A new multiattribute decision making method based on multiplication operations of interval-valued intuitionistic fuzzy values and linear programming methodology

An Integrated Approach for Failure Mode and Effects Analysis Based on Weight of Risk Factors and Fuzzy PROMETHEE Ⅱ

Design experts need to fully understand the failure risk of a product to improve its quality and reliability. However, design experts have different understandings of and concepts in the risk evaluation process, which will lead to cognitive asymmetry in the product’s redesign. This phenomenon of cognitive asymmetry prevents experts from improving the reliability of a product, increasing the risk of product development failure. Traditionally, failure mode and effects analysis (FMEA) has been widely used to identify the failure risk in redesigning products and a system’s process. The risk priority number (RPN), which is determined by the risk factors (RF), namely, the occurrence (O), severity (S), and detection (D), is the index used to determine the priority ranking of the failure modes (FM). However, the uncertainty about the evaluation information for the RF and the coupling relationship within the FM have not been taken into account jointly. This paper presents an integrated approach for FMEA based on an interval-valued intuitionistic fuzzy set (IVIFS), a fuzzy information entropy, a non-linear programming model, and fuzzy PROMETHEE Ⅱ to solve the problem of cognitive asymmetry between experts in the risk evaluation process. The conclusions are as follows: Firstly, an IVIFS is used to present the experts’ evaluation information of the RF with uncertainty, and the fuzzy information entropy is utilized to obtain the weight of the experts to integrate the collective decision matrix. Secondly, a simplified non-linear programming model is utilized to obtain the weight of the RF to derive the weighted preference index of the FM. Subsequently, the coupling relationship within the FM is estimated by fuzzy PROMETHEE Ⅱ, where the net flow is given to estimate the priority ranking of the FM. Finally, the proposed approach is elaborated on using a real-world case of a liquid crystal display. Methods comparison and sensitivity analyses are conducted to demonstrate the validity and feasibility of the proposed approach.

Analysis of Interval-Valued Intuitionistic Fuzzy Aczel–Alsina Geometric Aggregation Operators and Their Application to Multiple Attribute Decision-Making

When dealing with the haziness that is intrinsic in decision analysis-driven decision making procedures, interval-valued intuitionistic fuzzy sets (IVIFSs) can be quite effective. Our approach to solving the multiple attribute decision making (MADM) difficulties, where all of the evidence provided by the decision-makers is demonstrated as interval-valued intuitionistic fuzzy (IVIF) decision matrices, in which all of the components are distinguished by an IVIF number (IVIFN), is based on Aczel–Alsina operational processes. We begin by introducing novel IVIFN operations including the Aczel–Alsina sum, product, scalar multiplication, and exponential. We may then create IVIF aggregation operators, such as the IVIF Aczel–Alsina weighted geometric operator, the IVIF Aczel–Alsina ordered weighted geometric operator, and the IVIF Aczel–Alsina hybrid geometric operator, among others. We present a MADM approach that relies on the IVIF aggregation operators that have been developed. A case study is used to demonstrate the practical applicability of the strategies proposed in this paper. By contrasting the newly developed technique with existing techniques, the method is capable of demonstrating the advantages of the newly developed approach. A key result of this work is the discovery that some of the current IVIF aggregation operators are subsets of the operators reported in this article.

Developing a Conceptual Partner Selection Framework: Digital Green Innovation Management of Prefabricated Construction Enterprises for Sustainable Urban Development

Digital green innovation management activities are the core of low-carbon intelligent development of prefabricated construction enterprises (PCEs) for sustainable urban development. PCEs have to seek joint venture partners to avoid the financial risk of digital green innovation projects. The purpose of this study is to develop a conceptual partner selection framework for the digital green innovation management of prefabricated construction towards urban building 5.0. In this study, first, symbiosis theory and six analysis methods were integrated to innovatively build a 3W1H-P framework system for the joint venture capital partner selection of digital green innovation projects. Second, the dual combination weighting method was innovatively proposed to avoid subjective and objective deviation in attribute weight and time weight. Finally, empirical research was carried out to verify the scientific nature, reliability, and practicability of the framework system and selection model. The results of this study show that the framework system and selection model proposed can be used to assist PCEs to select joint investment partners of digital green and innovative projects for sustainable urban development.

