This research study keenly employs the ground-breaking theory of ELECTRE method in order to advance the literature with a more competent technique for the frequently implemented and incredibly practical model of spherical fuzzy sets. The eminent characteristics, broader approach and adaptable model of spherical fuzzy set empowers the proposed strategy to captivate each type of the imprecise human judgement (whether in favor, against, neutral or hesitant) using a dependent and three independent membership grades. The remarkable novelty of the proposed approach is its successful application even with no criteria weights knowledge. Furthermore, the proposed technique processes the spherical fuzzy data and examines different types of preferences among alternatives using three threshold values. These preferences contribute to classify the outranking relations among the alternatives within five different levels of dominance. Later on, the iterative approach of distillation is deployed to figure out the final ranking. The proposed strategy is applied to meet the challenges in the implementation of autonomous vehicles in Turkey. After a through evaluation of five corridors via proposed technique in reference to fifteen criteria, metrobus corridor appears as the most appropriate for the autonomous vehicle operation. In the last, the consistency of the proposed approach is delineated via comparative analysis with existing spherical fuzzy CODAS and spherical fuzzy PROMETHEE approaches and other convincing evidences.

Energy production from the waste is an innovative idea to be implemented that can significantly raise one's energy production capacity via some adaptable waste-to-energy technology. This study ponders over the municipal solid waste management problem to dispose off the waste in a sanitary, beneficial and environmental friendly manner to reduce the large volume of waste. To target the waste management problem, this article designs a multi-criteria group decision-making technique to capture all the elements of the considered problem within the governance of a decision-making team. The proposed approach, spherical fuzzy ELECTRE III method, has the supplementary potential to delicately treat the pseudo criteria for the authentic investigation of the outranking relations unlike the traditional variants of ELECTRE methods which proceed on the concept of concordance and discordance sets. The proposed technique is privileged to derive the preferences in terms of indifference, strong and weak preference relations by carefully examining the explicit behavior of each criterion in accordance to indifference, preference and veto threshold values. Nextly, this study addresses the case of municipal waste management of the Azerbaijan region in Iran and investigates different waste-to-energy technologies by the proposed SF-ELECTRE III method. To enlighten the consistency of proposed approach, a comparative study with existing SF-PROMETHEE methods is conducted that includes the numerical results and logical arguments.

The digitalization of the traditional technologies have facilitated humans globally as these technologies are not only time saving, modern, environment friendly but are economic as well. This study is concerned with the digitalization of the public transportation system in Istanbul to reduce the environmental pollution that is a big cause of different harmful diseases and climate changes. This article aims to manifest the decision-making aptitude of the elimination and choice translating reality methods working within the boundaries of modern, well structured and highly adaptable model of spherical fuzzy sets keenly focusing on group decision-making by presenting two significant techniques. Thus, the proposed methodologies operate by considering the dominance and subordination between alternatives relying on the prime concepts of concordance, discordance and indifferent sets. Further, these sets are exploited to determine the concordance and discordance indices in accordance with the weights of the decision criteria. Finally, the decision is made by observing the outranking relations among alternatives using the threshold values. The proposed strategies seek help from the technique of spherical fuzzy analytical hierarchy process for the evaluation of criteria weights. Noticing the widespread scope and appealing benefits of digital systems, this article targets the digitalization of the public transportation system in Istanbul. The potential of proposed approaches are highlighted via comparative studies.

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.

This study mainly aims to develop two effective and practical multi-criteria group decision-making approaches by taking advantage of the ground-breaking theory of PROMETHEE family of outranking methods. The presented variants of Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) method are acknowledged to address the complex decision-making problems carrying the ambiguous information, expressible in terms of yes, no, abstinence and refusal, owing to the preeminent condition and wider structure of spherical fuzzy sets. Both of the proposed approaches seek help from the Shannon's entropy formula to evaluate the object weights of the decision criteria. The proposed techniques operate by taking into account the deviation between each pair of potential alternatives in accordance to different types of preference functions to determine the preference indices. The proposed technique of spherical fuzzy PROMETHEE I method carefully compares the positive and negative outranking flows of the alternative to get partial rankings. In contrast, the spherical fuzzy PROMETHEE II method has the edge to eliminate the incomparable pair by employing the net outranking flow to derive the final ranking. The application of proposed approaches is explained via a case study in the field of medical concerning the selection of appropriate site to establish Fangcang shelter hospital in Wuhan to treat COVID-19 patients. The convincing comparisons of the proposed methodologies with q-rung orthopair fuzzy PROMETHEE and spherical fuzzy TOPSIS methods are also included to verify the aptitude of the proposed methodology.

