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The concept of T-spherical fuzzy sets (T-SFSs) provides a robust optimization approach to deal with uncertainties in environmental concerns. The main objective of this paper is to introduce a hybrid approach for the power system reforms and advances of low-carbon technology to address environmental concerns as well as transition towards a more sustainable energy infrastructure. To meet these objectives, various aggregation operators (AOs) are developed named as T-spherical fuzzy Dubois–Prade (T-SFDP), T-spherical fuzzy interactive Dubois–Prade weighted average (T-SFIDPWA), T-spherical fuzzy interactive Dubois–Prade ordered weighted average (T-SFIDPOWA), T-spherical fuzzy interactive Dubois–Prade weighted geometric (T-SFIDPWG), and T-spherical fuzzy interactive Dubois–Prade ordered weighted geometric (T-SFIDPOWG). These AOs are integrated in the construction CRITIC-EDAS framework, facilitating a comprehensive assessment and ranking of proposals. This paper underscores the methodology's efficacy and precision through rigorous validation with CRITIC-MAUT, CRITIC-ARAS, CRITIC-EDAS, and CRITIC-MABAC analyses, showcasing its ability to discern and prioritize reform initiatives with exactitude. Beyond enhancing the comprehension of reform proposals, this hybrid approach establishes a benchmark for future evaluations, significantly contributing to the dynamic landscape of power system optimization. The methodology's clarity and precision offer decision-makers a valuable tool for the thorough assessment and prioritization of power system reforms initiatives, fostering sustainability and environmentally conscious advancements.

Pooling the opinions of the decision makers about premier alternative from a list of given choices is the most crucial phenomenon theory of decision making. The MSM operator is an effective approach and can identify the collective connection among various input viewpoints. So, tacking the fully benefit of MSM operator, this paper presents a new novel in depth investigation of MSM in context of Neutrosophic fuzzy variables. Initially we developed the structure of One-dimension uncertain linguistic interval valued neutrosophic fuzzy variables, deliberate their fundamental properties along with meaningful laws. Moreover, we encompass the MSM operator to the extent of one dimensional uncertain-linguistic Neutrosophic fuzzy variables and introduced some novel aggregations operators including one-dimensional uncertain linguistic interval-valued Neutrosophic fuzzy, weighted fuzzy and ordered weighted fuzzy McLaurin symmetric mean operator. The practical utilization of the proposed aggregation operators in business analytic are also included in the paper. In last comparison is made between current vs old studies which proved solidity and reliability of the new operator’s vs existing operators in the literature.

The creation of sustainable artificial tropical forests is of utmost importance for addressing critical environmental issues like deforestation, habitat loss, and climate change. This research paper presents an innovative approach that considers ecological, socioeconomic, and technological factors. The proposed approach integrates multi-criteria decision-making (MCDM) methods that take into account the preferences and opinions of stakeholders. To analyze the various criteria involved, cubic picture fuzzy numbers (CPFNs) are utilized. To ensure fairness in evaluating CPFNs, the study focuses on developing operational laws and aggregation operators that promote neutrality and fairness. Specifically, the paper introduces the “cubic picture fuzzy fairly weighted average (CPFFWA) operator” and the “cubic picture fuzzy fairly ordered weighted averaging (CPFFOWA) operator.” By considering stakeholders and prioritizing their long-term sustainability and resilience, this approach proves to be highly valuable for policymakers, forest managers, and other relevant parties. This research avenue bridges the gap in current literature where limited exploration of fairly aggregation operators in tandem with picture fuzzy sets within tropical forest contexts exists. Ultimately, the research strives to contribute to the practical management of these vital ecosystems, fostering environmental conservation and sustainability through a cross-disciplinary approach amalgamating ecology, fuzzy logic, decision theory, and environmental science.

$p,q,r-$ spherical fuzzy ( $p,q,r-$ SF) sets are a significant advancement in fuzzy set (FS) theory, providing an effective way to describe hesitation inside a set. This development goes beyond membership degrees (MDs) by incorporating three parameters (p, q and r) that shape and define the spread of FS. The presence of these parameters makes $p,q,r-$ SF sets ideal for dealing with complicated decision-making (DM) scenarios in a wide range of applications. In this paper, we proposed a new reliable method for smart DM in logo design projects that uses $p,q,r-$ SF Einstein aggregation operators (AOs). First, we present the $p,q,r-$ SF Einstein operators, which are accomplished of capturing the relationship and interrelationship of numerous criteria while making decisions on logo design, including originality, relevance, beauty, and usability. Next, we use the proposed framework, a multi-criteria decision analysis tool, to rank the choices. We demonstrate the practical application and efficiency of our method in a scenario in which a team of three designers is entrusted with developing five different logo styles for diverse enterprises. Moreover, we compare proposed procedure with some existing methods, demonstrating its advantages in terms of precision and reliability.

During the transitional phase spanning from the realm of fuzzy logic to the realm of neutrosophy, a multitude of hybrid models have emerged, each surpassing its predecessor in terms of superiority. Given the pervasive presence of indeterminacy in the world, a higher degree of precision is essential for effectively handling imprecision. Consequently, more sophisticated variants of neutrosophic sets (NSs) have been conceived. The key objective of this paper is to introduce yet another variant of NS, known as the q-rung orthopair fuzzy-valued neutrosophic set (q-ROFVNS). By leveraging the extended spatial range offered by q-ROFS, q-ROFVNS enables a more nuanced representation of indeterminacy and inconsistency. Our endeavor commences with the definitions of q-ROFVNS and q-ROFVN numbers (q-ROFVNNs). Then, we propose several types of score and accuracy functions to facilitate the comparison of q-ROFVNNs. Fundamental operations of q-ROFVNSs and some algebraic operational rules of q-ROFVNNs are also provided with their properties, substantiated by proofs and elucidated through illustrative examples. Drawing upon the operational rules of q-ROFVNNs, the q-ROFVN weighted average operator (q-ROFVNWAO) and q-ROFVN weighted geometric operator (q-ROFVNWGO) are proposed. Notably, we present the properties of these operators, including idempotency, boundedness and monotonicity. Furthermore, we emphasize the applicability and significance of the q-ROFVN operators, substantiating their utility through an algorithm and a numerical application. To further validate and evaluate the proposed model, we conduct a comparative analysis, examining its accuracy and performance in relation to existing models.

