A Novel Approach to Multi-Attribute Group Decision-Making based on Interval-Valued Intuitionistic Fuzzy Power Muirhead Mean

Online Teaching Quality Evaluation of Business Statistics Course Utilizing Fermatean Fuzzy Analytical Hierarchy Process with Aggregation Operator

Due to the full-scale outbreak of COVID-19, many universities have adopted the way of online teaching to ensure the orderly development of teaching plans and teaching contents. However, whether online and offline teaching can develop homogeneously and how to ensure the teaching effect is a major challenge for colleges and universities. Therefore, it is urgent to construct a reasonable index system and evaluation approach for the quality of network teaching. Combined with the influencing factors and characteristics of online teaching, this study first puts forward a multi-index evaluation index system and then proposes a novel evaluation method for online teaching based on the analytical hierarchy process (AHP) and Dombi weighted partitioned Muirhead Mean (PMM) operator under Fermatean fuzzy (FF) environment. This presented method not only adapts to changeable evaluation information but also handles the elusive interrelationships among indexes, realizing the flexibility and comprehensiveness both in form and in the polyaddition process. The applicability and feasibility of this presented method are then discussed through the practical online teaching quality evaluation of a business statistics course case, and a group of tentative about the sensitivity analysis and comparative analysis further demonstrates the effectiveness and flexibility of the proposed method.

Power Muirhead Mean Operators for Interval-Valued Linear Diophantine Fuzzy Sets and Their Application in Decision-Making Strategies

It is quite beneficial for every company to have a strong decision-making technique at their disposal. Experts and managers involved in decision-making strategies would particularly benefit from such a technique in order to have a crucial impact on the strategy of their company. This paper considers the interval-valued linear Diophantine fuzzy (IV-LDF) sets and uses their algebraic laws. Furthermore, by using the Muirhead mean (MM) operator and IV-LDF data, the IV-LDF power MM (IV-LDFPMM) and the IV-LDF weighted power MM (IV-LDFWPMM) operators are developed, and some special properties and results demonstrated. The decision-making technique relies on objective data that can be observed. Based on the multi-attribute decision-making (MADM) technique, which is the beneficial part of the decision-making strategy, examples are given to illustrate the development. To demonstrate the advantages of the developed tools, a comparative analysis and geometrical interpretations are also provided.

Multiple attribute group decision-making based on interval-valued q-rung orthopair uncertain linguistic power Muirhead mean operators and linguistic scale functions

Fuzzy set theory and its extended form have been widely used in multiple-attribute group decision-making (MAGDM) problems, among which the interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs) got a lot of attention for its ability of capturing information denoted by interval values. Based on the previous studies, to find a better solution for fusing qualitative quantization information with fuzzy numbers, we propose a novel definition of interval-valued q-rung orthopair uncertain linguistic sets (IVq-ROULSs) based on the linguistic scale functions, as well as its corresponding properties, such as operational rules and the comparison method. Furthermore, we utilize the power Muirhead mean operators to construct the information fusion method, and provide a variety of aggregation operators based on the proposed information description environment. A model framework is constructed for solving the MAGDM problem utilizing the proposed method. Finally, we illustrate the performance of the new method and investigate its advantages and superiorities through comparative analysis.

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.

Q-Rung Probabilistic Dual Hesitant Fuzzy Sets and Their Application in Multi-Attribute Decision-Making

The probabilistic dual hesitant fuzzy sets (PDHFSs), which are able to consider multiple membership and non-membership degrees as well as their probabilistic information, provide decision experts a flexible manner to evaluate attribute values in complicated realistic multi-attribute decision-making (MADM) situations. However, recently developed MADM approaches on the basis of PDHFSs still have a number of shortcomings in both evaluation information expression and attribute values integration. Hence, our aim is to evade these drawbacks by proposing a new decision-making method. To realize this purpose, first of all a new fuzzy information representation manner is introduced, called q-rung probabilistic dual hesitant fuzzy sets (q-RPDHFSs), by capturing the probability of each element in q-rung dual hesitant fuzzy sets. The most attractive character of q-RPDHFSs is that they give decision experts incomparable degree of freedom so that attribute values of each alternative can be appropriately depicted. To make the utilization of q-RPDHFSs more convenient, we continue to introduce basic operational rules, comparison method and distance measure of q-RPDHFSs. When considering to integrate attribute values in q-rung probabilistic dual hesitant fuzzy MADM problems, we propose a series of novel operators based on the power average and Muirhead mean. As displayed in the main text, the new operators exhibit good performance and high efficiency in information fusion process. At last, a new MADM method with q-RPDHFSs and its main steps are demonstrated in detail. Its performance in resolving practical decision-making situations is studied by examples analysis.

A Comprehensive Evaluation Model for Curtain Grouting Efficiency Assessment Based on Prospect Theory and Interval-Valued Intuitionistic Fuzzy Sets Extended by Improved D Numbers

Grouting-efficiency evaluation is a key element in grouting-construction control. However, most existing grouting-efficiency evaluation models do not consider the hesitation and bounded rationality of experts and have difficulty in handling the problem of incomplete decision-making information generated by experts. Furthermore, the diversity of the evaluation indicators used can be further improved. This study conducts a comprehensive evaluation model to address these problems. An objective and reasonable fuzzy evaluation method is demonstrated through the integration of interval-valued intuitionistic fuzzy sets, prospect theory, and improved D numbers. The secondary permeability index is introduced to establish a more scientific evaluation indicator system. The proposed model is implemented in evaluating the curtain-grouting efficiency of a hydropower station, and its consistency, representativeness, and superiority are validated and analyzed.