A TOPSIS method by using generalized trapezoidal hesitant fuzzy numbers and application to a robot selection problem

Utilizing aggregation operators based on q-rung orthopair neutrosophic soft sets and their applications in multi-attributes decision making problems

Neutrosophic sets provide greater versatility in dealing with a variety of uncertainties, including independent, partially independent, and entirely dependent scenarios, which q-ROF soft sets cannot handle. Indeterminacy, on the other hand, is ignored completely or partially by q-ROF soft sets. To address this issue, this study offers a unique novel concept as known as q-RONSS, which combines neutrosophic set with q-ROF soft set. This technique addresses vagueness using a set of truth, indeterminacy, and false membership degrees associated with the parametrization tool, with the condition that the sum of the qth power of the truth, indeterminacy, and false membership degrees be less than or equal to one. In addition, this study outlines operational laws for the suggested structure. The main purpose this article is to define some averaging and geometric operators based on the q-rung orthopair neutrosophic soft set. Furthermore, this article provides a step-by-step method and a mathematical model for the suggested techniques. To solve a MADM issue, this research article proposes a numerical example of people selection for a specific position in a real estate business based on a variety of criteria. Finally, to demonstrate the proposed model's superiority and authenticity, this article performs several analyses, including sensitivity analysis, to address the reliability and influence of various parameter "q" values on the alternatives and the ultimate ranking outcomes using the averaging and geometric operators. A comparison of the proposed operators to current operators demonstrates the validity of the proposed structure. Furthermore, a comparison of the proposed structure to current theories demonstrates its superiority by overcoming their limits and offering a more flexible and adaptable framework. Finally, this study reviews the findings and consequences of our research.

Various aggregation operators of the generalized hesitant fuzzy numbers based on Archimedean t-norm and t-conorm functions

This paper intends to introduce mathematical tools for aggregation of the generalized hesitant fuzzy numbers in order to increase the use of them in the real world. The proposed operators, are based on general form of t-norm and t-conorm functions, enable us to do some mathematical computations and aggregate the given generalized hesitant fuzzy numbers. At first, some famous Archimedean t-norms and t-conorms, i.e., Algebraic, Einstein, Hamacher, and Frank t-norms and t-conorms, and their properties, have been developed to be employed with generalized hesitant fuzzy numbers. Then, several averaging and geometric-based aggregation operators for generalized hesitant fuzzy numbers have been proposed. Later on, a decision-making algorithm has been defined based on such operators to address the problems. The necessity and application of the proposed concepts have been explained by some numerical examples.

New extension of ordinal priority approach for multiple attribute decision-making problems: design and analysis

The selection and assessment process of appropriate robots became a more complex and complicated task due to various available alternatives and conflicting attributes which must take into consideration. Also, uncertainty which exists usually in the selection process is an unavoidable component that needs to be thoughtfully measured and traditional multi-attribute decision-making approaches failed to deal precisely with it. Since almost all decisions originate from subjective ordinal preferences, handling uncertainty using linguistic variables is also not enough. Thus, the objective of the current study is to present a new extended ordinal priority approach in the neutrosophic environment for the first time to select an appropriate robot. Since neutrosophic is one of the most effective and accommodating tools for handling uncertainty, thus, this method goes to transform linguistic information into triangular neutrosophic numbers using a new presented scale. This scale was used to determine the importance degree of attributes and alternatives regarding experts' opinions. Also, the score function of the triangular neutrosophic number is used for prioritizing attributes and alternatives. The experts in our proposed method have the same degree of importance, since each expert is a person with special skills and knowledge representing mastery of a particular subject. To measure the applicability and efficiency of the proposed approach, an experimental case study has been established for the robot selection problem of a new pharmaceutical city in Egypt for the first time. The source of data in this case study is experts, interviews, and questionnaires. Also, sensitivity and comparative analysis are further made for verifying the power of the proposed approach. The outcome of this study shows that the suggested approach for robot selection is quite helpful and has a great performance under uncertainty over classical and fuzzy ordinal priority approaches. Also, the suggested approach is less consumption of time and simpler than the fuzzy ordinal priority approach. Therefore, we recommend firms and governments to apply it for increasing product quality, hence the profitability of manufacturing industries and decrease needless costs.

Supplementary Information

The online version contains supplementary material available at 10.1007/s40747-022-00721-w.