This paper presents novel operational laws for $p,q,r-$ spherical fuzzy sets ( $p,q,r-$ SFSs) by harnessing the Dombi t-norm (DTN) and t-conorm (DTCN). These laws serve as the foundation for a set of aggregation operators (AOs) designed to consolidate $p,q,r-$ spherical fuzzy ( $p,q,r-$ SF) information. Additionally, a multi-criteria decision-making (MCDM) method is outlined for addressing practical decision-making (DM) challenges. To demonstrate the application of the proposed approach, a numerical example is offered. Furthermore, we conducted a comparative study to validate the efficacy of the suggested approach. Finally, we discuss both the advantages and limitations of this innovative approach.

The neutrosophic sets and numbers have an important role in modeling the problems. Recently, studies on neutrosophic numbers and single-valued neutrosophic numbers which is a subclass of neutrosophic numbers have increased, rapidly. Cauchy distribution is an important concept in the statistic. In this paper, the notion of Cauchy single-valued neutrosophic numbers (CSVNNs) and α−cuts are introduced based on the Cauchy distribution formula. Summation, multiplication, and division operations between two CSVNNs are defined and given related examples. Also, the score functions of CSVNNs, arithmetic and geometric aggregation operators of them are described. Based on the defined new concepts, a multi-attribute group decision-making method is developed. Finally, to illustrate how the proposed method works, an application of the proposed method in the selection of a project to be supported and funded is developed. In this method, for each of the criteria, different score functions are determined by using the aggregation operators and score functions of the CSVNNs. Then, evaluations of the decision-makers are transformed into new values under the derived score functions for the decision. In applications, in general, decision-makers assign to criteria some values between 0 and 1 directly. In the method proposed in this paper, weights of the criteria are considered as the different functions. Therefore this method presents a more general perspective on decision-making problems.

In this paper, we expended the concept of neutrosophic sets (NS) by introducing the idea α,β,γ− neutrosophic set (α,β,γ− NS). The existing models under conventional NSs, fail to adequately address the management of membership degree influence during the aggregation process. While the proposed framework manages the influence of membership degree (MD), indeterminacy membership degree (IMD), and non-membership degree (NMD) by incorporating parameters α, β, and γ. Furthermore, we defined some fundamental operational laws for α,β,γ− NSs and introduced a series of aggregation operators (AOs) to effectively combine α,β,γ− neutrosophic information. Based on these AOs, a new Multiple Criteria Decision Making (MCDM) model is proposed for solving real-life decision-making (DM) challenges.An illustrative case study is presented to showcase the effectiveness of the proposed model in selecting an optimal location for a software office. The article concludes by validating the proposed model's authenticity and effectiveness through a comparative analysis with existing approaches.

The concept of p,q− quasirung orthopair fuzzy (p,q− QOF) sets is an advanced extension of q− rung orthopair fuzzy sets (q− ROFSs). This paper introduces the adaptation of Hamacher t-norm and t-conorm to the p,q− QOF environment. A series of Hamacher aggregation operators (AOs) and their associated properties are presented. This study extends its application to multi-criteria group decision-making (MCGDM) for practical problem-solving, illustrated through the analysis of mobile payment platforms. The influence of the aggregation operator parameters, denoted as p and q, on the outcomes of decisions is effectively showcased. Moreover, a comparative analysis is carried out to validate the credibility and authenticity of the proposed model. Finally, the advantages and limitations of the proposed model are outlined.

In modern society, people concern more about the evaluation of medical service quality. Evaluation of medical service quality is helpful for medical service providers to supervise and improve their service quality. Also, it will help the public to understand the situation of different medical providers. As a multi-criteria decision-making (MCDM) problem, evaluation of medical service quality can be effectively solved by aggregation operators in interval-valued q-rung dual hesitant fuzzy (IVq-RDHF) environment. Thus, this paper proposes interval-valued q-rung dual hesitant Maclaurin symmetric mean (IVq-RDHFMSM) operator and interval-valued q-rung dual hesitant weighted Maclaurin symmetric mean (IVq-RDHFWMSM) operator. Based on the proposed IVq-RDHFWMSM operator, this paper builds a novel approach to solve the evaluation problem of medical service quality including a criteria framework for the evaluation of medical service quality and a novel MCDM method. What’s more, aiming at eliminating the discordance between decision information and weight vector of criteria determined by decisionmakers (DMs), this paper proposes the concept of cross-entropy and knowledge measure in IVq-RDHF environment to extract weight vector from DMs’ decision information. Finally, this paper presents a numerical example of the evaluation of medical service for hospitals to illustrate the availability of the novel method and compares our method with other MCDM methods to demonstrate the superiority of our method. According to the comparison result, our method has more advantages than other methods.

A bipolar complex fuzzy credibility set (BCFCS) is a new approach in computational intelligence and decision-making under uncertainty. Bipolar complex fuzzy credibility (BCFC) information has been employed as a strategy for dealing with confusing and unreliable situations that arise in everyday life. In this paper, we used the concept of aggregation operators to diagnose the well-known averaging and geometric aggregation operators, as well as evaluate some properties and related results. Using described operators, an algorithm for multiple criteria group decision making is proposed. Then, a numerical example of a case study of Hospital selection is discussed. Lastly, the comparative analysis of suggested operators with existing operators are also given to discuss the rationality, efficiency and applicability of these operators.

Decision-making is a complex issue, especially for attributes being more than one and further bifurcated. Correlation analysis plays an important role in decision-making problems. For neutrosophic hypersoft sets (NHSSs), they have bifurcated sub-attributes so that we cannot compare the attributive values. Thus, Correlation Coefficient (CC) should be a good tool for decision-making in NHSSs. Moreover, in decision-making problems, most of the times opinion of more than one expert is involved. For dealing this, m-polar values can be better used. The basic purpose of this paper is to propose the concept of CC and Weighted CC (WCC) for m-polar NHSSs with some aggregation operators, theorems, and propositions. Algorithms, based on CC and WCC are also been proposed to solve decision-making problems. Two case studies have been solved by applying the proposed algorithms. The results obtained are compared with existing approaches. The experiment and comparison results reveal the validity and superiority of the proposed methods. They are more accurate and precise. In the future, the proposed methods can be applied to case studies, in which attributes are more than one and further bifurcated along with more than one decision-maker. They can be extended for several existing approaches, like TOPSIS, VIKOR, AHP, and many others.

