A Hypervolume Based Approach to Rank Intuitionistic Fuzzy Sets and Its Extension to Multi-criteria Decision Making Under Uncertainty

Ranking intuitionistic fuzzy sets with distance based ranking methods requires to calculate the distance between intuitionistic fuzzy set and a reference point which is known to have either maximum (positive ideal solution) or minimum (negative ideal solution) value. These group of approaches assume that as the distance of an intuitionistic fuzzy set to the reference point is decreases, the similarity of intuitionistic fuzzy set with that point increases. This is a misconception because an intuitionistic fuzzy set which has the shortest distance to positive ideal solution does not have to be the furthest from negative ideal solution for all circumstances when the distance function is nonlinear. This paper gives a mathematical proof of why this assumption is not valid for any of the non-linear distance functions and suggests a hypervolume based ranking approach as an alternative to distance based ranking. In addition, the suggested ranking approach is extended as a new multicriteria decision making method, HyperVolume based ASsessment (HVAS). HVAS is applied for multicriteria assessment of Turkey's energy alternatives. Results are compared with three well known distance based multicriteria decision making methods (TOPSIS, VIKOR, and CODAS).Comment: 8 pages, 3 figure

An interval-valued intuitionistic fuzzy multiattribute group decision making framework with incomplete preference over alternatives

This article proposes a framework to handle multiattribute group decision making problems with incomplete pairwise comparison preference over decision alternatives where qualitative and quantitative attribute values are furnished as linguistic variables and crisp numbers, respectively. Attribute assessments are then converted to interval-valued intuitionistic fuzzy numbers (IVIFNs) to characterize fuzziness and uncertainty in the evaluation process. Group consistency and inconsistency indices are introduced for incomplete pairwise comparison preference relations on alternatives provided by the decision-makers (DMs). By minimizing the group inconsistency index under certain constraints, an auxiliary linear programming model is developed to obtain unified attribute weights and an interval-valued intuitionistic fuzzy positive ideal solution (IVIFPIS). Attribute weights are subsequently employed to calculate distances between alternatives and the IVIFPIS for ranking alternatives. An illustrative example is provided to demonstrate the applicability and effectiveness of this method

Location Planning of Urban Distribution Center under Uncertainty: A Case Study of Yogyakarta Special Region Province, Indonesia

Purpose: The paper aims at proposing a framework of hybrid spatial-fuzzy multi-criteria decision-making and demonstrating application of the framework to evaluate and select the appropriate location for Urban Distribution Center in Yogyakarta Special Region Province, Indonesia. The study has been inspired by the need to evaluate the Urban Distribution Center initiative, i.e., Jogja Inland Port by local government that has been hampered due to lack of participating companies. Design/methodology/approach: The proposed framework consists of two steps of analysis. First, spatial analysis to generate alternative locations using weighted Geographical Information System data; second, fuzzy multi-criteria decision-making to select the best location. Fuzzy Technique for Order of Preference by Similarity to Ideal Solution was applied to deal with multi-criteria, multiple stakeholders, and uncertainty. Accessibility, security, connectivity of multi-modal transport, costs, environmental impact, proximity to customers, proximity to suppliers, resource availability, expansion possibility, service quality, are taken as the decision criteria. Local government of Yogyakarta province, practitioners, and logistic expert, are involved as representative participants in evaluating the Urban Distribution Center location of Yogyakarta Special Region Province. Findings: The proposed framework has indicated that the Jogja Inland Port is not the best alternative. A joint warehouse managed by a group of private companies located in Berbah (Sleman district) appears to be the best alternative location for Urban Distribution Center. Consistent results are also found by using other approaches (Intuitionistic Fuzzy Technique for Order Preference by Similarity to Ideal Solution and Set Pair Analysis). Research limitations/implications: In addition to the government, expert, and practitioners that involved in this study, future research could engage local residents as decision makers to refine the results, as various stakeholders may come up with different preferences. Practical implications: From a practical point of view, the application of combined approach (integrating spatial analysis using weighted Geographical Information System data and fuzzy multi-criteria decision making) is a promising approach in dealing with Urban Distribution Center location problem which is characterized by multi-criteria, multiple stakeholders, spatial-related issues, and uncertainty. Social implications: The unsuccessful establishment of Jogja Inland Port implies that Urban Distribution Center location problem is a complex system, involving multifaceted factors that should be considered simultaneously. Originality/value: The research proposes a framework to evaluate and select the appropriate location for Urban Distribution Center through combined approach of weighted Geographical Information System data and fuzzy multi-criteria decision-making which involves relevant stakeholders.Peer Reviewe

Sustainability performance assessment with intuitionistic fuzzy composite metrics and its application to the motor industry

The performance assessment of companies in terms of sustainability requires to find a balance between multiple and possibly conflicting criteria. We here rely on composite metrics to rank a set of companies within an industry considering environmental, social and corporate governance criteria. To this end, we connect intuitionistic fuzzy sets and composite programming to propose novel composite metrics. These metrics allow to integrate important environmental, social and governance principles with the gradual membership functions of fuzzy set theory. The main result of this paper is a sustainability assessment method to rank companies within a given industry. In addition to consider multiple objectives, this method integrates two important social principles such as maximum utility and fairness. A real-world example is provided to describe the application of our sustainability assessment method within the motor industry. A further contribution of this paper is a multicriteria generalization of the concept of magnitude of a fuzzy number