This paper targets to investigate the numerical solution of -th order fuzzy differential equations with fuzzy environment using Homotopy Perturbation Method (HPM). Triangular fuzzy convex normalized sets are used for the fuzzy parameter and variables. Obtained results are compared with the existing solution depicted in term of plots to show the efficiency of the applied method.

an orthogonal approach to the fuzzification of both multisets and hybridsets is presented. in particular, we introduce $l$-multi-fuzzy and$l$-fuzzy hybrid sets, which are general enough and in spirit with thebasic concepts of fuzzy set theory. in addition, we study the properties ofthese structures. also, the usefulness of these structures is examined inthe framework of mechanical multiset proc...

In this paper the egalitarian solution for convex cooperative fuzzy games is introduced. The classical Dutta-Ray algorithm for finding the constrained egalitarian solution for convex crisp games is adjusted to provide the egalitarian solution of a convex fuzzy game. This adjusted algorithm is also a finite algorithm, because the convexity of a fuzzy game implies in each step the existence ∗This...

One of the most important aspects of the (statistical) analysis of imprecise data is the usage of a suitable distance on the family of all compact, convex fuzzy sets, which is not too hard to calculate and which reflects the intuitive meaning of fuzzy sets. On the basis of expressing the metric of Bertoluzza et al. (1995) in terms of the mid points and spreads of the corresponding intervals we ...

Problem of defining convexity of a digital region is considered. Definition of DL− (digital line) convexity is proposed, and it is shown to be stronger than the other two definitions, T−(triangle) convexity and L−(line) convexity. In attempt to connect the convexity of digital sets, to the fact that digital set can be a fuzzy set, the notion of convexity of the membership function is introduced...

This paper presents a new approach to compare fuzzy numbers using α-distance. Initially, the metric distance on the interval numbers based on the convex hull of the endpoints is proposed and it is extended to fuzzy numbers. All the properties of the α-distance are proved in details. Finally, the ranking of fuzzy numbers by the α-distance is discussed. In addition, the proposed method is compare...

Optimization is a procedure of finding and comparing feasible solutions until no better solution can be found. It can be divided into several fields, one of which is the Convex Optimization. It is characterized by a convex objective function and convex constraint functions over a convex set which is the set of the decision variables. This can be viewed, on the one hand, as a particular case of ...

we have the crisp vector → PQ= (y(1)−x(1),y(2)−x(2), . . . ,y(n)−x(n)) in a pseudo-fuzzy vector space Fn p (1)= {(a(1),a(2), . . . ,a(n))1∀(a(1),a(2), . . . ,a(n))∈Rn}. There is a one-to-one onto mapping P = (x(1),x(2), . . . ,x(n)) ↔ P̃ = (x(1),x(2), . . . , x)1. Therefore, for the crisp vector → PQ, we can define the fuzzy vector → P̃ Q̃= (y(1)− x(1),y(2)−x(2), . . . ,y(n)−x(n))1 = Q̃ P̃ . Let the...

When we regard the plane as a set of points, we can deene various geometric properties of subsets of the plane|connectedness, convexity, area, diameter, etc. It is well known that the plane can also be regarded as a set of lines. This note considers methods of deening sets (or fuzzy sets) of lines in the plane, and of deening (analogs of) \geometric properties" for such sets.

we have the crisp vector → PQ= (y(1)−x(1),y(2)−x(2), . . . ,y(n)−x(n)) in a pseudo-fuzzy vector space Fn p (1)= {(a(1),a(2), . . . ,a(n))1∀(a(1),a(2), . . . ,a(n))∈Rn}. There is a one-to-one onto mapping P = (x(1),x(2), . . . ,x(n)) ↔ P̃ = (x(1),x(2), . . . , x)1. Therefore, for the crisp vector → PQ, we can define the fuzzy vector → P̃ Q̃= (y(1)− x(1),y(2)−x(2), . . . ,y(n)−x(n))1 = Q̃ P̃ . Let the...