We present some properties regarding diffusion and semi-convexity for fuzzy set multifunctions defined on a ring of subsets of an abstract nonvoid space and taking values in the family of all nonvoid closed subsets of a real normed space. Key–Words: diffused, semi-convex, fuzzy set multifunction, non-atomicity, Darboux property, regular, multimeasure, null-additive.

in most of the multi–criteria decision–analysis (mcda) problems in which the choquet integral is used as aggregation function, the coefficients of choquet integral (capacity) are not known in advance. actually, they could be calculated by capacity definition methods. in these methods, the preference information of decision maker (dm) is used to constitute a possible solution space. the methods ...

This paper considers testing additive error structure in nonparametric structural models, against the alternative hypothesis that the random error term enters the nonparametric model non-additively. We propose a test statistic under a set of identification conditions considered by Hoderlein, Su and White (2012), which require the existence of a control variable such that the regressor is indepe...

We provide a characterization of the consequences of the assumption that a decision maker with a given utility function is Choquet rational : She maximizes expected utility, but possibly with respect to non-additive beliefs, so that her preferences are represented by Choquet expected utility (CEU). The characterization shows that this notion of rationality allows in general to rationalize more ...

We propose SonOpt, the first (open source) data sonification application for monitoring progress of bi-objective population-based optimization algorithms during search, to facilitate algorithm understanding. SonOpt provides insights into convergence/stagnation evolution approximation set shape, location recurring points in set, and population diversity. The benefits have been shown various non-...

We apply the Piecewise Constant Level Set Method (PCLSM) to interface problems, especially for elliptic inverse and multiphase motion problems. PCLSM allows using one level set function to represent multiple phases, and the interfaces are represented implicitly by the discontinuity of a piecewise constant level set function. The inverse problem is solved using a variational penalization method ...

in this manuscript, we study the inverse problem for non self-adjoint sturm--liouville operator $-d^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. by defining  a new hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

In this research, the multi-objective project management decision problem with fuzzy goals and fuzzy constraints are considered. We constitute α-cut approach and two various fuzzy goal programming solution methods for solving the Multi-Objective Project Management (MOPM) decision problem under fuzzy environments. The Interactive fuzzy multi-objective linear programming (i-FMOLP) and Weighted Ad...

1. We say that g(n) is additive if g(mn)=g(m)+g(n) holds for every coprime pairs m, n of positive integers . If, moreover, g(p') =g(p)' for every prime power pa , then g(n) is called strongly additive . By p, pi , p2 , . . ., q, qr , q2 , . . . we denote prime numbers, c, Cl, c2i . . . are suitable positive constants . F(n) and x(n) denote the largest and the smallest prime factor of n . The sy...

In the present paper terminology “total” is used for a generalization of the Burkill integral and multiplicative integral, respectively. The functions, the totals of which are considered, take their values from a Banach algebra B with a unity. This means a Banach space B in which for every pair f ∈ B, g ∈ B a product fg ∈ B is defined such that ‖fg‖ ≤ ‖f‖ ‖g‖ and if h ∈ B, then f(g + h) = fg + ...