Pythagorean fuzzy set, generalized by Yager, is a new tool to deal with vagueness considering the membership grade $$\mu $$
 and non-membership $$\nu $$
 satisfying the condition $$\mu ^2+\nu ^2\le 1$$
 . It can be used to characterize the uncertain information more sufficiently and accurately than intuitionistic fuzzy set. Pythagorean fuzzy set has attracted great attention of many scholars that have been extended to new types and these extensions have been used in many areas such as decision making, aggregation operators, and information measures. Because of such a growth, we present an overview on Pythagorean fuzzy set with aim of offering a clear perspective on the different concepts, tools and trends related to their extension. In particular, we provide two novel algorithms in decision making problems under Pythagorean fuzzy environment. It may be served as a foundation for developing more algorithms in decision making.

Pythagorean fuzzy set: state of the art and future directions

This paper presents a new approach for the treatment of uncertainty which is based on interval-valued fuzzy-rough numbers (IVFRN). It is shown that by integrating the rough approach with the traditional fuzzy approach, the subjectivity that exists when defining the borders of fuzzy sets is eliminated. IVFRN make decision making possible using only the internal knowledge in the operative data available to the decision makers. In this way objective uncertainties are used and there is no need to rely on models of assumptions. Instead of different external parameters in the application of IVFRN, the structure of the given data is used. On this basis an original multi-criteria model was developed based on an IVFRN approach. In this multi-criteria model the traditional steps of the BWM (Best–Worst method) and MABAC (Multi-Attributive Border Approximation area Comparison) methods are modified. The model was tested and validated on a study of the optimal selection of fire fighting helicopters. Testing demonstrated that the model based on IVFRN enabled more objective expert evaluation of the criteria in comparison with traditional fuzzy and rough approaches. A sensitivity analysis of the IVFRN BWM-MABAC model was carried out by means of 57 scenarios, the results of which showed a high degree of stability. The results of the IVFRN model were validated by comparing them with the results of the fuzzy and rough extension of the MABAC, COPRAS and VIKOR models.

Modification of the Best–Worst and MABAC methods: A novel approach based on interval-valued fuzzy-rough numbers

Materials selection, as a essential link for manufacturing enterprises, has an important driving-force to comprehensively upgrade material properties and service life, especially in building and decoration fields. To qualitatively select the optimal green decoration materials, a hybrid multi-criteria decision making (MCDM) approach integrating analytical hierarchy process (AHP) and grey correlation technique for order performance by similarity to ideal solution (GC-TOPSIS) is proposed. The weights vector of hierarchical index structure, which is established based on interior environmental characteristics, i.e., physiological comfort, psychological satisfaction and interior environmental effect, is determined by AHP. GC-TOPSIS is applied to obtain the final ranking of green decoration materials to select the optimal one. A case study, i.e., 10 kinds of solid woods, is illustrated to validate the proposed method. Additionally, a sensitivity analysis of nine experiments is carried out to monitor the robustness of solution ranking to changes. The results proved that this method furnishes an rational and efficient decision support tool for performance assessment of green decoration materials.

Green decoration materials selection under interior environment characteristics: A grey-correlation based hybrid MCDM method

In this paper, we initiate a new axiomatic definition of single-valued neutrosophic distance measure and similarity measure, which is expressed by single-valued neutrosophic number that will reduce the information loss and remain more original information. Meanwhile, a novel score function is proposed. Then, the objective weights of various attributes are determined via gray system theory. Moreover, we present the combined weights, which can show both the subjective information and the objective information. Later, we present three algorithms to deal with multi-attribute decision-making problem based on revised Technique for Order Preference by Similarity to an Ideal Solution, Multi-Attributive Border Approximation area Comparison and similarity measure. Finally, the effectiveness and feasibility of approaches are demonstrated by two numerical examples.

Approaches to single-valued neutrosophic MADM based on MABAC, TOPSIS and new similarity measure with score function

An integrated approach for failure mode and effect analysis under interval-valued intuitionistic fuzzy environment

