Picture fuzzy normalized projection and extended VIKOR approach to software reliability assessment

A Hybrid Picture Fuzzy Similarity Measure and Improved VIKOR Method

Picture fuzzy set (PFS) can intuitively express the answers of “yes”, “neutral”, “no” and “reject”, which have strong advantages in solving uncertain information. The similarity measure is an effective tool to determine the relationship between two picture fuzzy sets (PFSs). In this paper, we propose a hybrid picture fuzzy (PF) similarity measure which combines the Hamming distance and the transformed tetrahedral centroid distance and verifies that it satisfies the four properties of the similarity measure. The proposed and existing picture fuzzy similarity measures are compared and investigated through numerical examples and some applications of pattern recognition. The results show that the proposed similarity measure not only produces no unreasonable results, but also overcomes the shortcomings of the existing similarity measures. Furthermore, we investigate an improved VIKOR method based on the proposed similarity measure of PFS. Finally, through an example, several multi-attribute decision-making (MADM) methods are compared and analyzed to illustrate the effectiveness and practicability of the improved VIKOR method.

Picture fuzzy WASPAS method for selecting last-mile delivery mode: a case study of Belgrade

Background

Last-mile delivery (LMD) is becoming more and more demanding due to an increasing number of users and traffic problems in cities. Besides, medical crises (like the COVID-19 outbreak) and air pollution represent additional motives for the transition from traditional to socially and environmentally sustainable LMD mode. An emerging problem for companies in the postal and logistics industry is how to determine the best LMD mode in a multi-criteria setting under uncertainty.

Method

For the first time, an extension of the Weighted Aggregated Sum Product ASsessment (WASPAS) method under the picture fuzzy environment is presented to solve the LMD mode selection problem. The introduced picture fuzzy set (PFS) based multi-criteria decision-making (MCDM) method can be highly beneficial to managers who are in charge of LMD since it can take into account the neutral/refusal information and efficiently deal with high levels of imprecise, vague, and uncertain information. The comparative analysis with the existing state-of-the-art PFS-based MCDM methods approved the high reliability of the proposed picture fuzzy WASPAS method. Its high robustness and consistency are also confirmed. The presented method can be used to improve LMD in urban areas worldwide. Besides, it can be applied to solve other emerging MCDM problems in an uncertain environment.

Findings

A real-life case study of Belgrade is presented to fully illustrate the potentials and applicability of the picture fuzzy WASPAS method. The results show that postomates are the best mode for LMD in Belgrade, followed by cargo bicycles, drones, traditional delivery, autonomous vehicles, and tube transport.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12544-021-00501-6.

An Integrated Decision Support Model Based on BWM and Fuzzy-VIKOR Techniques for Contractor Selection in Construction Projects

Sustainable development of any country to some extent depends on successful accomplishment of construction projects, particularly infrastructures. Contractors have a key role in the success of these projects. Hence, the selection of a competent contractor as a complicated and hard decision process has a vital importance in the destiny of any construction project. Contractor selection is in essence a multicriteria decision-making that ought to encompass so many aspects of the project and the client’s requirements on one hand and the capabilities and past records of the contractors on the other hand. Failure in selecting a competent contractor may cause time and cost overruns; quality shortcomings; increasing in claims, disputes and change orders; and even failure of the project. In spite of deficiencies of selecting a contractor by the rule of “the lowest bid price”, it still prevails in many countries including Iran. In this paper, a new contractor selection model based on the best-worst method (BWM) and well-known Fuzzy-VIKOR techniques is proposed as a solution to overcome the deficiencies of the traditional “lowest bid price” rule. An illustrative example of a water channel construction project verified the applicability of the proposed model in practice.