Interval-valued fermatean fuzzy sets with multi-criteria weighted aggregated sum product assessment-based decision analysis framework

A new approach to MADM problem using interval-valued hesitant Fermatean fuzzy Hamacher operators and statistical variance

Water ecological civilization construction (WECC) is regarded as the core and cornerstone of ecological civilization construction. However, a lot of uncertainty is involved in assessing the WECC level, which presents serious and intricate difficulties for the related multiple- attribute decision-making (MADM) processes. The interval-valued hesitant Fermatean fuzzy set (IVHFFS) is a powerful tool for handling uncertainty in MADM issues. However, in the existing MADM approaches, attribute weight calculation involves high data redundancy and low computational efficiency. The existing aggregation operators ignore the importance of the attributes and their ordered positions. In order to solve these problems, in this paper, we propose a novel MADM model using interval-valued hesitant Fermatean fuzzy (IVHFF) Hamacher aggregation operator (AO) and statistical variance (SV) weight calculation. Firstly, the SV weight calculation method is given under IVHFFSs, aiming to computing objective weights of attributes. This greatly reduces data redundancy and improves the computational complexity. Secondly, we propose some IVHFF Hamacher AOs, such as IVHFF Hamacher (ordered) weighted averaging operator, IVHFF Hamacher (ordered) weighted geometric operator, IVHFF Hamacher hybrid averaging operator and geometric operator which consider the significance of the attributes and their ordered positions. Thirdly, a new MADM model based on the above information AOs and SV weight calculation is proposed. Finally, a comparative study on the real-world application for WECC and randomly generated data sets is also carried out to further demonstrate that our method outperforms the existing methods.

An investment decision framework for offshore CCUS project under interval-valued fermatean fuzzy environment

Carbon Capture, Utilization and Storage (CCUS) is an indispensable technology for achieving a net-zero emission society. The offshore CCUS project is still in its infancy. To promote its sustainable development, developing a comprehensive framework for investment decision-making is very crucial. First, a comprehensive evaluation criteria system is established. Second, in order to characterize the ambiguity and uncertainty of information in the process of making decisions, the interval-valued fermatean fuzzy set (IVFFS) is introduced, and the extended variance method of IVFFS is proposed to systematically calculate the weights of experts. Then, the power weighted average (PWA) operator based similarity measure of IVFFSs is developed to aggregate different expert information. Meanwhile, the fuzzy-weighted zero-inconsistency (FWZIC) method and the method based on the removal effects of criteria (MEREC) are used to determine the criteria weights. In addition, considering the interactions between the criteria, we introduce the Hamacher operator into the measurement of alternatives and ranking according to the compromise solution (MARCOS) method to select the optimal alternative in the interval-valued fermatean fuzzy (IVFF) environment. The suggested framework is then used to analyse a case study. After that, sensitivity and comparative analyses are conducted to confirm its robustness and viability. This study creates a practical investment framework for offshore CCUS projects, identifies a number of investment-sensitive criteria and provides management insights. The proposed framework expands the methods and applications in the field of decision-making and provides a scientific approach for investment decision-making in offshore CCUS projects, which can be a useful reference for managers.

A circular economy based nonlinear corrugated waste management system using Fermatean bipolar hesitant fuzzy logic

In the era of increasing environmental awareness, the importance of efficient waste management cannot be overstated. Cardboard stands out among the many materials contributing to waste generation. With proper cardboard collection and recycling practices, one can make a significant difference and lead the way towards a more sustainable future. In this regard, this article attempts to configure an integrated green non-linear transportation system with circular economy approach to mitigate the negative effect of corrugated waste on social, economic and environmental sites. This non-linear transportation system aims to optimize objectives including overall transport expenditure, carbon footprints and travel time. One sub model is further developed from the proposed model by disuniting the effect of the circular economy. Here, to depict the uncertainty time sequential Fermatean bipolar hesitant fuzzy set theory is devised along with its all-dimensional aspects. The suggested transportation system is addressed by employing two approaches, weighted sum approach and global criterion methodology. Additionally, a case study is conducted to elaborate on the relevance of the devised model for sustainable management of corrugated waste. The results show that global criterion approach produces better results when three objectives are optimally valued as [Formula: see text]. The results indicate that the integration of circular economy into a supply chain model brings sustainability and reduces the ecological and human hazards associated with it. Finally, there is a sensitivity analysis, management insights, and a conclusion with limitations and future plans.

