In addition, as it was mentioned if decisions are assumed fuzzy in tactical level, more flexibility and proper decisions can be made for the strategic decisions.
where x βi t, and x βi t + 1 represent each pixel in the t and t + 1 frames that fulfills the assumed fuzzy rule conditions, respectively, with α = 0.875.
The proposed method in this research is more complete than (Kabak and Ülengin 2011)'s approach (hereafter KÜ approach), because in this study all parameters and decision variables are assumed fuzzy.
Conventional works on fuzzy logic assume that fuzzy sets satisfy the conditions of convexity and normality (the height is one) which are called fuzzy numbers.
In that study, both of the decision variables and parameters are assumed as fuzzy values.
In LP-1 it is assumed that fuzzy variables are as crisp variables and the problem is optimized twice.
The decision variables are assumed as fuzzy triangular numbers for example (tilde{x}_{smt}) is considered as (x1 smt, x2 smt, x3 smt ).
In tactical level, the total cost of controlling raw materials, cost of controlling finished products at the plant echelon, and cost of controlling finished products at the distribution center echelon are assumed as fuzzy goals.
As some researches mentioned, since we consider strategic level decisions, hence it is more satisfactory that the decision variables are not handled as crisp and certain and they are assumed as fuzzy triangular numbers.
In that research two objectives and the capacities, demands and reverse rates are uncertain and are assumed as fuzzy number to incorporate the logistics manager's imprecise aspiration levels.
s: set of suppliers s = 1, ldots), S; m: set of manufacturers/plants m = 1, ldots), M; d: set of distribution centers d = 1, ldots), D; c: set of customer zones c = 1, ldots), C; k: set of collection centers k = 1, ldots), K; t: transportation types t = 1, ldots), T. The parameters are assumed as fuzzy triangular numbers for example (tilde{f}_{m}) is considered as (f1 m, f2 m, f3 m ).
