Intuitionistic fuzzy induced ordered weighted averaging distance operator and its application to decision making

Common prosperity level evaluation: A comprehensive method based on probabilistic linguistic ordered weighted distance measure, prospect theory, and TOPSIS

Introduction

Common prosperity is a major research project in China, and the scientific measurement and evaluation of common prosperity is very important.

Methods

In this study, firstly, we construct a comprehensive evaluation index system for the common prosperity level (CPL). We then develop an evaluation model of CPL based on prospect theory, probabilistic linguistic ordered weighted distance measure, and the TOPSIS method, wherein we use a probabilistic linguistic term set (PLTS) to describe the uncertainty and complexity of the assessment process. Above all, we use prospect theory to reflect the preferences of experts to meet the unique needs for the evaluation of common prosperity. Moreover, we apply the proposed evaluation index system and model to evaluate the CPL of Zhejiang Province, China's first common prosperity demonstration zone, as an example to conduct relevant research. The advantages and effectiveness of the proposed method are verified by the sensitivity and comparative analysis.

Results

The findings prove that the application of the new PLTS evaluation framework in CPL assessment is robust.

Discussion

We propose specific suggestions for improving the development of common prosperity.

Multiple-Attribute Decision Making Based on Interval-Valued Intuitionistic Fuzzy Generalized Weighted Heronian Mean

Due to the complexity and uncertainty of objective things, interval-valued intuitionistic fuzzy (I-VIF) numbers are often used to describe the attribute values in multiple-attribute decision making (MADM). Sometimes, there are correlations between the attributes. In order to make the decision-making result more objective and reasonable, it is often necessary to take the correlation factors into account. Therefore, the study of MADM based on the correlations between attributes in the I-VIF environment has important theoretical and practical significance. Thus, in this paper, we propose new operators (AOs) for I-VIF information that are able to reflect the completeness of the information, attribute relevance, and the risk preference of decision makers (DMs). Firstly, we propose some new AOs for I-VIF information, including I-VIF generalized Heronian mean (I-VIFGHM), I-VIF generalized weighted Heronian mean (I-VIFGWHM), and I-VIF three-parameter generalized weighted Heronian mean (I-VIFTPGWHM). The properties of the obtained operators, including their idempotency, monotonicity, and boundedness are studied. Furthermore, an MADM method based on the I-VIFGWHM operator is provided. Finally, an example is provided to explain the rationality and feasibility of the proposed method.

Multiple Attribute Decision Making Based on Linguistic Generalized Weighted Heronian Mean

In actual multiple attribute decision making, people often use language to evaluate attributes of the object, and sometimes there are associations between the attributes. Therefore, the study of multiple attribute decision making with language as attributes and associations between attributes is of great theoretical significance and practical value. The Heronian mean is not only an operator which reflects the associations between attributes, but also has excellent properties, including idempotency, monotonicity, boundedness, parameter symmetry, and alternate symmetry. In this paper, firstly a new linguistic generalized weighted Heronian mean (LGWHM) was provided, and its properties including idempotency, monotonicity, boundedness, and limit were studied. Then, a new three-parameter linguistic generalized weighted Heronian mean (TPLGWHM) and its idempotency, monotonicity, and boundedness properties were proposed. Finally, multi-attribute decision making methods based on the new linguistic generalized weighted Heronian mean were given, and an example was analyzed and compared with other methods.

Multiple Attribute Decision-Making Based on Three-Parameter Generalized Weighted Heronian Mean

For the aggregation problem of attributes with a correlation relationship, it is often necessary to take the correlation factor into account in order to make the decision results more objective and reasonable. The Heronian mean is an aggregation operator which reflects the interaction between attributes. It is of great theoretical and practical significance to study and popularize the multiple attribute decision-making methods based on the Heronian mean operator. In this paper, we first give a new three-parameter generalized weighted Heronian mean (TPGWHM), which has a series of excellent properties such as idempotency, monotonicity and boundedness. At the same time, the relationship between the TPGWHM and the existing aggregation operators is given. Then, we propose the intuitionistic fuzzy three-parameter generalized weighted Heronian mean (IFTPGWHM) and give its idempotency, monotonicity, boundedness and limit properties. On this basis, a multiple attribute decision-making method based on the TPGWHM and a multiple attribute decision-making method based on the IFTPGWHM are given, and corresponding examples are given and analyzed.

Single-Valued Neutrosophic Linguistic-Induced Aggregation Distance Measures and Their Application in Investment Multiple Attribute Group Decision Making

This paper studied the single-valued neutrosophic linguistic distance measures based on the induced aggregation method. Firstly, we proposed a single-valued neutrosophic linguistic-induced ordered weighted averaging distance (SVNLIOWAD) measure, which is a new extension of the existing distance measures based on the induced aggregation view. Then, based on the proposed SVNLIOWAD, a novel induced distance for single-valued neutrosophic linguistic sets, namely the single-valued neutrosophic linguistic weighted induced ordered weighted averaging distance (SVNLWIOWAD), was developed to eliminate the defects of the existing methods. The relationship between the two proposed distance measures was also explored. A multiple attribute group decision making (MAGDM) model was further presented based on the proposed SVNLWIOWAD measure. Finally, a numerical example concerning an investment selection problem was provided to demonstrate the usefulness of the proposed method under a single-valued neutrosophic linguistic environment and, then, a comparison analysis was carried out to verify the flexibility and effectiveness of the proposed work.

Intuitionistic Linguistic Multiple Attribute Decision-Making with Induced Aggregation Operator and Its Application to Low Carbon Supplier Selection

The main focus of this paper is to investigate the multiple attribute decision making (MADM) method under intuitionistic linguistic (IL) environment, based on induced aggregation operators and analyze possibilities for its application in low carbon supplier selection. More specifically, a new aggregation operator, called intuitionistic linguistic weighted induced ordered weighted averaging (ILWIOWA), is introduced to facilitate the IL information. Some of its desired properties are explored. A further generalization of the ILWIOWA, called intuitionistic linguistic generalized weighted induced ordered weighted averaging (ILGWIOWA), operator is developed. Furthermore, by employing the proposed operators, a MADM approach based on intuitionistic linguistic information is presented. Finally, an illustrative example concerning low carbon supplier selection and comparative analyses are conducted to demonstrate the effectiveness and practicality of the proposed approach.