This study elevates the potential of ELECTRE IV method using the logical backgrounds of fuzzy sets in the proposed fuzzy ELECTRE IV method to capture the water supply problem of Iran. ELECTRE IV method, being an advanced variant of ELECTRE family, operates on the outranking principle to achieve the results using three types of preferences and five dominance relations that exhibit different levels of superiorities among alternatives. The proposed procedure is designed to exhibit the linguistic preferences via triangular fuzzy numbers which are compared on the basis of their corresponding magnitudes. The proposed approach successfully captures the pseudo criteria using three threshold values to filter out the preferences and then classifying the level of dominance. Moreover, ranking is derived by combining two pre-orders, i.e., ascending and descending pre-orders. The main contribution of this study is the implementation of outranking caliber of proposed fuzzy ELECTRE IV method to address the water supply problem in the Kermanshah province of Iran, concerning the selection of optimal site for Kandoleh dam. The comparisons with two existing techniques, fuzzy TOPSIS method and integrated fuzzy delphi and fuzzy ELECTRE method, are conducted to verify the authenticity and competency of the proposed technique.

This study exploits the tremendous theory of ELimination and Choice Expressing REality (ELECTRE) method to enhance the number of outranking approaches for the ground-breaking and recent extension of fuzzy set theory, namely, complex spherical fuzzy set. The noticeable edge of this striking model is its wider and flexible structure that empowers it to encompass the abstinence part of vague information in addition to satisfaction and dissatisfaction in two dimensional scenarios. In short, this article delivers the compact procedure of the widely applicable, high skilled and multi-purpose complex spherical fuzzy ELECTRE II approach. The designed algorithm of the presented methodology cumulates the worthy opinions of the decision-making experts in the light of complex spherical fuzzy weighted averaging operator. Furthermore, proposed method is privileged with the remarkable notions of concordance and discordance sets in order to unfold the pairwise relation between the alternatives regarding any criterion. The proposed approach predicts the final ranking of alternatives with the aid of crisp strong and weak outranking relations to filter the strict and weak precedence between any pair of alternatives. The practical application of the proposed approach is demonstrated via a case study to opt the most efficient technology to treat cadmium-contaminated water. A comparative study with complex spherical fuzzy ELECTRE I (CSF-ELECTRE I) and spherical fuzzy TOPSIS (SF-TOPSIS) methods is conducted to collect the enough evidence to foreground the authenticity and aptitude of proposed technique.

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.

This research article is devoted to present a decision-making approach pertaining the excellent tendencies of traditional TOPSIS method under the broader environment of complex spherical fuzzy sets (CSFSs). TOPSIS method is regarded as one of the authentic decision-making strategies that follows the scheme to point out the alternative acquiring favorable distances from the ideal solutions. On the other hand, the pre-eminent feature of the CSFS includes the tendency to handle both aspects of two-dimensional information involved in the satisfaction, abstinence and dissatisfaction nature of human decisions. This study aims to expand the number of multiple criteria group decision-making (MCGDM) techniques by presenting a strategy, named complex spherical fuzzy TOPSIS (CSF-TOPSIS) method that cumulates the novel features of complex spherical fuzzy sets with the potential of TOPSIS method. In proposed method, we merge the independent decisions of all experts about the capabilities of alternatives and priorities of criteria using the CSFWA operator. We rank the alternatives in an ascending order of revised closeness index, evaluated by deploying normalized Euclidean distance. We establish the proposed CSF-TOPSIS method by an explanatory numerical example for the selection of best water supply strategy for Nohoor village in Iran. Further, we conduct the comparative study with spherical fuzzy TOPSIS method and complex spherical fuzzy VIKOR method to explicate the adequacy of the proposed strategy and consistency of the results.

