scholarly journals Fuzzy Goal Programming with an Imprecise Intuitionistic Fuzzy Preference Relations

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1548
Author(s):  
Abdul Razzaq Abdul Ghaffar ◽  
Md. Gulzarul Hasan ◽  
Zubair Ashraf ◽  
Mohammad Faisal Khan
Keyword(s):  
Goal Programming ◽  
Distance Measure ◽  
Optimization Problems ◽  
Fuzzy Goal Programming ◽  
Preference Relations ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Preference Relations ◽  
Fuzzy Goals ◽  
Fuzzy Goal ◽  
Fuzzy Preference

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.

Role of Distance Metric in Goal Geometric Programming Problem (G^2 P^2) Under Imprecise Environment

2019 ◽  
Vol 8 (1) ◽  
pp. 65-82
Author(s):  
Payel Ghosh ◽  
Tapan Kumar Roy
Keyword(s):  
Goal Programming ◽  
Fuzzy Number ◽  
Geometric Programming ◽  
Distance Measure ◽  
Fuzzy Optimization ◽  
Fuzzy Goal Programming ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Goal

The objective of this article is to tie a knot between distance measure and fuzzy and intuitionistic fuzzy optimization through goal programming. Firstly, a distance measure for an intuitionistic fuzzy number is developed, and then it is implemented into an intuitionistic fuzzy nonlinear goal programming. Then using some conditions, the distance measure of intuitionistic fuzzy number is converted into distance measure of fuzzy number and a comparative study using a numerical example is shown for highest applicability of distance measure based intuitionistic fuzzy goal programming than distance measure based fuzzy goal programming.

A novel intuitionistic fuzzy preference relations for multiobjective goal programming problems

2021 ◽  
pp. 1-17
Author(s):  
Abdullah Ali H. Ahmadini ◽  
Firoz Ahmad
Keyword(s):  
Goal Programming ◽  
Convex Combination ◽  
Research Direction ◽  
Future Research ◽  
Preference Relations ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Preferences ◽  
Fuzzy Preference Relations ◽  
Fuzzy Goals ◽  
The Comparative Study

This paper investigates novel intuitionistic fuzzy preferences relations to determine the imprecise linguistic terms with fuzzy goals. The proposed intuitionistic fuzzy goal programming (IFGP) considers the degree of vagueness and hesitations simultaneously. Different sorts of membership functions such as linear, exponential, parabolic, and hyperbolic have been introduced to depict the linguistic importance term. The overall satisfaction level is achieved by maximizing the convex combination of each fuzzy goals and the preference relations simultaneously. To verify and validate the proposed IFGP model, a numerical example is presented with the comparative study. Further, it is also applied to a banking financial statement management system problem. The proposed IFGP approach outperforms over others. At last, the conclusion and future research direction are suggested based on the performed study.

Decision making based on intuitionistic fuzzy preference relations with additive approximate consistency

2020 ◽  
Vol 39 (3) ◽  
pp. 4041-4058
Author(s):  
Fang Liu ◽  
Xu Tan ◽  
Hui Yang ◽  
Hui Zhao
Keyword(s):  
Decision Making ◽  
Decision Makers ◽  
Real Interval ◽  
Preference Relations ◽  
Intuitionistic Fuzzy ◽  
Proposed Model ◽  
Fuzzy Preference Relations ◽  
Novel Concept ◽  
Fuzzy Weights ◽  
Fuzzy Preference

Intuitionistic fuzzy preference relations (IFPRs) have the natural ability to reflect the positive, the negative and the non-determinative judgements of decision makers. A decision making model is proposed by considering the inherent property of IFPRs in this study, where the main novelty comes with the introduction of the concept of additive approximate consistency. First, the consistency definitions of IFPRs are reviewed and the underlying ideas are analyzed. Second, by considering the allocation of the non-determinacy degree of decision makers’ opinions, the novel concept of approximate consistency for IFPRs is proposed. Then the additive approximate consistency of IFPRs is defined and the properties are studied. Third, the priorities of alternatives are derived from IFPRs with additive approximate consistency by considering the effects of the permutations of alternatives and the allocation of the non-determinacy degree. The rankings of alternatives based on real, interval and intuitionistic fuzzy weights are investigated, respectively. Finally, some comparisons are reported by carrying out numerical examples to show the novelty and advantage of the proposed model. It is found that the proposed model can offer various decision schemes due to the allocation of the non-determinacy degree of IFPRs.

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