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In this article, the parameter of the decision maker’s familiarity with the attributes of the alternatives is introduced for the first time in dynamic multi-attribute group decision making to avoid the disadvantages arising from the inappropriate grouping of decision makers. We combine it with fuzzy soft rough set theory and dynamic multi-attribute-grouping decision making to obtain a new decision model, i.e., dynamic chaotic multiple-attribute group decision making. Second, we provide an algorithm for solving this model under a weighted T-spherical fuzzy soft rough set, which can not only achieve symmetry between decision evaluation and fuzzy information but also establish a good symmetrical balance between decision makers and attributes (evaluation indexes). Finally, a specific numerical computation case is proposed to illustrate the convenience and effectiveness of our constructed algorithm. Our contributions to the literature are: (1) We introduced familiarity for the first time in dynamic multi-attribute group decision making. This makes our given dynamic chaotic multi-attribute group decision-making (DCMAGDM) model more general and closer to the actual situation; (2) we combined dynamic chaotic multi-attribute group decision making with T-spherical fuzzy soft rough set theory to make the model more realistic and reflect the actual situation. In addition, our choice of T-spherical fuzzy soft rough set allows the decision maker to engage in a sensible evaluation rather than sticking to numerical size choices; and (3) we constructed a new and more convenient sorting/ranking algorithm based on weighted T-spherical fuzzy soft rough sets.

Air pollution affects public health and the environment, creating great concern in developed and developing countries. In India, there are numerous reasons for air pollution, and festivals like Diwali also contribute to air contamination. Determining the polluted region using several air contaminants is significant and should be analyzed carefully. This study aims to analyze the air quality in Tamil Nadu, India, during the Diwali festival from 2019 to 2021, based on multiple air pollutants. The study models the impact of air pollution as a Multi-Attribute Decision-Making (MADM) problem. It introduces a hybrid approach, namely the Analytical Hierarchy Process-Entropy-VlseKriterijumska Optimizacija I Kompromisno Resenje (AHP-Entropy-VIKOR) model, to analyze and rank the areas based on the quality of air. A combined approach of AHP and entropy is employed to determine the weights of multiple air pollutants. The VIKOR approach ranks the areas and identifies the areas with the worst air quality during the festival. The proposed model is validated by performing the Spearman’s rank correlation with two existing MADM methods: Combinative Distance Based Assessment (CODAS) and Weighted Aggregates Sum Product Assessment (WASPAS). Sensitivity analysis is carried out to assess the effects of the priority weights and the dependency of the pollutants in ranking the regions. The highest air pollution level during the festival was seen in Cellisini Colony (2019), Rayapuram (2020), T. Nagar and Triplicane (2021) in their respective year. The results demonstrate the consistency and efficiency of the proposed approach.

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.

Multi-attribute decision-making (MADM) has been receiving great attention in recent years due to two major issues which are basically to describe attribute values and secondly to aggregate the described information to generate a ranking of alternatives. For the first case it entails the hesitant fuzzy elements (HFEs) as a more flexible and general tool in comparison to fuzzy set theory and for the second one, we allow the aggregation operator (AO) as an effective tool. Having said that there is not yet reported an AO which can provide desirable generality and flexibility in aggregating attribute values under hesitant fuzzy (HF) environment, although many AOs have been developed earlier to attempt to meet above such eventualities. So, the primary objective of this paper is to develop some general as well as flexible AOs that can be exploited to solve MADM problems with the HF information. From this perspective, at the very beginning, we develop some operations between HFEs by uniting the features of Dombi and Archimedean operations. Next, we bring up some HF weighted AOs based on Dombi and Archimedean operations. We discuss in detail some intriguing properties of the proposed AOs. Secondly, we emphasize establishing a procedure of MADM endowed by the proposed operators under the HF environment. Finally, we present a practical example concerning human resource selection to gloss the decision steps of the proposed method and at the same time, we explore the feasibility of the new method.

In this paper, a new multiple attribute decision-making (MADM) method under q-rung dual hesitant fuzzy environment from the perspective of aggregation operators is proposed. First, some aggregation operators are proposed for fusing q-rung dual hesitant fuzzy sets (q-RDHFSs). Afterwards, we present properties and some desirable special cases of the new operators. Second, a new entropy measure for q-RDHFSs is developed, which defines a method to calculate the weight information of aggregated q-rung dual hesitant fuzzy elements. Third, a novel MADM method is introduced to deal with decision-making problems under q-RDHFSs environment, wherein weight information is completely unknown. Finally, we present numerical example to show the effectiveness and performance of the new method. Additionally, comparative analysis is conducted to prove the superiorities of our new MADM method. This study mainly contributes to a novel method, which can help decision makes select optimal alternatives when dealing with practical MADM problems.

Electric power distribution networks plays a significant role in providing continuous electrical energy to different categories of customers. In the context of the present advancements, future load expansion in the active distribution networks (ADNs) poses the key challenge of planning to be derived as a multi-stage optimization task, including the optimal expansion planning scheme optimization (EPSO). The planning scheme optimization is a multi-attribute decision-making issue with high complexity and solving difficulty, especially when it involves a large-scale planning zone. This paper proposes a novel approach of a multi-year planning scheme for the effective solution of the EPSO problem in large planning zones. The proposed approach comprises three key parts, where the first part covers two essential aspects, i.e., (i) suggesting a project condition set that considers the elements directly related to a group of specific conditions and requirements (collectively referred to as conditions) to ADN planning projects; and (ii) Developing a condition scoring system to evaluate planning projects. The second part of our proposed scheme is a quantization method of correlativity among projects based on two new concepts: contribution index (CI) and dependence index (DI). Finally, considering the multi-year rolling optimization, a detailed mathematical model of condition evaluation and spatiotemporal optimization sequencing of ADN planning projects is developed, where the evaluation and optimization are updated annually. The proposed model has been successfully validated on a practical distribution network located in Xiantao, China. The investigated case study and comparisons verify the various advantages, suitability, and effectiveness of the proposed planning scheme, consequently saving more than 10% of the investment compared with the existing implemented scheme.

