Hesitant Pythagorean fuzzy ELECTRE-II method for multi-criteria decision-making problems

An appropriate artificial intelligence technique for plastic materials recycling using bipolar dual hesitant fuzzy set

Plastic recycling has become more important than ever as the globe struggles with growing environmental issues. This research explores the significant environmental impact of recycling plastic and its growing relevance. The pervasive material known as plastic presents a complex risk to both human health and ecosystems in contemporary life. It exacerbates problems including marine pollution, habitat damage, and wildlife entanglement because of its persistence in landfills and seas, which leads to serious ecological deterioration. In addition, producing plastic uses a lot of energy and produces a lot of greenhouse gas emissions, which exacerbate climate change. Through the use of multi-criteria decision making (MCDM), this study emphasizes how vital it is to support recycling activities in order to protect the environment and promote a sustainable future. The elimination and choice ex-pressing reality (ELECTRE) approach is used to rank the alternatives in this proposed research study that employs bipolar dual hesitant fuzzy sets (BDHFs). The most efficient and versatile outranking method for making decisions is the BDHF-ELECTRE approach. The weights of environment, economic, social, technical, and finally safety is computed using the entropy distance metric. The economic factor received the highest score of 0.2945 among the other factors since economic considerations are crucial in choosing the most efficient plastic recycling method, as they ensure sustainability, cost-effectiveness, resource allocation, and overall feasibility in managing plastic waste. The decision-makers determined that the mechanical recycling approach ought to be prioritized over all others for the efficient recycling of plastic waste. The robustness of the system is examined in the sensitive and comparative analyses. The proposed MCDM technique thus presents a viable solution, mitigating the adverse effects of plastic waste by conserving resources, reducing energy consumption, and curbing pollution.

Multi-attribute decision-making method based on q-rung orthopair probabilistic hesitant fuzzy schweizer-sklar power weighted hamy mean operator

In order to further improve the computing power of the information aggregation operator in the q-rung orthopair probabilistic hesitant fuzzy environment, this paper proposes a multi-attribute decision-making method based on the q-rung orthopair probabilistic hesitant fuzzy Schweizer-Sklar power weighted Hamy mean operator. Firstly, the algorithm of q-rung orthopair probabilistic hesitant fuzzy set is improved based on the Schweizer-Sklar T-norm. In order to better reflect the degree of hesitation of decision-making experts, a new q-rung orthopair probabilistic hesitant fuzzy distance measure is proposed, which provides a basis for subsequent power weighted calculations. Furthermore, considering the correlation between attributes and the influence of data extremes, some information aggregation operators and their power weighted forms are proposed. Finally, a multi-attribute decision-making model based on the q-rung orthopair probabilistic hesitant fuzzy Schweizer-Sklar power weighted Hamy mean operator is established, and the reliability and validity of the research content in this paper are verified through decision-making examples and comparative analysis.

Archimedean Aggregation Operators Based on Complex Pythagorean Fuzzy Sets Using Confidence Levels and Their Application in Decision Making