The operational properties of linguistic interval valued q-Rung orthopair fuzzy information and its VIKOR model for multi-attribute group decision making

As a generalization of linguistic q-rung orthopair fuzzy set (Lq-ROFS), linguistic interval valued q-Rung orthopair fuzzy set (LIVq-ROFS) is a new concept to deal with complex and uncertain decision making problems which Lq-ROFS cannot handle. Due to the lack of information in decision making process, decision makers mostly prefer to give their preferences in interval form rather than a crisp number. In this situations, LIVq-ROFS appears up as a useful tool. In this work, we define operational laws of LIVq-ROFS and prove some properties. Furthermore, we propose the conception of the LIVq-ROF weighted averaging operator and give its formula by mathematical induction. To compare two or more linguistic interval valued q-Rung orthopair fuzzy numbers (LIVq-ROFNs), the improved form of score function is also given. Considering the powerfulness of LIVq-ROFSs handling ambiguity and complex uncertainty in practical problems, the key innovation of this paper is to develop the linguistic interval-valued q-rung orthopair fuzzy VIKOR model that is significantly different from the existing VIKOR methodology. The computing steps of this newly created model are briefly presented. Finally, the effectiveness of model is verified by an example and through comparative analysis, the superiority of VIKOR method is further illustrated.

Consensus-based group decision-making methods with probabilistic dual hesitant fuzzy preference relations and their applications

Probabilistic dual hesitant fuzzy sets (PDHFSs) have good flexibility and integrity in expressing fuzzy and uncertain information. However, some crucial problems related to PDHFSs remain unsolved, such as how to define probabilistic dual hesitant fuzzy preference relations (PDHFPRs) and solve group decision-making (GDM) problems with PDHFPRs. This paper establishes the concept of PDHFPRs and investigates consensus-based GDM methods with PDHFPRs. First, a new distance measure is proposed to quantify the difference between two PDHFPRs, which does not increase the virtual elements of membership and non-membership degrees, and can contain all distance combination of membership and non-membership elements. Therefore, the distance calculation results are not affected by the subjectivity of decision-makers (DMs). Second, the consensus measures for PDHFPRs are proposed, which are effective tool to measure the consensus level among DMs. Moreover, two consensus-based GDM methods are proposed, which can improve the group consensus level for PDHFPRs by changing the PDHFPR with the worst consensus level or modifying the weights of DMs. Finally, the proposed methods are applied to the location selection of large-scale industrial solid waste treatment facilities. The comparison with existing methods illustrates the validity and feasibility of the proposed methods.

Multiattribute decision-making under Fermatean fuzzy bipolar soft framework

Fermatean fuzzy set theory is emerging as a novel mathematical tool to handle uncertainties in different domains of real world. Fermatean fuzzy sets were presented in order that uncertain information from quite general real-world decision-making situations could be mathematically tractable. To that purpose, these sets are more flexible and reliable than intuitionistic and Pythagorean fuzzy sets. This paper presents a novel hybrid model, namely, the Fermatean fuzzy bipolar soft set (FFBSS, in short) model as a general extension of two powerful existing models, that is, fuzzy bipolar soft set and Pythagorean fuzzy bipolar soft set models. Some fundamental properties of the proposed FFBSS model, namely, subset-hood, equal FFBSSs, relative null and relative absolute FFBSSs, restricted intersection and union, extended intersection and union, AND operation and OR operation are investigated along with numerical examples. In addition, certain basic operations, including Fermatean fuzzy weighted average and score function of FFBSSs are proposed. Furthermore, two applications of FFBSS are explored to deal with different multiattribute decision-making situations, that is, selection of best surgeon robot and analysis of most affected country due to COVID-19 ('CO' stands for corona, 'VI' for virus, 'D' for disease, and '19' stands for its year of emergence, that is, 2019). The proposed methodology is supported by an algorithm. At the end, a comparison analysis of the proposed hybrid model with some existing models, including Pythagorean fuzzy bipolar soft sets is provided.

