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This paper aims to present Bipolar valued probabilistic hesitant fuzzy sets (BVPHFSs) by combining bipolar fuzzy sets and probabilistic hesitant fuzzy sets (PHFSs). PHFSs are a strong version of hesitant fuzzy sets (HFSs) in terms of evaluated as probabilistic of each element. Probabilistic hesitant fuzzy sets (PHFSs) are a set structure that argues that each alternative should be evaluated probabilistically. In this framework, the proposed cluster allows probabilistic evaluation of decision- makers' opinions as negative. Thus, this case proposes flexibility about selection of an element and aids to overcome with noise channels. Furthermore, some new aggregation operators are discussed called bipolar valued probabilistic hesitant fuzzy weighted average operator (BVPHFWA), Generalized bipolar valued probabilistic hesitant fuzzy weighted average operator (GBVPHFWA), bipolar valued probabilistic hesitant fuzzy weighted geometric operator (BVPHFWG), Generalized bipolar valued probabilistic hesitant fuzzy weighted geometric operator (GBVPHFWG), bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric operator (BVPHFHWAG) and Generalized bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric (GBVPHFHWAG) and some basic properties are presented. A score function is defined ranking alternatives. Moreover, two different algorithms are put forward with helping to TOPSIS method and by using aggregation operators over BVPHFSs. The validity of proposed operators are analyzed with an example and results are compared in their own. [ABSTRACT FROM AUTHOR]

Hypersoft sets (HSSs) have gained popularity because of their ability to formulate data in the form of several trait-valued disjoint sets that blend various traits. Motivated by this idea, in this study, we present a new hyper-approach referred to as bipolar neutrosophic hypersoft sets (BNHSSs) by a generalization of neutro-sophic hypersoft sets (NHSSs) and bipolar fuzzy hypersoft sets (BFHSSs) or by merging and subjecting both HSSs and neutrosophic sets (NSs) to a bipolarity property of real numbers. By utilizing positive and negative neutrosophic structures, we construct different notions and operations on the basis of BNHSSs, such as an absolute BNHSS, a null BNHSS, a complement, subset-hood, a restricted and extended union, and a restricted and extended intersection, along with their related properties. Also, some operations like OR and AND on BNHSS have been initiated. In addition, some properties are displayed paired together, and some numerical hypothetical examples are given to clarify the mechanism of using these instruments. Finally, to prove the efficiency and applicability of the proposed model, we established two novel algorithms based on mathematical techniques (aggregation operator and score function) applied to our model (BNHSS). The aforementioned meth-ods have been utilized in the resolution of a multi-attribute group decision-making (MAGDM) problem. Some discussions and comparisons between the given techniques are also presented to demonstrate their effectiveness and applicability. [ABSTRACT FROM AUTHOR]

Renewable energy sources play an influential role in the world's climate and reduce the rate of harmful gasses such as carbon dioxide, methane, nitrous oxide, and many other greenhouse gasses that contribute to global warming. The theoretical concept of the T-spherical fuzzy (T-SF) set (T-SFS) is the most suitable model to evaluate energy resources under uncertainty. This article illustrates appropriate operations based on Dombi triangular norm and t-conorm. We derived a series of new aggregation approaches, such as T-SF Dombi Hamy mean (T-SFDHM) and T-SF weighted Dombi Hamy Mean (T-SFDWHM) operators. Further authors illustrated a list of new approaches such as T-SF Dual Dombi Hamy mean (T-SFDDHM), and T-SF Dombi weighted Dual Hamy mean (T-SFDWDHM) operators. Some exceptional cases and desirable properties of our derived approaches are also studied. We illustrate an application of renewable energy resources to be evaluated using a multi-attribute group decision-making (MAGDM) method. A case study was also studied to choose appropriate energy resources using our proposed methodology of the T-SFDWHM and T-SFDWDHM operators. To show the effectiveness and validity of our current methods, we compared the existing results with currently developed aggregation operators (AOs). [ABSTRACT FROM AUTHOR]