A Multicriteria Decision-Making Approach of “Tree” Meaning in the New Urban Context

Future cities will need to plan and design urban green spaces and woodlands to meet diverse interests and needs, provide ecosystem services required by an evolving urban society and improve continuity between urban and rural spaces. This future planning approach calls for more sustainable patterns of urban growth, where forests and green spaces can help create more sustainable, resilient and inclusive cities, and address the challenges of a growing urban population. Green areas are of strategic significance because in addition to absorbing harmful pollutants, improving temperatures, and mitigating the impacts of climate change, they have a positive effect on people’s health and well-being and help to create inclusive societies. The values considered are manifold and a multi-criteria assessment, including an evaluation of citizens’ perceived needs, allowing policy-makers to steer choices towards green-oriented urban planning tools, where green spaces and urban forests enable them to meet the challenges of future cities. The research presented here is part of this line of study in order to propose a tool to support stakeholders’ decisions on urban green planning. The objectives of the study are to find out about the perception of urban green spaces and examine what kind of relationship should be established between the local authority and the population with regard to information and participation in the planning of green areas. The results highlight that citizens recognise the importance of ecosystem services and perceive green areas as strategic elements of urban quality of life, in agreement with some previous studies conducted in Italy and other countries.

Harmonic Aggregation Operator with Trapezoidal Picture Fuzzy Numbers and Its Application in a Multiple-Attribute Decision-Making Problem

Picture fuzzy sets (PFSs) can be used to handle real-life problems with uncertainty and vagueness more effectively than intuitionistic fuzzy sets (IFSs). In the process of information aggregation, many aggregation operators under PFSs are used by different authors in different fields. In this article, a multi-attribute decision-making (MADM) problem is introduced utilizing harmonic mean aggregation operators with trapezoidal fuzzy number (TrFN) under picture fuzzy information. Three harmonic mean operators are developed namely trapezoidal picture fuzzy weighted harmonic mean (TrPFWHM) operator, trapezoidal picture fuzzy order weighted harmonic mean (TrPFOWHM) operator and trapezoidal picture fuzzy hybrid harmonic mean (TrPFHHM) operator. The related properties about these operators are also studied. At last, an MADM problem is considered to interrelate among these operators. Furthermore, a numerical instance is considered to explain the productivity of the proposed operators.

Archimedean t-Norm and t-Conorm-Based Aggregation Operators of HFNs, with the Approach of Improving Education

The aim of this paper is to develop the calculus of hesitant fuzzy numbers (HFNs), have been recently proposed as the newest extension of hesitant fuzzy sets. At first, based on the willingness of decision maker to each part of HFNs, a new method has been proposed to compare them. Then, several t -norm and t -conorm-based aggregation operators of HFNs, i.e., algebraic t -norm and t -conorm, Einstein t -norm and t -conorm, Hamacher t -norm and t -conorm, Frank t -norm and t -conorm have been defined, and some of their mathematical properties are also discussed. As the special cases of the above t -norm and t -conorm-based aggregation operators of HFNs, Archimedean t -norm and t -conorm-based HFN weighted averaging operator, Archimedean t -norm and t -conorm-based HFN weighted geometric operator, Archimedean t -norm and t -conorm-based HFN ordered weighted averaging operator, and Archimedean t -norm and t -conorm-based HFN ordered weighted geometric operator have been proposed. The new problem of improving the process of educational activities under the Covid-19 epidemic conditions, for instance, has been defined as a multi-attribute group decision-making (MAGDM) problem, in which students are its options, courses are its criteria, and teachers are members of the decision-making team. Then, the scores of final exams and teachers’ assessments merged together as HFNs, and a new method has been proposed based on the before mentioned operators to solve the resulting MAGDM problem. A numerical example, the results of which are also analyzed, is responsible for explaining what is proposed in this article. Finally, subsequent studies in this area are briefly stated.

Introducing a new type of HFSs and its application in solving MAGDM problems

Uncertainty has long been explored as an objective and inalienable reality, and then modeled via different theories such as probability theory, fuzzy sets (FSs) theory, vague sets, etc. Hesitant fuzzy sets (HFSs) as a generalization of FSs, because of their flexibility and capability, extended and applied in many practical problems very soon. However, the above theories cannot meet all the scientific needs of researchers. For example, in some decision-making problems we encounter predetermined definite data, which have inductive uncertainties. In other words, the numbers themselves are crisp in nature, but are associated with varying degrees of satisfaction or fairness from the perspective of each decision-maker/judge. To this end, in this article, hesitant fuzzy numbers as a generalization of hesitant fuzzy sets will be introduced. Some concepts such as the operation laws, the arithmetic operations, the score function, the variance of hesitant fuzzy numbers, and a way to compare hesitant fuzzy numbers will be proposed. Mean-based aggregation operators of hesitant fuzzy numbers, i.e. hesitant fuzzy weighted arithmetic averaging (HWAA), hesitant fuzzy weighted geometric averaging (HWGA), hesitant fuzzy ordered weighted arithmetic averaging (HOWAA), and hesitant fuzzy ordered weighted geometric averaging (HOWGA) operators have been discussed in this paper, too. These new concepts will be used to model, and solve an uncertain multi-attribute group decision making (MAGDM) problem. The proposed method will be illustrated by a numerical example and the validity of the obtained solution will be checked by test criteria.