A hybrid group decision making approach is proposed for material selection.Uncertain and vague information is handled by interval-valued intuitionistic fuzzy sets.A maximizing optimization model is established for determining criteria weights.An extended group decision making method is used to rank alternative materials.The applicability and effectiveness are illustrated with two application examples. In engineering design, selecting the most suitable material for a particular product is a typical multiple criteria decision making (MCDM) problem, which generally involves several feasible alternatives and conflicting criteria. In this paper, we aim to propose a novel approach based on interval-valued intuitionistic fuzzy sets (IVIFSs) and multi-attributive border approximation area comparison (MABAC) for handling material selection problems with incomplete weight information. First, individual evaluations of experts concerning each alternative are aggregated to construct the group interval-valued intuitionistic fuzzy (IVIF) decision matrix. Consider the situation where the criteria weight information is partially known, a linear programming model is established for determining the criteria weights. Then, an extended MABAC method within the IVIF environment is developed to rank and select the best material. Finally, two application examples are provided to demonstrate the applicability and effectiveness of the proposed IVIF-MABAC approach. The results suggest that for the automotive instrument panel, polypropylene is the best, for the hip prosthesis, Co-Cr alloys-wrought alloy is the optimal option. Finally, based on the results, comparisons between the IVIF-MABAC and other relevant representative methods are presented. It is observed that the obtained rankings of the alternative materials are good agreement with those derived by the past researchers.

An interval-valued intuitionistic fuzzy MABAC approach for material selection with incomplete weight information

Nowadays selecting the most suitable robot is a difficult task for manufacturing firms due to increase in production demands and availability of various robot models. Robot evaluation and selection can be regarded as a multiple criteria decision-making (MCDM) problem and three key issues are the assessment of robots, the determination of criteria weights and the prioritisation of alternatives. This paper aims to propose an integrated model based on hesitant 2-tuple linguistic term sets and an extended QUALIFLEX approach for handling robot selection problems with incomplete weight information. The new model can not only manage uncertain and imprecise assessment information of decision-makers with the aid of hesitant 2-tuple linguistic term sets, but also derive the important weights of criteria objectively when the weight information is incompletely known. Moreover, based on the extended QUALIFLEX algorithm, the priority orders of robots can be clearly determined and a more reasonable and credible solution...

An integrated linguistic MCDM approach for robot evaluation and selection with incomplete weight information

Electric Vehicles (EVs) are considered to be a potential viable technology to address the persistent unsustainable problems in transport sector. In this paper, we focus on analyzing the transition processes of EVs in China because the sustainability of developing countries is essential for the worldwide sustainability. The two-round demonstration programs of EVs in China were analyzed by adopting the strategic niche management (SNM) approach so as to find out what niche protection has been provided and which obstacles hamper the further development of EVs. The results show that the financial subsidy is the most important protective measure. However, the diffusion results of EVs in different pilot cities are greatly different. The main reason lies in the uneven geographical landscape. In addition, some obstacles were exposed during the niche internal processes including low quality of expectations and poor alignment within the network. Based on the analysis results, we develop a list of suggestions that are important to consider when developing EVs.

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Adopting Strategic Niche Management to Evaluate EV Demonstration Projects in China

It is widely accepted that EV (electric vehicles) is one of the several green technologies to address environmental issues associated with the transport sector and promote the transition to sustainable mobility. In spite of this, a number of barriers still need to be overcome before EVs achieve widespread market penetration. This paper is a contribution to understanding the key tools and strategies that might support the take-up of EVs by adopting a social-technical approach to explore the main barriers encountered in the Chinese EV Demonstration Program. The key findings of the research are that interest conflict between different stakeholders and the inaction of related actors are the key barriers inhibiting the further development of EVs. So the policies that put much pressure on the current auto regime are necessary.

Understanding Socio-Technical Barriers to Sustainable Mobility – Insights from Demonstration Program of EVs in China

EVs (electric vehicle), as sustainable technologies, hold the potential to achieve the sustainability of the transport system and challenge the prevailing business models of internal combustion engines (ICEs). To unlock the dominant logic of ICEs and promote the diffusion of EVs, Business model (BM) innovation is necessary. However, BM innovation for EVs still faces many obstacles. This paper makes contribution theoretically and practically by constructing a “3-7” system and proposing a two-phase conceptual frame-work for BM innovation of EVs. The case of Shenzhen City, China is studied to illustrate how the “3-7” system and two-phase conceptual framework is applied. Based on the case study, this paper concludes two new barriers that are not highlighted by the previous literature and makes a number of suggestions to help address the issues found in BM innovation.

https://papers.ssrn.com/sol3/Delivery.cfm?abstractid=2478597

Yixi Xue

Papers

An interval-valued intuitionistic fuzzy MABAC approach for material selection with incomplete weight information

An integrated linguistic MCDM approach for robot evaluation and selection with incomplete weight information

Adopting Strategic Niche Management to Evaluate EV Demonstration Projects in China

Understanding Socio-Technical Barriers to Sustainable Mobility – Insights from Demonstration Program of EVs in China

A Conceptual Framework for Business Model Innovation: The Case of Electric Vehicles in China