During the COVID-19 pandemic, identifying face masks with artificial intelligence was a crucial challenge for decision support systems. To address this challenge, we propose a quadratic Diophantine fuzzy decision-making model to rank artificial intelligence techniques for detecting masks, aiming to prevent the global spread of the disease. Our paper introduces the innovative concept of quadratic Diophantine fuzzy sets (QDFSs), which are advanced tools for modeling the uncertainty inherent in a given phenomenon. We investigate the structural properties of QDFSs and demonstrate that they generalize various fuzzy sets. In addition, we introduce essential algebraic operations, set-theoretical operations, and aggregation operators. Finally, we present a numerical case study that applies our proposed algorithms to select a unique face mask detection method and evaluate the effectiveness of our techniques. Our findings demonstrate the viability of our mask identification methodology during the COVID-19 outbreak.

Many aggregation operators are studied to deal with multi-criteria group decision-making problems. Whenever information has two aspects, intuitionistic fuzzy sets and Pythagorean fuzzy sets are employed to handle the information. However, q-rung orthopair fuzzy sets are more flexible and suitable because they cover information widely. The current paper primarily focuses on the multi-criteria group decision-making technique based on prioritization and two robust aggregation operators based on Aczel–Alsina t-norm and t-conorm. This paper suggests two new aggregation operators based on q-rung orthopair fuzzy information and Aczel–Alsina t-norm and t-conorm, respectively. Firstly, novel q-rung orthopair fuzzy prioritized Aczel–Alsina averaging and q-rung orthopair fuzzy prioritized Aczel–Alsina geometric operators are proposed, involving priority weights of the information. Several related results of the proposed aggregation operators are investigated to see their diversity. A multi-criteria group decision-making algorithm based on newly established aggregation operators is developed, and a comprehensive numerical example for the selection of the most suitable energy resource is carried out. The proposed aggregation operators are compared with other operators to see some advantages of the proposed work. The proposed aggregation operators have a wider range for handling information, with priority degrees, and are based on novel Aczel–Alsina t-norm and t-conorm.

This paper aims to amalgamate the notion of a T-spherical fuzzy set (T-SFS) and a linear Diophantine fuzzy set (LDFS) to elaborate on the notion of the T-spherical linear Diophantine fuzzy set (T-SLDFS). The new concept is very effective and is more dominant as compared to T-SFS and LDFS. Then, we advance the basic operations of T-SLDFS and examine their properties. To effectively aggregate the T-spherical linear Diophantine fuzzy data, a T-spherical linear Diophantine fuzzy weighted averaging (T-SLDFWA) operator and a T-spherical linear Diophantine fuzzy weighted geometric (T-SLDFWG) operator are proposed. Then, the properties of these operators are also provided. Furthermore, the notions of the T-spherical linear Diophantine fuzzy-ordered weighted averaging (T-SLDFOWA) operator; T-spherical linear Diophantine fuzzy hybrid weighted averaging (T-SLDFHWA) operator; T-spherical linear Diophantine fuzzy-ordered weighted geometric (T-SLDFOWG) operator; and T-spherical linear Diophantine fuzzy hybrid weighted geometric (T-SLDFHWG) operator are proposed. To compare T-spherical linear Diophantine fuzzy numbers (T-SLDFNs), different types of score and accuracy functions are defined. On the basis of the T-SLDFWA and T-SLDFWG operators, a multiple attribute decision-making (MADM) method within the framework of T-SLDFNs is designed, and the ranking results are examined by different types of score functions. A numerical example is provided to depict the practicality and ascendancy of the proposed method. Finally, to demonstrate the excellence and accessibility of the proposed method, a comparison analysis with other methods is conducted.

The Pythagorean Probabilistic Hesitant Fuzzy (PyPHF) Environment is an amalgamation of the Pythagorean fuzzy set and the probabilistic hesitant fuzzy set that is intended for some unsatisfactory, ambiguous, and conflicting situations where each element has a few different values created by the reality of the situation membership hesitant function and the falsity membership hesitant function with probability. The decision-maker can efficiently gather and analyze the information with the use of a strategic decision-making technique. In contrast, ambiguity will be a major factor in our daily lives while gathering information. We describe a decision-making technique in the PyPHF environment to deal with such data uncertainty. The fundamental operating principles for PyPHF information under Choquet Integral were initially established in this study. Then, we put up a set of new aggregation operator names, including Pythagorean probabilistic hesitant fuzzy Choquet integral average and Pythagorean probabilistic hesitant fuzzy Choquet integral geometric aggregation operators. Finally, we explore a multi-attribute decision-making (MADM) algorithm based on the suggested operators to address the issues in the PyPHF environment. To demonstrate the work and contrast the findings with those of previous studies, a numerical example is provided. Additionally, the paper provides sensitivity analysis and the benefits of the stated method to support and reinforce the research.

T-spherical fuzzy sets (T-SPFSs) have gained popularity because of their ability to account for uncertainty more effectively and spanning a larger domain. The sum of the t-th power of membership grades in T-SPFSs is close to a unit interval, allowing for greater uncertainty. As a result, this set outperforms traditional fuzzy structures. The "multi-criteria decision-making" (MCDM) approach is a widely used technique that requires the use of some aggregation tools, and various such aggregation operators (AOs) have been developed over the years to achieve this purpose. The purpose of this paper is to propose some new operational laws and AOs for use in a T-spherical fuzzy environment. In this regard, we presented some new neutral or fair operational rules that combine the concept of proportional distribution to provide a neutral or fair solution to the membership, abstinence, and non-membership of T-spherical fuzzy numbers (T-SPFNs). Based on the obtained operational rules, we presented the "T-spherical fuzzy fairly weighted average operator" and the "T-spherical fuzzy fairly ordered weighted averaging operator". Compared to earlier methodologies, the proposed AOs provide more generalised, reliable, and accurate information. In addition, under T-SPFSs, an MCDM approach is developed employing suggested AOs with several decision-makers (DMs) and partial weight details. Finally, to demonstrate the applicability of the innovative technique, we give an actual case study of "food waste treatment technology" (FWTT) selection under T-SPFSs scenarios. A comparison with an existing model has also been undertaken to confirm the validity and robustness of the acquired results.