The diagnosed complex Pythagorean fuzzy (CPF) set is a more valuable and dominant tool than the Pythagorean and intuitionistic fuzzy sets to describe awkward and unreliable information more effectively. Further, Archimedean t-norm and t-conorm have a significant influence to depict the relation among aggregated values. To take advantage of the CPF set and Archimedean t-norm and t-conorm, and assume the relation among Archimedean norms and algebraic, Einstein, Hamacher, and frank norms at the same time, in this analysis, first, we proposed the fundamental Archimedean operational laws. Second, based on these laws, we developed confidence CPF Archimedean-weighted averaging (CCPFSAWA), confidence CPF Archimedean-ordered weighted averaging (CCPFSAOWA), confidence CPF Archimedean-weighted geometric (CCPFSAWG), confidence CPF Archimedean-ordered weighted geometric (CCPFSAOWG) operators and implemented their valuable results and properties. We know that Archimedean t-norm and t-conorm are the general form of the all-aggregation operators, so by using different values of t-norm and t-conorm, we explored the confidence CPF-weighted averaging (CCPFWA), confidence CPF-ordered weighted averaging (CCPFOWA), confidence CPF Einstein-weighted averaging (CCPFEWA), confidence CPF Einstein-ordered weighted averaging (CCPFEOWA), confidence CPF Hamacher-weighted averaging (CCPFHWA), confidence CPF Hamacher-ordered weighted averaging (CCPFHOWA), confidence CPF frank-weighted averaging (CCPFFWA), confidence CPF frank-ordered weighted averaging (CCPFFOWA), confidence CPF-weighted geometric (CCPFWG), confidence CPF-ordered weighted geometric (CCPFOWG), confidence CPF Einstein-weighted geometric (CCPFEWG), confidence CPF Einstein-ordered weighted geometric (CCPFEOWG), confidence CPF Hamacher-weighted geometric (CCPFHWG), confidence CPF Hamacher-ordered weighted geometric (CCPFHOWG), confidence CPF frank-weighted geometric (CCPFFWG), and confidence CPF frank-ordered weighted geometric (CCPFFOWG) operators. Then, we developed a multi-attribute decision-making (MADM) method based on the proposed operators. Finally, many examples are used to do comparative analysis among proposed and existing methods to show the validation of the new approaches.

The differential measure for Pythagorean fuzzy multiple criteria group decision-making

Pythagorean fuzzy sets (PFSs) proved to be powerful for handling uncertainty and vagueness in multi-criteria group decision-making (MCGDM). To make a compromise decision, comparing PFSs is essential. Several approaches were introduced for comparison, e.g., distance measures and similarity measures. Nevertheless, extant measures have several defects that can produce counter-intuitive results, since they treat any increase or decrease in the membership degree the same as the non-membership degree; although each parameter has a different implication. This study introduces the differential measure (DFM) as a new approach for comparing PFSs. The main purpose of the DFM is to eliminate the unfair arguments resulting from the equal treatment of the contradicting parameters of a PFS. It is a preference relation between two PFSs by virtue of position in the attribute space and according to the closeness of their membership and non-membership degrees. Two PFSs are classified as identical, equivalent, superior, or inferior to one another giving the degree of superiority or inferiority. The basic properties of the proposed DFM are given. A novel method for multiple criteria group decision-making is proposed based on the introduced DFM. A new technique for computing the weights of the experts is developed. The proposed method is applied to solve two applications, the evaluation of solid-state drives and the selection of the best photovoltaic cell. The results are compared with the results of some extant methods to illustrate the applicability and validity of the method. A sensitivity analysis is conducted to examine its stability and practicality.

New optimization technique for group decision analysis with complex pythagorean fuzzy sets

The striking theory of ELECTRE III approach, being a marvelous strategy to deal with pseudo criterion, prevails over the traditional variants of ELECTRE method and other decision-making approaches for veracious decision-making. The noticeable efficiency and broader space of complex Pythagorean fuzzy model make it more significant and dominant for modeling two dimensional imprecise knowledge. The remarkable contribution of this study is to present a high aptitude variant of ELECTRE method by taking the advantage of the flexible structure of complex Pythagorean fuzzy sets closely following the outranking principles of ELECTRE III method. The proposed complex Pythagorean fuzzy ELECTRE III method is accredited to employ the theory of ELECTRE III technique to excellently deal with pseudo criterion as well as the two dimensional imprecise data for authentic decision-making. The proposed methodology uses three different threshold values, including preference, indifference and veto threshold values, to check the preference relation between alternatives. The presented strategy is applied to a case study for material selection to get the befitting decision. The comparative study with Pythagorean fuzzy ELECTRE III method is also included in this article to verify its decision-making aptitude.