The objectives of flood control, power generation, water supply and ecology for reservoir operation are neither completely coordinated nor completely opposed, and its optimal operation and decision-making is very complicated. This study proposed a method of multi-objective optimization and multi-attribute decision making for reservoir operation (MODRO). The correlation analysis method was used to analyze the competitive relationship among the extracted objectives, and the multi-objective optimal operation model was constructed. The NSGA-II-SEABODE algorithm was applied to solve the MODRO problem. The objective extraction, model construction, optimization solution and scheme selection were coupled to form a multi-objective optimization and multi-attribute decision making method with the whole process of “Objective-Modeling-Optimization-Selection”. Huangjinxia Reservoir, which is located in Shaanxi, China, was selected as the case study. The results show that: (1) Quantifying the degree of conflict among objectives makes the construction of the multi-objective optimal operation model more reasonable. (2) The NSGA-II-SEABODE algorithm are used to obtain the decision-making scheme, which provides decision-making basis for managers. (3) For Huangjinxia Reservoir, water diversion is negatively related to power generation and ecology, and power generation is positively related to ecology. The results can promote the efficient utilization of water resources, improve the comprehensive benefits of reservoirs, and provide decision-making support for actual reservoir operation.

Nutritional manipulation with functional nutrients like polyunsaturated fatty acids can boost milk production efficiency in dairy farming. It is important to consider the animal's physiological periods, especially the second half of the first pregnancy for mammary gland development. By considering multiple factors and comparing them, multi-attribute decision-making (MADM) can be utilized to conduct further assessments and select the best diet for the animals. Forty primiparous Saanen does, from the last 2 months of pregnancy up to 4 months of lactation, have been assigned to four iso-energetic and iso-nitrogenous diets. Four dietary groups included: no external sources of fat (negative control, CT), saturated palm oil (positive control), roasted soybeans (omega-6, SB) and extruded flaxseed (omega-3, FS). Twenty-two performance criteria such as feed intake, milk yield and composition, body weight, blood metabolites and hormones, the milk fatty acid profile, as well as morphological and histological measurements of the mammary gland, in the form of least-square means, were considered. A decision-making tool was used to select the best form of fat supplements in late pregnancy and early lactation diets, to improve lactation performance in Saanen goats. For this purpose, a MADM method was applied to determine the order of preference similarity to the ideal solution. According to the score of this method, the FS group had the highest coefficients (0.689), and the CT group had the lowest coefficients (0.281). Incorporating flaxseed into the diets of Saanen goats during late pregnancy and early lactation is a valuable strategy for enhancing milk performance. This supplement is recommended as a source of fat. Additionally, the implementation of decision-making tools, such as the MADM method in animal science, can significantly improve management decision-making processes by reducing both time and cost. This presents a new avenue for making well-informed decisions.

This paper presents a fuzzy approach for ranking discrete alternatives in multi-attribute decision-making under uncertainty. Linguistic variables approximated by fuzzy numbers were applied for facilitating the making of pairwise comparison by the decision maker in determining the alternative performance and attribute importance using fuzzy extent analysis. The resultant fuzzy assessments were aggregated using the simple additive utility method for calculating the fuzzy utility of each alternative across all the attributes. An ideal solution-based procedure was developed for comparing and ranking these fuzzy utilities, leading to the determination of the overall ranking of all the discrete multi-attribute alternatives. An example is provided that shows the proposed approach is effective and efficient in solving the multi-attribute decision making problem under uncertainty, due to the simplicity and comprehensibility of the underlying concept and the efficiency and effectiveness of the computation involved.

Multi-attribute decision-making (MADM) is usually used to aggregate fuzzy data successfully. Choosing the best option regarding data is not generally symmetric on the grounds that it does not provide complete information. Since Aczel-Alsina aggregation operators (AOs) have great impact due to their parameter variableness, they have been well applied in MADM under fuzzy construction. Recently, the Aczel-Alsina AOs on intuitionistic fuzzy sets (IFSs), interval-valued IFSs and T-spherical fuzzy sets have been proposed in the literature. In this article, we develop new types of Pythagorean fuzzy AOs by using Aczel-Alsina t-norm and Aczel-Alsina t-conorm. Thus, we give these new operations Aczel-Alsina sum and Aczel-Alsina product on Pythagorean fuzzy sets based on Aczel-Alsina t-norm and Aczel-Alsina t-conorm. We also develop new types of Pythagorean fuzzy AOs including Pythagorean fuzzy Aczel-Alsina weighted averaging and Pythagorean fuzzy Aczel-Alsina weighted geometric operators. We elaborate some characteristics of these proposed Aczel-Alsina AOs on Pythagorean fuzzy sets, such as idempotency, monotonicity, and boundedness. By utilizing the proposed works, we solve an example of MADM in the information of the multinational company under the evaluation of impacts in MADM. We also illustrate the comparisons of the proposed works with previously existing AOs in different fuzzy environments. These comparison results demonstrate the effectiveness of the proposed Aczel-Alsina AOs on Pythagorean fuzzy sets.