The single-valued neutrosophic hesitant fuzzy set (SV-NHFS) is a hybrid structure of the single-valued neutrosophic set and the hesitant fuzzy set that is designed for some incomplete, uncertain, and inconsistent situations in which each element has a few different values designed by the truth membership hesitant function, indeterminacy membership hesitant function, and falsity membership hesitant function. A strategic decision-making technique can help the decision-maker accomplish and analyze the information in an efficient manner. However, in our real lives, uncertainty will play a dominant role during the information collection phase. To handle such uncertainties in the data, we present a decision-making algorithm in the SV-NHFS environment. In this paper, we first presented the basic operational laws for SV-NHF information under Einstein's t-norm and t-conorm. Furthermore, important properties of Einstein operators, including the Einstein sum, product, and scalar multiplication, are done under SV-NHFSs. Then, we proposed a list of novel aggregation operators' names: Single-valued neutrosophic hesitant fuzzy Einstein weighted averaging, weighted geometric, order weighted averaging, and order weighted geometric aggregation operators. Finally, we discuss a multi-attribute decision-making (MADM) algorithm based on the proposed operators to address the problems in the SV-NHF environment. A numerical example is given to illustrate the work and compare the results with the results of the existing studies. Also, the sensitivity analysis and advantages of the stated algorithm are given in the work to verify and strengthen the study.

Aiming at the problem that the existing aggregation operators only consider the weight of the data itself or the weight of the data position when aggregating data, a group decision information fusion model based on the combinatorial ordered weighted average operator is proposed, which considers the incompleteness, uncertainty and plurality of the decision information, and effectively improves the accuracy of group consensus. In this paper, an interval intuitionistic fuzzy combinatorically weighted average operator is proposed, which embodies the weight of the set data itself and the weight of data position, and can adjust the importance of the two weights in the operator through parameters, and prove that the operator has the properties of boundedness, monotonicity, idempotency and permutation invariance. Secondly, a position weight solving model of interval intuitionistic fuzzy combinatorial ordered weighted average operator is established, and the position weight is solved with the help of cross-entropy and Orness measures. Finally, a group decision information fusion process based on IVIFCOWA operators is designed, and the decision maker weight information is obtained according to the decision matrix, and the comprehensive decision matrix is obtained by fusion of IVIFCOWA operators, and then the mean similarity is obtained. Through specific case analysis, it is proved that the proposed operator can make full use of the decision data, and can better reach group consensus after data fusion than the existing operator.

In this paper, the use of the Fermatean fuzzy number (FFN) in a significant research problem of disaster decision-making by defining operational laws and score function is demonstrated. Generally, decision control authorities need to brand suitable and sensible disaster decisions in the direct conceivable period as unfitting decisions may consequence in enormous financial dead and thoughtful communal costs. To certify that a disaster comeback can be made, professionally, we propose a new disaster decision-making (DDM) technique by the Fermatean fuzzy Schweizer-Sklar environment. First, the Fermatean fuzzy Schweizer-Sklar operators are employed by decision-makers to rapidly analyze their indefinite and vague assessment information on disaster choices. Then, the DDM technique based on the FFN is planned to identify highly devastating disaster choices and the best available choices. Finally, the proposed regret philosophy DDM technique is shown functional to choose the ideal retort explanation for a communal fitness disaster in Pakistan. The dominance and realism of the intended technique are further defensible through a relative study with additional DDM systems.

Many fuzzy concepts have been researched and described with uncertain information. Collecting data under uncertain information is a difficult task, especially when there is a difference between the opinions of experts. To deal with such situations, different types of operators have been introduced. This paper aims to develop the Maclaurin symmetric mean (MSM) operator for the information in the shape of the interval-valued spherical fuzzy set (IVSFS). In this article, a family of aggregation operators (AOs) is proposed which consists of interval valued spherical fuzzy Maclaurin symmetric mean operator (IVSFMSM), interval valued spherical fuzzy weighted Maclaurin symmetric mean (IVSFWMSM), interval valued spherical fuzzy dual Maclaurin symmetric mean (IVSFDMSM), and interval valued spherical fuzzy dual weighted Maclaurin symmetric mean (IVSFDWMSM) operators. In this paper, we studied an elucidative example to discuss the evaluation of multi-national companies for the application of the proposed operator. Then the obtained results from the proposed operators are compared. The results obtained are graphed and tabulated for a better understanding.

The multi-criteria decision-making (MCDM) tool is a robust decision-making technique utilized in several fields like networking, risk management, digital analysis, cybercrime investigation, artificial intelligence, waste management enterprises and many other selection criteria. Complex SFS (CSFS) is a new edition of the spherical fuzzy set (SFS) that offers substantial information about any item in terms of amplitude and phase terms in a wider range of real terms. Complex SFS (CSFS) can be an extension of the spherical fuzzy set (SFS). The Aczel-Alsina aggregation tools are more appropriate aggregation operators (AOs), and they are used to conquer the impact of inconsistent and uncertain data. In this paper, we reveal some new approaches based on Aczel-Alsina aggregation tools under consideration of Complex Spherical Fuzzy (CSF) information. These new approaches include the CSF Aczel-Alsina weighted average (CSFAWA) operator, and the CSF Aczel-Alsina ordered weighted average (CSFOWA) operator. In addition to this, we also introduce a list of novel techniques by making use of the theory of Aczel-Alsina aggregation tools such as CSF Aczel-Alsina weighted geometric (CSFAWG) and CSF Aczel-Alsina ordered weighted geometric (CSFOWG) operators. To demonstrate the resilience and efficacy of the approaches that have been mentioned, we will examine a few exceptional examples and remarkable properties of the methodology that we have devised. In addition, a characterization is provided for an approach to the MCDM issue using the CPF information system. We use the example of electric automobiles as a case study to illustrate the uniformity and dependability of the methodology that we have established. This example was chosen because of the high cost of fuel and the present economic challenges that are being encountered by families in the middle class. An empirical case study is also constructed to determine an electric car that is desirable based on the techniques that we have proposed. To evaluate the correctness and superiority of the established strategies, we compare the outcomes of previously used techniques with the AOs currently being provided.