Assessing the adoption barriers for the AI in food supply chain finance applying a hybrid interval-valued Fermatean fuzzy CRITIC-ARAS model

The identification and evaluation of barriers to artificial intelligence (AI) adoption in food supply chain finance (FSCF) can be addressed as a multiattribute decision-making problem. However, only a few studies have reported the application of decision models for evaluating barriers to the implementation of AI in FSCF, especially within an uncertain context. Hence, this work explores the evaluation issue of implementation barriers via an integrated decision model. In this model, the conventional additive ratio assessment (ARAS) model integrated with the Choquet integral and criteria importance through intercriteria correlation (CRITIC) is extended into the interval-valued Fermatean fuzzy (IVFF) setting for ranking the barriers. The IVFF weighted average operator based on the Choquet integral is introduced to form a group decision matrix. Then, the developed ARAS model with the IVFF-CRITIC method is proposed to evaluate the implementation barriers for AI in FSCF, which can depict the interactions between the barriers. Finally, a case of an FSCF, including four participants, is presented to illustrate the application of the reported model and demonstrate its reliability. The result shows that "Data privacy" ([Formula: see text]) is the main barrier impeding AI adoption in FSCF, and the participant "small and medium-sized processing enterprises" ([Formula: see text]) has the highest barrier level to AI adoption.

Fermatean fuzzy Linguistic term set based on linguistic scale function with Dombi aggregation operator and their application to multi criteria group decision -making problem

The selection of an industrial location is a challenging multiple-criteria decision-making (MCDM) problem that depends on taking a variety of locations as well as incompatible and inconsistent criteria. This paper proposed a comprehensive framework for the strategic selection of industrial locations, considering both quantitative and qualitative aspects. Decision-makers (DMs) have to deal with ambiguous information throughout this process due to a complex decision environment or their insufficient knowledge. We present a new Fermatean Fuzzy (FF) Linguistic term set based on the Dombi aggregation operators (AOs). By combining the FF set with Linguistic variables, the FF Linguistic (FFL) set is an effective approach for thoroughly representing uncertain evaluation information. We establish a basic operational principles and certain aggregation operator under FFL information, such as the FF Linguistic Dombi weighted averaging (FFLDWA) operator FF Linguistic Dombi weighted geometric (FFLDWG) operator and some fundamental properties of these operators with appropriated elaboration. Based on these operators, a multi-criteria group decision-making technique is developed. Finally, we used a numerical example to compare the flexibility of the suggested technique with other existing methods. Thus, by knowing priorities industries, the best site can be selected.

A new multi-attribute group decision-making method based on Einstein Bonferroni operators under interval-valued Fermatean hesitant fuzzy environment

Faced with the increasing complexity and uncertainty of decision-making information, interval-valued Fermatean hesitant fuzzy sets (IVFHFSs) were presented as a novel mathematical model that handled uncertain data more effectively. However, existing multi-attribute group decision-making (MAGDM) methods based on IVFHFSs do not thoroughly investigate the operational laws. Also, these existing MAGDM methods do not take into account the connections between attributes and are less flexible. To address these issues, this paper proposes a new MAGDM method based on Einstein Bonferroni operators under IVFHFSs. First, we thoroughly examine the operational laws of Einstein t-norms under the IVFHFSs to further extend the study of the operational laws. Then, we introduce the interval-valued Fermatean hesitant fuzzy Einstein Bonferroni mean operator and the interval-valued Fermatean hesitant fuzzy Einstein weighted Bonferroni mean operator under Einstein t-norms. Our suggested aggregation operators consider the relationship between attributes and are far more flexible in comparison to the current approaches. Later, a novel MAGDM method based on Einstein Bonferroni operators under the IVFHFSs is given. Finally, the practicality and validity of the proposed method are demonstrated by a cardiovascular disease diagnosis application.