The main objective of this study is to set up the foundations of a new model, namely, complex spherical fuzzy (CSF) model that is highly proficient to express the two dimensional ambiguous information. The absence of neutral membership in complex Pythagorean fuzzy sets to express abstinence part of opinion and limitation of spherical fuzzy sets to capture the two dimensional data motivated us to build up the theory of complex spherical fuzzy sets. To establish the ground-breaking CSF model, we elaborate the essential and rudimentary concepts including score degree, accuracy degree and comparison rule. Further, we define the primary operations that serve as helping tools to found four new aggregation operators, namely, complex spherical fuzzy weighted average (CSFWA) operator, complex spherical fuzzy ordered weighted average (CSFOWA) operator, complex spherical fuzzy weighted geometric (CSFWG) operator and complex spherical fuzzy ordered weighted geometric (CSFOWG) operator. These operators are of vital importance in aggregation of complex spherical fuzzy numbers (CSFNs). Moreover, we present a multi-skilled and high potential multi-criteria group decision-making (MCGDM) technique, namely, complex spherical fuzzy VIKOR (CSF-VIKOR) method using the grounds of VIKOR method and motivation of CSF model which is adequate to deal with two dimensional data. The working rule of the proposed technique emphasizes to propose a compromise solution depending upon two focal properties, namely, group utility and individual regret of opponent. We sort the alternatives via the ranking measure by the dint of ascending order. We accomplish the proposed MCGDM strategy by the means of a numerical example in the field of business to rank the objectives of an advertisement on Facebook. We validate the precision and veracity of the proposed strategy by comparing the results with spherical fuzzy VIKOR (SF-VIKOR) method. Finally, we analyze the proposed method to unfold its edge and dominance over the existing approaches.

This article takes advantage of advancements in two different fields in order to produce a novel decision-making framework. First, we contribute to the theory of aggregation operators, which are mappings that combine large amounts of data into more advantageous forms. They are extensively used in different settings from classical to fuzzy set theory alike. Secondly, we expand the literature on complex Pythagorean fuzzy model, which has an edge over other models due to its ability to handle uncertain data of periodic nature. We propose some aggregation operators for complex Pythagorean fuzzy numbers that depend on the Hamacher t-norm and t-conorm, namely, the complex Pythagorean fuzzy Hamacher weighted average operator, the complex Pythagorean fuzzy Hamacher ordered weighted average operator, and the complex Pythagorean fuzzy Hamacher hybrid average operator. We explore some properties of these operators inclusive of idempotency, monotonicity, and boundedness. Then, the operators are applied to multicriteria decision-making problems under the complex Pythagorean fuzzy environment. Furthermore, we present an algorithm along with a flow chart, and we demonstrate their applicability with the assistance of two numerical examples (selection of most favorable country for immigrants and selection of the best programming language). We investigate the adequacy of this algorithm by conducting a comparative study with the case of complex intuitionistic fuzzy aggregation operators.

This paper contributes to the expanding literature on VIKOR, a well-known multi-criteria decision-making technique. It is abundantly used to find the compromise solution regarding some significant criteria under different models. The general VIKOR methodology implements the principle that a recommended response must be a feasible solution which is nearest to positive ideal solution having maximum group utility and minimum individual regret. In this article, we propose a new strategy to address multi-criteria group decision-making problems named complex Pythagorean fuzzy VIKOR (CPF-VIKOR) method. It is designed to handle a great deal of vagueness and hesitation which are often present in human decisions. The CPF-VIKOR method allows the linguistic terms to express individual opinions of experts about the performance of alternatives and the weights of the criteria. We combine the individual judgments of experts with the help of complex Pythagorean fuzzy weighted averaging operator. Further, we compute the ranking measure with the help of group utility and regret measures by adjusting the weight of strategy of maximum group utility within the unit interval. We sort the alternatives in an ascending order relative to group utility measure and individual regret measure. Moreover, we demonstrate our proposed method with the help of a flow chart and two numerical examples: one for the selection of the most beneficial renewable energy project in Spain and another for the selection of the most suitable logistic village location in Turkey. Finally, we present the comparative analysis of our proposed method with the CPF-TOPSIS method to prove its validity.