Abstract Intuitionistic fuzzy sets, characterized by membership degree $$\mu $$ μ , non-membership degree $$\upsilon $$ υ and hesitation degree $$\pi $$ π , are a meaningful extension of fuzzy set. Inequalities on intuitionistic fuzzy sets/values are very important in solving real problems. In this paper, some inequalities on intuitionistic fuzzy sets are derived from operations. Moreover, three unweighted intuitionistic fuzzy aggregation operators, including unweighted intuitionistic fuzzy Square, unweighted intuitionistic fuzzy Arithmetic and unweighted intuitionistic fuzzy Geometric, are developed. Later, some corresponding inequality relations on them are deeply explored. Finally, some inequalities on intuitionistic fuzzy value are constructed by equality $$\mu +\upsilon +\pi =1$$ μ + υ + π = 1 in critical definition and proved by some existing famous inequalities, which provide a novel basis for the intuitionistic fuzzy inequalities in operations and aggregation operators.

Tools for decision making need to be simple to use. In previous papers, we advocated that decision engineering needs to provide these tools, as well as a list of necessary properties that aggregation functions need to satisfy. When we model decisions using aggregation functions, andness-directedness is one of them. A crucial aspect in any decision is the degree of compromise between criteria. Given an aggregation function, andness establishes to what degree the function behaves in a conjunctive manner. That is, to what degree some criteria are mandatory. Nevertheless, from an engineering perspective, what we know is that some criteria are strongly required and we cannot ignore a bad evaluation even when other criteria are correctly evaluated. That is, given our requirements of andness, what are the aggregation functions we need to select. Andness is not only for mean-like functions, but it also applies to t-norms and t-conorms. In this paper, we study this problem and show how to select t-norms and t-conorms based on the andness level.

Aggregation operators can be used to combine and synthesise a finite number of numerical values into a single numerical value. Many areas, including decision-making, expert systems, risk analysis, and image processing, rely heavily on aggregating functions. In real-world situations, the neutrosophic set can manage the uncertainties associated with information from any decision-making challenge, whereas the fuzzy set and intuitionistic set cannot. The term "bipolarity" refers to the propensity of the human mind to weigh pros and drawbacks when thinking through decisions. Triangular norms are aggregation operators in a variety of fields, including fuzzy set theory, probability and statistics, and decision sciences. Thus, the individual assessments in this paper's study of and approach to multi-criteria decision-making (MCDM) problems that use bipolar neutrosophic numbers as the individual evaluations. Frank operational laws of bipolar neutrosophic numbers, bipolar neutrosophic Frank weighted geometric aggregation (BNFWGA) and the bipolar neutrosophic frank ordered weighted geometric aggregation (BNFOWGA) operators have been developed with its desirable properties. Additionally, the suggested aggregation operators have been used in the selection of bridges. The outcomes demonstrate the applicability and validity of the suggested approach. Comparative analysis has been performed using the current approach.

The mutual identification of spatial objects is a fundamental issue when updating geographic data with other data sets. Representations of spatial objects in different sources may not have the same identifiers, which would unambiguously assign them to each other. Intersections of spatial objects can be used for this purpose, but this does not allow for the detection of possible changes and their quantification. The aim of this paper is to propose a simple, applicable procedure for calculating the shape similarity measure, which should be able to efficiently identify different representations of spatial objects in two data sources, even though they may be changed or generalised. The main result is the aggregated index of shape similarity and instructions for its calculation and implementation. The shape similarity index is based on the calculation of the set similarity, the distance of the boundaries, and the differences in the area, perimeter, and number of the vertices of areal spatial objects. In the case study, the footprints of the building complexes in Dúbravka (part of the city of Bratislava, the capital of Slovakia) are compared using data from OpenStreetMap and INSPIRE (Infrastructure for Spatial Information in Europe) Buildings. A contribution to the quality check of the OpenStreetMap data is then a secondary result. The proposed method can be effectively used in the semi-automatic integration of heterogeneous data sources, updating the data source with other spatial data, or in their quality control.

Aczel-Alsina t-norm (TN) and t-conorm (TCN) were proposed by Aczel and Alsina in 1982 are more flexible than the other TN and TCN. Since Aczel-Alsina TN and TCN have a great impact due to the variableness of involved parameters, they have good applications in multi-attribute decision making (MADM) under fuzzy sets (FSs) construction. Recently, Senapati et al. (2022) developed Aczel-Alsina aggregation operators (AOs) under intuitionistic FSs (IFSs) and interval-valued IFSs (IVIFSs) with their applications in solving IFS and IVIFS MADM problems. We know that T-spherical FSs (TSFSs) are a recently developed approach to uncertain information with less information loss and more reliability than IFSs and IVIFSs. In this paper, we develop these AOs on TSFSs as a new approach to solve MADM problems by using Aczel-Alsina TN and Aczel-Alsina TCN under T-spherical fuzzy (TSF) information. Furthermore, the basic operations of TSF numbers (TSFNs) are developed and exemplified. Based on these operations, two types of AOs, i.e., TSF Aczel-Alsina weighted average (TSFAAWA), and TSF Aczel-Alsina weighted geometric (TSFAAWG) operators, are introduced and investigated. The reliability and accuracy of the newly developed AOs are tested numerically and theoretically by the induction methods. To further give applications and also study the sensitivity of these TSF Aczel-Alsina operators, the problem of project evaluation using these proposed operators is comprehensively observed. The results obtained by using these TSF Aczel-Alsina operators are compared with some previously existing AOs of TSFSs. According to comparison results, we observe the reliability and efficiency of the proposed methods.

In several practical decision procedures, it is not accessible to denote assessments by a single crisp number due to a lack of information. However, representing information by an interval number within [0, 1] is a more credible approach. In multi-criteria decision making (MCDM) such an interval number can significantly catch information. In addition, the combination of soft sets with interval-valued q-rung orthopair fuzzy sets can be viewed as interval-valued q-rung orthopair fuzzy soft sets (IVq-ROFSs). It can be a reliable tool to cope with uncertainties. Usually, aggregation operators are functional in MCDM techniques; therefore, aggregation operators on IVq-ROFSs can significantly aggregate pieces of information in intervals with IVq-ROFSs. In this paper, we investigated some crucial properties of interval valued q-rung orthopair fuzzy soft sets (IVq-ROFSSs) and expressed a different representation of IVq-ROFSS in the form of IVq-ROFS number. Based on this representation, we investigated IVq-ROF weighted averaging, IVq-ROF weighted geometric operators and given their basic properties. Moreover, we consider interactions between non-memberships and memberships of different interval-valued q-rung orthopair fuzzy values and defined IVq-ROF weighted interaction averaging, IVq-ROF weighted interaction geometric aggregation operators in IVq-ROFS environments. A decision-making process is given, and an illustration is provided by tackling application in automation company evaluation.

