-This study presents an approximate approach for ranking fuzzy numbers based on the left and right dominance. The proposed approach only requires a few left and right spreads at some a-levels of fuzzy numbers to determine the respective dominance of one fuzzy number over the other. The total dominance is then determined by combining the left and right dominance based on a decision maker's optim...

In this article we develop a new approach to duality theory for convex vector optimization problems. We modify a given (set-valued) vector optimization problem such that the image space becomes a complete lattice (a sublattice of the power set of the original image space), where the corresponding infimum and supremum are sets that are related to the set of (minimal and maximal) weakly efficient...

Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...

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...

We will address these questions in order, and provide good partial answers, especially for nite lattices which are bounded homomorphic images of a free lattice. Recall that a nite lattice is bounded if and only if it can be obtained from the one element lattice by a sequence of applications of Alan Day's doubling construction for intervals. In particular, nite distributive lattices are bounded....

The path of the rook is a curve γ (possibly, self-intersecting) inside an 8 × 8square. The length of γ should be at least 64 since all squares are visited. Next, I assumed that the rook turned each time by 90 degrees (and never 180). Then the total turn of γ is nπ/2, where n is the number of moves. Thus I traded the original problem for the following one: What is the smallest total turn of a cu...

We study a natural generalization of stable matching to the maximumweight stable matching problem and we obtain a combinatorial polynomial time algorithm for it by reducing it to the problem of finding a maximum weight ideal cut in a DAG. We give the first polynomial time algorithm for the latter problem; this algorithm is also combinatorial. The combinatorial nature of our algorithms not only ...

We present a survey of some results published recently by the authors regarding fuzzy aspects finitely supported structures. Considering notion finite support, we introduce new degree membership association between crisp set and function modelling for each element in set. define study notions invariant set, complete lattices, monoids strong inductive sets. The (fuzzy) subgroups an group, as wel...

Fuzzy Newton-Cotes method for integration of fuzzy functions that was proposed by Ahmady in [1]. In this paper we construct error estimate of fuzzy Newton-Cotes method such as fuzzy Trapezoidal rule and fuzzy Simpson rule by using Taylor's series. The corresponding error terms are proven by two theorems. We prove that the fuzzy Trapezoidal rule is accurate for fuzzy polynomial of degree one and...