Interactive group decision making method based on probabilistic hesitant Pythagorean fuzzy information representation

Interactive group evaluation is a decision-making method to obtain group consensus by constantly modifying the initial weight of experts. Probabilistic hesitant Pythagorean fuzzy set (PrHPFS) is to be added the corresponding probability values for each membership degree and non-membership degree on the hesitant Pythagorean fuzzy set (HPFS). It is not only a generalization of HPFS and the Pythagorean fuzzy set (PFS), but also a more comprehensive and accurate reflection of the initial decision information given by experts. Especially, it can deal with the decision-making problem of multi-attribute fuzzy information in a wider area. In this paper, some basic definitions and related operations of the probabilistic hesitant Pythagorean fuzzy numbers (PrHPFNs) are first reviewed, and propose score function and accuracy function in PrHPFNs environment. Secondly, the concepts of Hamming distance measure, weighted distance measure and degree of similarity are put forward in PrHPFNs space, and the degree of similarity of two probabilistic hesitant Pythagorean fuzzy matrices (PrHPFMs) is suggested through the aggregation operator formula of PFNs. Finally, an interactive group decision-making method is designed based on the PrHPFM and the degree of similarity under the PrHPFNs environment, the effectiveness of the method is verified by an example, so as to overcome the hesitant psychological state of experts and achieve the consistent consensus evaluation of group preference.

Onsite/offsite social commerce adoption for SMEs using fuzzy linguistic decision making in complex framework

There has been a growing social commerce adoption trend among SMEs for few years. However, it is often a challenging strategic task for SMEs to choose the right type of social commerce. SMEs usually have a limited budget, technical skills and resources and want to maximise productivity with those limited resources. There is much literature that discusses the social commerce adoption strategy for SMEs. However, there is no work to enable SMEs to choose social commerce-onsite/offsite or hybrid strategy. Moreover, very few studies allow the decision-makers to handle uncertain, complex nonlinear relationships of social commerce adoption factors. The paper proposes a fuzzy linguistic multi-criteria group decision-making in a complex framework for onsite, offsite social commerce adoption to address the problem. The proposed approach uses a novel hybrid approach by combining FAHP, FOWA and selection criteria of the technological-organisation-environment (TOE) framework. Unlike previous methods, the proposed approach uses the decision maker's attitudinal characteristics and recommends intelligently using the OWA operator. The approach further demonstrates the decision behaviour of the decision-makers with Fuzzy Minimum (FMin), Fuzzy Maximum (FMax), Laplace criteria, Hurwicz criteria, FWA, FOWA and FPOWA. The framework enables the SMEs to choose the right type of social commerce considering TOE factors that help them build a stronger relationship with current and potential customers. The approach's applicability is demonstrated using a case study of three SMEs seeking to adopt a social commerce type. The analysis results indicate the proposed approach's effectiveness in handling uncertain, complex nonlinear decisions in social commerce adoption.

Improved ELECTRE II sustainability assessment framework in power generation technological evaluation

With the economic growth of the world, sustainable development is a popular issue in recent years. Sustainable assessment is an important part of sustainable development. There are many previous scholars have used multiple-criteria decision-making (MCDM) to develop different evaluation frameworks in different fields. Elimination et Choix Traduisant la Realite II (ELECTRE II) is one of the most commonly used methods for MCDM. ELECTRE II uses alternatives, criteria, and criteria weighting from decision-makers to calculate the concordance and discordance indices. These two indices are used to rank the alternatives. The concordance and discordance indices in ELECTRE II are important because they are the key to make accurate decisions. Previous scholars have failed to make comprehensive calculations for these indices, nor make their units of measure comparable, which negatively affected their results. This study improved the approach in calculating these indices and illustrated it using three case studies: (1) university examination results, (2) a sustainability assessment of groundwater remediation and (3) an assessment of power generation technologies. This improved ELECTRE II method offers decision-makers an objective basis for decision-making.