With the rapid increase in the number of infected people in COVID-19, medical supplies have been increasing significantly. Medical waste treatment scheme selection may have long-term impacts on the economy, society, and environment. Determining the best treatment option is a considerable challenge. To solve this problem, in this paper, we proposed a multi-criteria group decision making (MCGDM) method based on single-valued neutrosophic numbers and partitioned Maclaurin symmetric mean (PMSM) operator. Because of the complexity of the medical waste treatment scheme selection problem, the single-valued neutrosophic numbers are applied to express the uncertain evaluation information. For the medical waste treatment scheme selection problem, the factors or criteria (these two terms can be interchanged.) in the same clusters are closely related, and the criteria in different clusters have no relationships. The partitioned Maclaurin symmetric mean function can handle these complicated criterion relationships. Therefore, we extend the PMSM operator to process the single-valued neutrosophic numbers and propose the single-valued neutrosophic partitioned Maclaurin symmetric mean (SVNPMSM) operator and its weighted form (SVNWPMSM). Then, we analyze their properties and give typical examples of the proposed operators. An MCGDM model based on the SVNWPMSM aggregation operator is developed and applied to solve the medical waste treatment scheme selection problem. Finally, the validity and superiority of the developed model are verified by comparing it with the previous methods.

The picture fuzzy set is a generation of an intuitionistic fuzzy set. The aggregation operators are important tools in the process of information aggregation. Some aggregation operators for picture fuzzy sets have been proposed in previous papers, but some of them are defective for picture fuzzy multi-attribute decision making. In this paper, we introduce a transformation method for a picture fuzzy number and trapezoidal fuzzy number. Based on this method, we proposed a picture fuzzy multiplication operation and a picture fuzzy power operation. Moreover, we develop the picture fuzzy weighted geometric (PFWG) aggregation operator, the picture fuzzy ordered weighted geometric (PFOWG) aggregation operator and the picture fuzzy hybrid geometric (PFHG) aggregation operator. The related properties are also studied. Finally, we apply the proposed aggregation operators to multi-attribute decision making and pattern recognition.

Ecological risks are characterized by a high degree of uncertainty about the chances of unfavorable event outcomes and the losses associated with those outcomes. Subjective expert judgment is widely used when baseline data are insufficient. This introduces additional uncertainties in the results of risk analyses. In order to successfully model the existing uncertainties, this paper presents a methodology for ecological risk analysis that is based on input evaluations in the form of intuitionistic fuzzy values (IFVs). The advantage of this approach is the ability to model a wide range of uncertainties in ecological risk analysis tasks.

In this paper, we first introduce the concept of T-spherical hesitant fuzzy set (T-SHFS) on the basis of the combination of T-spherical fuzzy sets (T-SFSs) and hesitant fuzzy sets (HFSs). This model can provide more accuracy in expressing fuzzy and indeterminate data. Then, we develop the basic operational laws of T-SHFSs and study their properties. Also, we propose the T-spherical hesitant fuzzy weighted averaging (T-SHFWA) operator and the T-spherical hesitant fuzzy weighted geometric (T-SHFWG) operator and investigate their properties. Furthermore, two newly approaches to multi attribute decision making within the framework of T-SHFS are developed on the basis of the proposed aggregation operators. An illustrative example is given to demonstrate the effectiveness of the developed approaches in dealing with uncertain and indeterminate decision making problems. Finally, the proposed models’ performance is evaluated to the existing models. Results from this comparison analysis reveal a great similarity and consistency while using other models.

Hesitant neutrosophic sets can accomodate more uncertainty compare to hesitant fuzzy sets and hesitant intuitionistic sets. On the other hand, triangular neutrosophic numbers are often used by the decision makers to evaluate their opinion in multi-attribute group decision making problems. Based on the combination of triangular neutrosophic numbers and hesitant neutrosophic sets, in this paper, we propose hesitant triangular neutrosophic numbers. Also, we discuss various types of operations between them including some properties. Then, we propose various types of hesitant triangular neutrosophic weighted aggregation operators to aggregate the hesitant triangular neutrosophic information. Furthermore, we introduce score of hesitant triangular neutrosophic numbers to ranking the hesitant triangular neutrosophic numbers. Based on the hesitant triangular neutrosophic weighted aggregation operators and score of hesitant triangular neutrosophic numbers, we develop a multi attribute decision making (MADM) approach, in which the evaluation values of alternatives on the attribute are represented in terms of hesitant triangular neutrosophic numbers and the alternatives are ranked according to the values of the score of hesitant triangular neutrosophic numbers to select the most desirable one. Finally, we give a practical example, including a comparision study with the other existing method, for enterprise resource planning system selection to verify the application and effectiveness of the proposed method.

Neutrosophic cubic fuzzy sets (NCFSs) involve interval valued and single valued neutrosophic sets, and are used to describe uncertainty or fuzziness in a more efficient way. Aggregation of neutrosopic cubic fuzzy information is crucial and necessary in a decision making theory. In order to get a better solution to decision making problems under neutrosophic cubic fuzzy environment, this paper introduces an aggregating operator to neutrosophic cubic fuzzy sets with the help of Bonferroni mean and geometric mean, and proposes neutrosophic cubic fuzzy geometric Bonferroni mean operator (NCF GBMu,v) with its properties. Then, an efficient decision making technique is introduced based on weighted operator WNCF GBMu,v w . An application of the established method is also examined for a real life problem.

The principal purpose of this paper is to analyze different methods for decision making, with a focus on entrepreneurship in Latin America. Decision-making methods may be informed by aggregation operators that are based on the use of probabilities, weighted averages (WAs) and generalized aggregation operators. The paper presents a new generalized probabilistic weighted averaging (GPWA) operator that unifies WAs and probability in the same formulation, considering the degree of importance of each concept used in the analysis. The fundamental advantage of this approach is that it includes a wide range of particular cases including the probabilistic weighted averaging (PWA) operator, the probabilistic weighted geometric averaging (PWGA) operator and the probabilistic weighted quadratic averaging (PWQA) operator. Quasi-arithmetic means are used to obtain the Quasi-PWA operator and to generalize the approach, which is then applied to a set of hypothetical entrepreneurial investment decisions in a politically unified Latin American region.

