Fuzzy Goal Programming with an Imprecise Intuitionistic Fuzzy Preference Relations

Abstract

Fuzzy goal programming (FGP) is applied to solve fuzzy multi-objective optimization problems. In FGP, the weights are associated with fuzzy goals for the preference among them. However, the hierarchy within the fuzzy goals depends on several uncertain criteria, decided by experts, so the preference relations are not always easy to associate with weight. Therefore, the preference relations are provided by the decision-makers in terms of linguistic relationships, i.e., goal A is slightly or moderately or significantly more important than goal B. Due to the vagueness and ambiguity associated with the linguistic preference relations, intuitionistic fuzzy sets (IFSs) are most efficient and suitable to handle them. Thus, in this paper, a new fuzzy goal programming with intuitionistic fuzzy preference relations (FGP-IFPR) approach is proposed. In the proposed FGP-IFPR model, an achievement function has been developed via the convex combination of the sum of individual grades of fuzzy objectives and amount of the score function of IFPRs among the fuzzy goals. As an extension, we presented the linear and non-linear, namely, exponential and hyperbolic functions for the intuitionistic fuzzy preference relations (IFPRs). A study has been made to compare and analyze the three FGP-IFPR models with intuitionistic fuzzy linear, exponential, and hyperbolic membership and non-membership functions. For solving all three FGP-IFPR models, the solution approach is developed that established the corresponding crisp formulations, and the optimal solution are obtained. The validations of the proposed FGP-IFPR models have been presented with an experimental investigation of a numerical problem and a banking financial statement problem. A newly developed distance measure is applied to compare the efficiency of proposed models. The minimum value of the distance function represents a better and efficient model. Finally, it has been found that for the first illustrative problem considered, the exponential FGP-IFPR model performs best, whereas for the second problem, the hyperbolic FGP-IFPR model performs best and the linear FGP-IFPR model shows worst in both cases.

A New Application for the Goal Programming—The Target Decision Rule for Uncertain Problems

“…Nevertheless, its name first appeared in Charnes and Cooper (1961). Although GP was developed many years ago, it is still applied to numerous theoretical and practical problems (Spivey and Hirokuni 1970;Spronk 1981;Vrat and Kriengkrairut 1986;Giokas 1997;Lin et al 2009;Gaspars-Wieloch 2017a, 2018aGupta et al 2018;Gür and Eren 2018;Ismail et al 2019;Mensah and Rocca 2019;Aliasghari et al 2020;Khan et al 2020).…”

“…The GP was initially formulated for M-DM under certainty (M-DMC), i.e., assuming that all the parameters of the decision problems are known. In subsequent years, this procedure has been extended to fuzzy multi-criteria problems (Ghaffar et al 2020;Khan et al 2020) or combined with other approaches for diverse purposes (Gaspars-Wieloch 2017a, 2018aGiokas 1997;Lin et al 2009).…”

Evaluation on the performance of highway companies using goal programming model

“…Since this involves several objectives and is a multi-objective situation, the goal programming (GP) model is used. The GP model is formed to minimize divergence from each goal [12][13][14][15][16][17]. The objectives are goals with respective aspirations.…”

Multi-objective vendor managed inventory system with interval type-2 fuzzy demand and order quantities

“…In the physical world, uncertainty in demand rate (D) and ordered quantities (Q) occurs primarily because of the items' specifications, trade surplus, development period and price levels. Further, some other factors may also affect the uncertainty and imprecision in D and Q (Abdul Ghaffar et al , 2020; Muhuri et al , 2017, 2020; Ashraf et al , 2014, 2017a). These are listed and explained as follows:Many parameters are used to estimate D and Q, such as inventory level, renewal rate, lead time, product, ordering, holding and back-ordered cost, etc.…”