Unsymmetrical basic uncertain information with some decision-making methods

Motivated by a specific decision-making situation, this work proposes the concept and definition of unsymmetrical basic uncertain information which is a further generalization of basic uncertain information and can model uncertainties in some new decision-making situations. We show that unsymmetrical basic uncertain information in some sense can model linguistic hedges such as “at least” and “at most”. Formative weighted arithmetic means and induced aggregations are defined for the proposed concept. Rules-based decision making and semi-copula based integral for this concept with some numerical examples are also presented.

Models for MAGDM with dual hesitant q-rung orthopair fuzzy 2-tuple linguistic MSM operators and their application to COVID-19 pandemic

In this article, we introduce dual hesitantq -rung orthopair fuzzy 2-tuple linguistic set (DHq-ROFTLS), a new strategy for dealing with uncertainty that incorporates a 2-tuple linguistic term into dual hesitantq -rung orthopair fuzzy set (DHq-ROFS). DHq-ROFTLS is a better way to deal with uncertain and imprecise information in the decision-making environment. We elaborate the operational rules, based on which, the DHq-ROFTL weighted averaging (DHq-ROFTLWA) operator and the DHq-ROFTL weighted geometric (DHq-ROFTLWG) operator are presented to fuse the DHq-ROFTL numbers (DHq-ROFTLNs). As Maclaurin symmetric mean (MSM) aggregation operator is a useful tool to model the interrelationship between multi-input arguments, we generalize the traditional MSM to aggregate DHq-ROFTL information. Firstly, the DHq-ROFTL Maclaurin symmetric mean (DHq-ROFTLMSM) and the DHq-ROFTL weighted Maclaurin symmetric mean (DHq-ROFTLWMSM) operators are proposed along with some of their desirable properties and some special cases. Further, the DHq-ROFTL dual Maclaurin symmetric mean (DHq-ROFTLDMSM) and weighted dual Maclaurin symmetric mean (DHq-ROFTLWDMSM) operators with some properties and cases are presented. Moreover, the assessment and prioritizing of the most important aspects in multiple attribute group decision-making (MAGDM) problems is analysed by an extended novel approach based on the proposed aggregation operators under DHq-ROFTL framework. At long last, a numerical model is provided for the selection of adequate medication to control COVID-19 outbreaks to demonstrate the use of the generated technique and exhibit its adequacy. Finally, to analyse the advantages of the proposed method, a comparison analysis is conducted and the superiorities are illustrated.

Group decision-making analysis with complex spherical fuzzy N-soft sets

This paper develops the ELiminating Et Choice Translating REality (ELECTRE) method under the generalized environment of complex spherical fuzzy $ N $-soft sets ($ CSFN\mathcal{S}_{f}Ss $) that have distinctive and empirical edge of non-binary parametrization and also indeed overcome the limitations and flaws of existing ELECTRE I methods. We propose an innovatory decision-making technique, namely, $ CSFN\mathcal{S}_{f} $-ELECTRE I method where the data and information are in modern modes. The proposed $ CSFN\mathcal{S}_{f} $-ELECTRE I method enjoys all the distinct and modern attributes of uncertain information which mainly comprises of parameterizations, neutral perspective, multi-valuation and two-dimensional representations. We support the proposed work by a flowchart along with an algorithm and then utilize it to solve the MAGDM problem under $ CSFN\mathcal{S}_{f} $ environment. This novel technique employs the principles of $ CSFN\mathcal{S}_{f} $ concordance and $ CSFN\mathcal{S}_{f} $ discordance sets which are established on score and accuracy functions and engrossed to enjoin the most superior alternative. Ultimately, the decision graph and aggregated outranking Boolean matrix are formulated by merging the outcomes of $ CSFN\mathcal{S}_{f} $ concordance and $ CSFN\mathcal{S}_{f} $ discordance indices which are evaluated through score function and distance measures, respectively. Moreover, linear-ranking order is evaluated which provides linear ordering of decision alternatives. A prime MAGDM problem of poverty alleviation is addressed from socio-economic field that approve the flexibility of the intended approach. We perform a sustaining comparison with another approach (CSF-ELECTRE I approach) to assure the productivity and potency of the proposed methodology. We also provide an allegorical line graph of this comparison that demonstrate the admissibility of the resulting outcomes.