In this paper, appropriate least-squares methods were developed to operate in data fusion scenarios. These methods generate optimal estimates by combining measurements from a finite collection of samples. The aggregation operators of the average type, namely, ordered weighted averaging (OWA), Choquet integral, and mixture operators, were applied to formulate the optimization problem. Numerical examples about fitting curves to a given set of points are provided to show the effectiveness of the proposed algorithms.

The key objective of the proposed work in this paper is to introduce a generalized form of linguistic picture fuzzy set, so-called linguistic spherical fuzzy set (LSFS), combining the notion of linguistic fuzzy set and spherical fuzzy set. In LSFS we deal with the vague and defective information in decision making. LSFS is characterized by linguistic positive, linguistic neutral and linguistic negative membership degree which satisfies the conditions that the square sum of its linguistic membership degrees is less than or equal to 1. In this paper, we investigate the basic operations of linguistic spherical fuzzy sets and discuss some related results. We extend operational laws of aggregation operators and propose linguistic spherical fuzzy weighted averaging and geometric operators based on spherical fuzzy numbers. Further, the proposed aggregation operators of linguistic spherical fuzzy number are applied to multi-attribute group decision-making problems. To implement the proposed models, we provide some numerical applications of group decision-making problems. In addition, compared with the previous model, we conclude that the proposed technique is more effective and reliable.

Aggregation operators perform a valuable and significant role in various decision-making processes. Averaging and geometric aggregation operators are both used for capturing the interrelationships of the aggregated preferences, even if the preferences are independent. The purpose of this paper is to analyze the theory of complex linguistic fuzzy (CLF) sets and their important laws, such as algebraic laws, score values, and accuracy values, and to describe the relationship between the score and accuracy values with the help of their properties. Additionally, based on the proposed CLF information, we introduce the theory of CLF weighted averaging (CLFWA), CLF ordered weighted averaging (CLFOWA), CLF hybrid averaging (CLFHA), CLF weighted geometric (CLFWG), CLF ordered weighted geometric (CLFOWG), and CLF hybrid geometric (CLFHG) operators. The fundamental properties and some valuable results of these operators are evaluated, and their particular cases are described. Based on the presented operators, a technique for evaluating the “multi-attribute decision-making” (MADM) problems in the consideration of CLF sets is derived. The superiority of the derived technique is illustrated via a practical example, a set of experiments, and significant and qualitative comparisons. The illustration results indicate that the derived technique can be feasible and superior in evaluating CLF information. Further, it can be used for determining the interrelationships of attributes and the criteria of experts. Moreover, it is valuable and capable of evaluating the MADM problems using CLF numbers.

Information management is a common paradigm in modern decision-making. A wide range of decision-making techniques have been proposed in the literature to model complex business processes. In this Special Issue, 16 selected and peer-reviewed original research articles contribute to business information management in various current real-world problems by proposing crisp or uncertain multiple-criteria decision-making (MCDM) models and techniques, mostly including multi-attribute decision-making (MADM) approaches in addition to a single paper proposing an interactive multi-objective decision-making (MODM) approach. The papers are mainly concentrated in three application areas: supplier selection and rational order allocation, the evaluation and selection of goods or facilities, and personnel selection/partner selection. A number of new approaches are proposed that are expected to attract great interest from the research community.

Literature of aggregation operators defined in the domains of linguistic and interval-valued linguistic information is extensive and vast. But, some operators are not well-defined and do not benefit the researchers. In this paper, we have highlighted the flaws in defining the operators and demonstrated them via examples. Further, some remedial suggestions for the improvement of the definitions are given.

Since its initiation, hesitant fuzzy sets (HFSs) have gained prominence thanks to their capability to describe the hesitation of experts to assign membership degrees to objects belonging to a concept. Proportional hesitant fuzzy sets (PHFSs) are an important extension of HFSs and are characterized by the combination of possible membership degrees and their associated proportional information. PHFSs have a huge application potential for hesitant fuzzy GDM problems, because the proportional information in PHFSs can be determined objectively and the introduction of this new information dimension can effectively reduce the uncertainty. Nevertheless, PHFSs have not yet attracted sufficient attention from researchers and practitioners, which motivates us to expand the theory of PHFSs and explore its application potential. The main work comprises the following three aspects: First, we define some basis operations on PHFSs, develop aggregation operators for PHFSs, and demonstrate their properties and interrelationships to lay the theoretical foundations for the application of PHFSs. Next, we construct two multicriteria group decision making (MCGDM) models based on the proposed PHFS-based aggregation operators to bridge between theory and practice for PHFSs. In this step, we propose a method for transforming HFSs or fuzzy sets (FSs) into PHFSs, and two methods based on the maximum entropy principle are proposed for specifying criterion weights. Finally, we investigate a practical case study of the problem of selecting an electric vehicle battery (EVB) supplier to validate the outstanding advantages of PHFSs, explore the compensation characteristics and the applicability of the PHFS-based aggregation operators, and demonstrate the effectiveness and feasibility of the proposed MCGDM models. This paper provides a useful reference for MCGDM in a hesitant fuzzy context.

Purpose – Intuitionistic linguistic fuzzy information (ILFI), characterized by linguistic terms and intuitionistic fuzzy sets (IFSs), can easily express the fuzzy information in the process of muticriteria decision making (MCDM) and muticriteria group decision making (MCGDM) problems. The purpose of this paper is to provide an overview of aggregation operators (AOs) and applications of ILFI. Design/methodology/approach – First, some meaningful AOs for ILFI are summarized, and some extended MCDM approaches for intuitionistic uncertain linguistic variables (IULVs), such as extended TOPSIS, extended TODIM, extended VIKOR, are discussed. Then, the authors summarize and analyze the applications about the AOs of IULVs. Findings – IULVs, characterized by linguistic terms and IFSs, can more detailed and comprehensively express the criteria values in the process of MCDM and MCGDM. Therefore, lots of researchers pay more and more attention to the MCDM or MCGDM methods with IULVs. Originality/value – The authors summarize and analyze the applications about the AOs of IULVs Finally, the authors point out some possible directions for future research.