A LSGDM method based on social network and IVIFN’s geometric characteristics for evaluating the collaborative innovation problem1

During the development of regional economy, introducing collaborative innovation is an important policy. Constructing a scientific and effective measurement for evaluating the collaborative innovation degree is essential to determine an optimum collaborative innovation plan. As this problem is complex and has a long-lasting impact, this paper will propose a novel large scale group decision making (LSGDM) method both considering decision makers’ social network and their evaluation quality. Firstly, the decision makers will be detected based on their social connections and aggregated into different subgroups by an optimization algorithm. Secondly, decision makers are weighted according to their important degree and decision information, where the information is carried by interval valued intuitionistic fuzzy number (IVIFN). During the information processing, IVIFN is put in rectangular coordinate system considering its geometric meaning. And some related novel concept are given based on the barycenter of rectangle region determined by IVIFN. Meanwhile, the criteria’s weights are calculated by the accurate degree and deviation degree. A classical example is used to illustrate the effect of weighting methods. In summary, a large scale group decision making method based on the geometry characteristics of IVIFN (GIVIFN-LSGDM) is proposed. The scientific and practicability of GIVIFN-LSGDM method is illustrated through evaluating four different projects based on the constructed criteria system. Comparisons with the other methods are discussed, followed by conclusions and further research.

Multi-attribute decision-making method based on a novel distance measure of linguistic intuitionistic fuzzy sets

Linguistic intuitionistic fuzzy sets can qualitatively rather than quantitatively express data in the form of membership degree. But quantitative tools are required to handle qualitative information. Therefore, an improved linguistic scale function, which can more accurately manifest the subjective feelings of decision-makers, is employed to deal with linguistic intuitionistic information. Subsequently, due to some commonly used distance measures do not comprehensively evaluate the information of linguistic intuitionistic fuzzy sets, an improved distance measure of linguistic intuitionistic fuzzy sets is designed. It considers the cross-evaluation information to get more realistic reasoning results. In addition, a new similarity measure defined by nonlinear Gaussian diffusion model is proposed, which can provide different response scales for different information between various schemes. The properties of these measures are also studied in detail. On this basis, a method in linguistic intuitionistic fuzzy environment is developed to handle multi-attribute decision-making problems. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method and the influence of the parameters is analyzed.

Fuzzy Attribute Expansion Method for Multiple Attribute Decision-Making with Partial Attribute Values and Weights Unknown and Its Applications

In the real world, there commonly exists types of multiple attribute decision-making (MADM) problems with partial attribute values and weights totally unknown. Symmetry among some attribute information that is already known and unknown, and symmetry between the pure attribute set and fuzzy attribute membership set can be a considerable way to solve this type of MADM problem. In this paper, a fuzzy attribute expansion method is proposed to solve this type of problem based on two key techniques: the spline interpolation technique and the attribute weight reconfiguration technique, which are respectively used for the determination of attribute values and the reconfiguration of attribute weights. The spline interpolation technique to expand attribute values can enhance the performance of some regression methods and clustering methods by the comparisons between the results of these methods dealing with practical cases with and without the application of the technique, which further illustrates the effectiveness of this technique. For MADM problems with partial attribute values and weights totally unknown, compared with traditional fuzzy comprehensive evaluation (FCE), FCE with the application of fuzzy attribute expansion method can obtain results more similar with the ones when all attribute values and weights are known, which is proved by the practical power quality evaluation example.