A Q-neutrosophic soft environment is an innovative hybrid tool that combines features of both a Q-neutrosophic set (Q-NS) and a parametric tool "soft set" (SS) in order to manage imprecise and indeterminate situations in various mathematical problems. In this article, we introduce a new algebraic approach called Q-neutrosophic soft matrices (Q-NSMs) to address the issues of two-dimensional (two variables) in a universal set by representing the concept of Q-neutrosophic soft sets (Q-NSSs) in matrices. On Q-NSMs, we define the fundamental set operations and some algebraic operations, i.e., complement, union, intersection, addition, subtraction, multiplication, and scalar multiplication, and prove related properties of these operations. Moreover, these operations are illustrated via several numerical examples. Then, two algorithms are proposed to tackle group decision making (GDM) problems: The first depends on the score function of Q-NSMs, and the second is based on the aggregation operator of Q-NSMs. Finally, this study is supported by a brief comparison with some relevant previous models. [ABSTRACT FROM AUTHOR]

Supplier selection is a very crucial process within a business or commercial enterprise because it depends upon different components like reliability, customer need, services, cost and reputation. A suitable supplier is familiar with developing a relationship between customer needs and business. To serve this purpose, the multiple attribute group decision-making (MAGDM) technique is a well-known and efficient aggregation model used to evaluate flexible optimal options by considering some appropriate criteria or attributes. Experts face some sophisticated challenges during the decision-making process due to uncertain and ambiguous information about human opinions. To address such conditions, we explore the notion of spherical fuzzy sets (SFS) and their reliable operations. Some flexible operational laws of Dombi t-norms are also developed in light of spherical fuzzy (SF) information. Combining the theory of Hamy mean (HM) models and Dombi aggregation tools, some robust strategies are also studied in this research work. The main objectives of this article are to propose some dominant strategies in the presence of SF information including spherical fuzzy Dombi Hamy mean (SFDHM), spherical fuzzy Dombi weighted Hamy mean (SFDWHM), spherical fuzzy Dombi Dual Hamy mean (SFDDHM) and spherical fuzzy Dombi weighted Dual Hamy mean (SFDWDHM) operators. The MAGDM techniques are utilized to evaluate the flexibility of our derived methodologies under considering SF information. An experimental case study is utilized to evaluate a notable supplier enterprise under consideration of our developed methodologies. Finally, a comprehensive overview of our research work is also presented. [ABSTRACT FROM AUTHOR]

Multiple-attribute group decision-making (MAGDM) technique is often used to make decisions when several optimal options are under consideration. It can be difficult to select a reasonable optimal option for the decision maker under consideration of insufficient information. The theory of Hamy mean (HM) operators are used to express correlation among different input arguments and provide a smooth approximation during the decision-making process. Recently, Aczel Alsina aggregating expressions gained a lot of attention from numerous mathematicians under different fuzzy circumstances. This article aims to illustrate the notion of a Pythagorean fuzzy (PyF) set (PyFS) with some restricted constraints, such as a sum of the square of truth membership value and falsity membership value. We developed a series of new approaches under consideration of the HM tools, including PyF Aczel Alsina Hamy mean (PyFAAHM), and PyF Aczel Alsina weighted Hamy mean (PyFAAWHM) operators. Further, we also extend the theory of Dual Hamy mean (DHM) operators and derived a series of new methodologies such as PyF Aczel Alsina Dual Hamy mean (PyFAADHM) and PyF Aczel Alsina weighted Dual Hamy mean (PyFAAWDHM) operators. To demonstrate the flexibility of our derived approaches, we illustrate an application of a multinational company considering the MAGDM technique. An experimental case study is also illustrated to evaluate a reasonable option from a group of options. We see the advantages and compatibility of our findings by comparing the results of existing approaches with the results of currently discussed methodologies. [ABSTRACT FROM AUTHOR]