In distributed processing systems it is often necessary to coordinate the allocation of shared resources that should be assigned in the processes in the modality of mutual exclusion; in such cases, the order in which the shared resources will be assigned in the processes that require them must be decided; in this paper we propose an aggregation operator (which could be used by a shared resources manager module) that will decide the order of allocation of the resources to the processes considering the requirements of the processes (shared resources) and the state of the distributed nodes where the processes operate (their computational load).

This paper elaborates the different methods to generate normalized weight vector in multi-criteria decision-making where the given information of both criteria and inputs are uncertain and can be expressed by basic uncertain information. Some general weight allocation paradigms are proposed in view of their convenience in expression. In multi-criteria decision-making, the given importance for each considered criterion may have different extents of uncertainty. Accordingly, we propose some special induced weight-allocation methods. The inputs can be also associated with varying uncertainty extents, and then we develop several induced weight-generation methods for consideration. In addition, we present some suggested and prescriptive weight allocation rules and analyze their reasonability.

The evaluation of the players' performance in sports teams is commonly based on the opinion of experts who do not always agree on the importance of the chosen indicators. This paper presents a novel approach based on fuzzy multi-criteria group decision-making tools for selecting those criteria that best represent the handball player's performance in a match and for setting their relevance weights. Our approach consists of a fuzzy model to aggregate expert judgments. This methodology overcomes some drawbacks of classical systems, including the definition of the relevance of each criteria using linguistic labels. A preliminary evaluation analyzes handball players' performance indicators and their application to a short tournament. Considering the obtained results, we can conclude that the proposal is relevant and provides useful insights regarding player performance in different matches. The proposed methodology has also been compared with a basic plus-minus rating methodology. This comparison illustrates the feasibility of our approach. Results suggest that plus-minus rating is not the best solution to represent the performance of specialized players who only play when their team attack or defense. Our approach demonstrates being more appropriate for sports such as handball because it includes the valuation of a full set of positive actions in defense and attack.

From last few decades criminal activities and terror attacks have been increased. In a big city or in highly populated city, it is very difficult to keep under surveillance each and every area of that city throughout whole day and night. Since, it will require huge amount of deployment of police duty and such type of deployment can cause heavy work load on the enforcement agencies. It has been seen that, some types of areas are often targeted by terrorist than others, mainly train junctions, bus stoppages, market places, near temples etc. In this paper, a new aggregation operator on generalized triangular fuzzy number has been defined. Through the newly developed aggregation operator, a fuzzy multi criteria decision making approach has been constructed which enables us to determine the area of a city which may be the potentially under threat, during any interval of time on a regular working day.

Interval-valued Pythagorean fuzzy (IVPF) set is one the successful extension of the existing theories for handling the uncertainties during the decision-making process. Under that environment, various aggregation operators have been developed by the authors to aggregate the different preferences of the decision makers under the different attributes. But these studies have conducted under the assumption that their corresponding pairs are independent and don’t consider the interaction between the pairs of the membership degrees. In this paper, these conditions have been relaxed by considering the interrelationship between the different inputs by using Maclaurin symmetric mean (MSM) operator. Further, based on the input and MSM operator, we proposed two aggregation operators namely, IVPF Maclaurin symmetric mean and IVPF weighted Maclaurin symmetric mean operators and studied their desirable properties. A decision-making method based on these operators has been discussed for solving the decision-making problems under IVPF set environment. Finally, an illustrative example and a comparative analysis have been presented to demonstrate the proposed approach.

The ordered weighted averaging (OWA) operator is one of the most used techniques in the operator’s aggregation procedure. This paper proposes a new assignment algorithm by using the OWA operator and different extensions of it in the Branch-and-bound algorithm. The process is based on the use of the ordered weighted average distance operator (OWAD) and the induced OWAD operator (IOWAD). We present it as the Branch-and-bound algorithm with the OWAD operator (BBAOWAD) and the Branch-and-bound algorithm with the IOWAD operator (BBAIOWAD). The main advantage of this approach is that we can obtain more detailed information by obtaining a parameterized family of aggregation operators. The application of the new algorithm is developed in a consumer decision-making model in the city of Barcelona regarding the selection of groceries by districts that best suit their needs. We rely on the opinion of local commerce experts in the city. The key advantage of this approach is that we can consider different sources of information independent of each other.

In this paper, we propose a multi-group SIR to simulate the spread of COVID-19 in an island context. The multi-group aspect enables us to modelize transmissions of the virus between non-vaccinated individuals within an age group as well as between different age groups. In addition, fuzzy subsets and aggregation operators are used to account for the increased risks associated with age and obesity within these different groups. From a conceptual point of view, the model emphasizes the notion of Hospitalization which is the major stake of this pandemic by replacing the compartment R (Removed) by compartment H (Hospitalization). The experimental results were carried out using medical and demographic data from the archipelago, Guadeloupe (French West Indies) in the Caribbean. These results show that without the respect of barrier gestures, a first wave would concern the elderly then a second the adults and the young people, which conforms to the real data.

Ambiguous and uncertain facts can be handled using a hesitant 2-tuple linguistic set (H2TLS), an important expansion of the 2-tuple linguistic set. The vagueness and uncertainty of data can be grabbed by using aggregation operators. Therefore, aggregation operators play an important role in computational processes to merge the information provided by decision makers (DMs). Furthermore, the aggregation operator is a potential mechanism for merging multisource data which is synonymous with cooperative preference. The aggregation operators need to be studied and analyzed from various perspectives to represent complex choice situations more readily and capture the diverse experiences of DMs. In this manuscript, we propose some valuable operational laws for H2TLS. These new operational laws work through the individual aggregation of linguistic words and the collection of translation parameters. We introduced a hesitant 2-tuple linguistic weighted average (H2TLWA) operator to solve multi-criteria group decision-making (MCGDM) problems. We also define hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator, hesitant 2-tuple linguistic geometric Bonferroni mean (H2TLGBM) operator, hesitant 2-tuple linguistic Heronian mean (H2TLHM) operator, and a hesitant 2-tuple linguistic geometric Heronian mean (H2TLGHM) operator based on the novel operational laws proposed in this paper. We define the aggregation operators for addition, subtraction, multiplication, division, scalar multiplication, power and complement with their respective properties. An application example and comparison analysis were examined to show the usefulness and practicality of the work.