A new outranking method for multicriteria decision making with complex Pythagorean fuzzy information

This article contributes to the advancement and evolution of outranking decision-making methodologies, with a novel essay on the ELimination and Choice Translating REality (ELECTRE) family of methods. Its primary target is to unfold the constituents and expound the implementation of the ELECTRE II method for group decision making in complex Pythagorean fuzzy framework. This results in the complex Pythagorean fuzzy ELECTRE II method. By inception, it is intrinsically superior to models using one-dimensional data. It is designed to perform the pairwise comparisons of the alternatives using the core notions of concordance, discordance and indifferent sets, which is then followed by the construction of complex Pythagorean fuzzy concordance and discordance matrices. Further, the strong and weak outranking relations are developed by the comparison of concordance and discordance indices with the concordance and discordance levels. Later, the forward, reverse and average rankings of the alternatives are computed by the dint of strong and weak outranking graphs. This methodology is supported by a case study for the selection of wastewater treatment process, and by a numerical example for the selection of the best cloud solution for a big data project. Its consistency is confirmed by an effectiveness test and comparison analysis with the Pythagorean fuzzy ELECTRE II and complex Pythagorean fuzzy ELECTRE I methods.

Enhancing ELECTRE I Method with Complex Spherical Fuzzy Information

This article is concerned to delineate the strategic approach of ELiminating Et Choice Translating REality (ELECTRE) method for multi-attribute group decision-making (MAGDM) in terms of complex spherical fuzzy sets. The feasible, well-suited, and marvelous structure of complex spherical fuzzy set compliments the decision-making efficiency and ranking calibre of ELECTRE I approach to present a beneficial and supreme aptitude strategy for MAGDM. Beside the proposed methodology, a few non-fundamental properties of complex spherical fuzzy weighted averaging (CSFWA) operator inclusive of shift invariance, homogenous, linearity, and additive property are also explored. The proposed procedure validates the individual opinions into an acceptable form by the dint of CSFWA operator and the aggregated opinions are further analyzed by the proposed complex spherical fuzzy- ELECTRE I (CSF-ELECTRE I) method. Within the consideration of proposed methodology, normalized Euclidean distances of complex spherical fuzzy numbers are also contemplated. In CSF-ELECTRE I method, the score, accuracy, and refusal degrees determine the concordance and discordance sets for each pair of alternatives to calculate the concordance and discordance indices, respectively. Based on aggregated outranking matrix, a decision graph is constructed to attain the ELECTREcally outranked solutions and the best alternative. This article provides supplementary approach at the final step to profess a linear ranking order of the alternatives. The versatility and feasibility of the presented method are embellished with two case studies from the business and IT field. Moreover, to ratify the intensity and aptitude of the presented methodology, we provide a comparative study with complex spherical fuzzy-TOPSIS method.

Belief and Possibility Belief Interval-Valued N-Soft Set and Their Applications in Multi-Attribute Decision-Making Problems

In this research article, we motivate and introduce the concept of possibility belief interval-valued N-soft sets. It has a great significance for enhancing the performance of decision-making procedures in many theories of uncertainty. The N-soft set theory is arising as an effective mathematical tool for dealing with precision and uncertainties more than the soft set theory. In this regard, we extend the concept of belief interval-valued soft set to possibility belief interval-valued N-soft set (by accumulating possibility and belief interval with N-soft set), and we also explain its practical calculations. To this objective, we defined related theoretical notions, for example, belief interval-valued N-soft set, possibility belief interval-valued N-soft set, their algebraic operations, and examined some of their fundamental properties. Furthermore, we developed two algorithms by using max-AND and min-OR operations of possibility belief interval-valued N-soft set for decision-making problems and also justify its applicability with numerical examples.