Complex Fermatean fuzzy extended TOPSIS method and its applications in decision making

The fuzzy set has its own limitations due to the membership function only. The fuzzy set does not describe the negative aspects of an object. The Fermatean fuzzy set covers the negative aspects of an object. The complex Fermatean fuzzy set is the most effective tool for handling ambiguous and uncertain information. The aim of this research work is to develop new techniques for complex decision-making based on complex Fermatean fuzzy numbers. First, we construct different aggregation operators for complex Fermatean fuzzy numbers, using Einstein t-norms. We define a series of aggregation operators named complex Fermatean fuzzy Einstein weighted average aggregation (CFFEWAA), complex Fermatean fuzzy Einstein ordered weighted average aggregation (CFFEOWAA), and complex Fermatean fuzzy Einstein hybrid average aggregation (CFFEHAA). The fundamental properties of the proposed aggregation operators are discussed here. The proposed aggregation operators are applied to the decision-making technique with the help of the score functions. We also construct different algorithms based on different aggregation operators. The extended TOPSIS method is described for the decision-making problem. We apply the proposed extended TOPSIS method to MAGDM problem "selection of an English language instructor". We also compare the proposed models with the existing models.

A decision-making technique under interval-valued Fermatean fuzzy Hamacher interactive aggregation operators

The evolution of a novel technique to handle multi-attribute decision-making (MADM) problems under interval-valued Fermatean fuzzy numbers is the main motivation of this paper. We aim to introduce several initiative aggregation operators (AOs), including Hamacher interactive weighted averaging, Hamacher interactive ordered weighted averaging, Hamacher interactive hybrid weighted averaging operations, etc., to acquire our desired outcomes. Then, the distinguished characteristics of these AOs are investigated. Furthermore, the suggested AOs are carried out to build a technique to MADM issues using interval-valued Fermatean fuzzy information. A case study of mine emergency plan selection is then narrated to elaborate the practicality and effectiveness of the developed method. The influence of parametric values on decision-making outcomes is investigated considering the distinct values of parameter. After discussing the developed work and seeing its applications, we come across with the conclusion that the dominant privilege of adaptation of the above-mentioned AOs is situated in the fact that these operators allow a progressively complete approach on the matters to decision-makers. Hence, the method recommended in this study offers progressively wide, enhanced accuracy and actual outcomes when compared with the prevailing associated strategies. Therefore, this technique plays a vital role in actual-life MADM problems.

A new multi-attribute decision making approach based on new score function and hybrid weighted score measure in interval-valued Fermatean fuzzy environment

Interval-valued Fermatean fuzzy sets (IVFFSs) were introduced as a more effective mathematical tool for handling uncertain information in 2021. In this paper, firstly, a novel score function (SCF) is proposed based on IVFFNs that can distinguish between any two IVFFNs. And then, the novel SCF and hybrid weighted score measure were used to construct a new multi-attribute decision-making (MADM) method. Besides, three cases are used to demonstrate that our proposed method can overcome the disadvantages that the existing approaches cannot obtain the preference orderings of alternatives in some circumstances and involves the existence of division by zero error in the decision procedure. Compared with the two existing MADM methods, our proposed approach has the highest recognition index and the lowest error rate of division by zero. Our proposed method provides a better approach to dealing with the MADM problem in the interval-valued Fermatean fuzzy environment.

Multi-attribute decision-making for electronic waste recycling using interval-valued Fermatean fuzzy Hamacher aggregation operators

The utilization of electrical and electronics equipments in waste recycling has become a paramount for various countries. The waste electrical and electronics equipment (WEEE) recyclers own a crucial position in the environmental growth of a country as they help to minimize the carbon emissions during the recycling of WEEE in the most eco-friendly way. Therefore, the selection and assessment of an appropriate WEEE recycling partner has become a most important part of DM (decision-making) applications. The collusion of numerous quantitative and qualitative factors makes the recycling partner selection problem, a multifaced and significant decision for the managerial experts. The main objective of this work is to propose MADM (multi-attribute decision-making) techniques to evaluate the WEEE recycling partners under interval-valued Fermatean fuzzy (IVFF) information. In this regard, certain Hamacher AOs (aggregation operators) are proposed to develop the required DM method. These AOs include Hamacher weighted averaging, ordered weighted averaging, weighted geometric, ordered weighted geometric, generalized Einstein weighted averaging, generalized Einstein ordered weighted averaging, generalized Einstein weighted geometric, etc. Then, these averaging operators are utilized to come up with a MADM techniques under IVFF environment. Furthermore, the constructed technique is applied to a case study in China to incorporate with the e-waste recycling partner selection problem. Moreover, a brief comparison of the proposed with is presented with various existing techniques to manifest the productivity and coherence of the proposed model. Finally, the accuracy and consistency of results shows that the proposed technique is fully compatible and applicable to handle any MADM problem.