order approximate in...

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)”.

Abstract In this study, we use the fuzzy order relation to show some novel variants of Hermite–Hadamard inequalities for pre-invex fuzzy-interval-valued mappings ( F-I∙V-Ms ), which term fuzzy-interval and Hermite–Hadamard–Fejér inequalities. This is defined as level space by Kulisch–Miranker relation. There are also new exceptional instances mentioned. The theory proposed in research shown wit...

in this paper we obtain a necessary and a sufficient condition for the set of ω_0-nearest points ( ω_0-farthest points) to be non-empty or a singleton set in normed linear spaces. we shall find a necessary and a sufficient condition for an uniquely remotal set to be a singleton set.

In this paper we present optimization problems with biconvex objective function and linear constraints such that the set of global minima of the optimization problems is the same as the set of Nash eqilibria of a n-player general-sum normal form game. We further show that the objective function is an invex function and consider a projected gradient descent algorithm. We prove that the projected...

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.