Abstract
This paper presents the concept of usage of hesitation index in optimization problem under uncertainty. Our technique is an extension of idea of intuitionistic fuzzy optimization technique, proposed by Plamen P. Angelov in 1997, which is widely considered as a successful intuitionistic fuzzy optimization tool by researchers all over the world. It is well known that the advantages of the intuitionistic fuzzy optimization problems are twofold: firstly, they give the richest apparatus for formulation of optimization problems and on the other hand, the solution of intuitionistic fuzzy optimization problems can satisfy the objective(s) with bigger degree of satisfaction than the analogous fuzzy optimization problem and the crisp one. Angelov’s approach is an application of the intuitionistic fuzzy (IF) set concept to optimization problems. In his approach, the degree of acceptance is maximized while the degree of rejection is minimized. In our approach, not only the degree of acceptance is maximized and the degree of rejection is minimized but also the degree of hesitation is minimized. For the sake simplicity alone, the same problem, as studied by Angelov, is considered. Varied importance (and hence weights) to each of the degree of acceptance and the degree of rejection and the degree of hesitation have been given. Tables with these results are formulated and compared among.
Highlights
As it is already mentioned by Angelov in his historic paper in 1997 [1], deterministic optimization problems are well studied, but they are very limited and in many cases they do not represent exactly the real problem
It must be noted that Szmidt and Kacprzyk [7] have already mentioned, in 2000, that taking into account the third parameter when calculating the Euclidean distance for intuitionistic fuzzy sets does have an influence on the final result
In 2000, Szmidt and Kacprzyk [7] have already mentioned that taking into account the third parameter when calculating the Euclidean distance for intuitionistic fuzzy sets does have a clear influence on the final result
Summary
As it is already mentioned by Angelov in his historic paper in 1997 [1], deterministic optimization problems are well studied, but they are very limited and in many cases they do not represent exactly the real problem. It must be noted that Szmidt and Kacprzyk [7] have already mentioned, in 2000, that taking into account the third parameter (degree of hesitation) when calculating the Euclidean distance for intuitionistic fuzzy sets does have an influence on the final result. It should be so because a two dimensional geometric interpretation is an orthogonal projection of a real situation as shown suitably in their historic paper. We have used different importance level to each of these three parameters and compared the result in a table and studied it
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