Picture fuzzy numbers (PFNs) are extremely reasonable to be utilized for delineating dubious or fuzzy data. In this article, we introduce the aggregation strategies of PFNs with assistance from ...Aczel–Alsina operations. We initially broaden the Aczel–Alsina t-norm and t-conorm to picture fuzzy (PF) situations and present a few new operations of PFNs; for example, Aczel–Alsina sum, Aczel–Alsina product, Aczel–Alsina scalar multiplication, and Aczel–Alsina exponentiation, in view of which we build up a few new PF aggregation operators; for instance, the PF Aczel–Alsina weighted average (PFAAWA) operator, PF Aczel–Alsina order weighted average (PFAAOWA) operator, and PF Aczel–Alsina hybrid average (PFAAHA) operator. We further build up various characteristics of those operators, keep several exceptional instances among themselves, and investigate the connections among such operators. Besides, we apply such operators to build up a methodology for managing multiple attribute decision-making (MADM) with PF data. A numerical example is stated to delineate the reasonableness, the viability of the created operators, and the approach. A comparative analysis is additionally introduced.
The “single-valued neutrosophic set (SVNS)” is used to simulate scenarios with ambiguous, incomplete, or inaccurate information. In this article, with the aid of the Aczel-Alsina (AA) operations, we ...describe the aggregation operators (AOs) of SVNSs and how they work. AA
t
-norm (
t
-NM) and
t
-conorm (
t
-CNM) are first extended to single-valued neutrosophic (SVN) scenarios, and then we introduce several novel SVN operations, such as the AA sum, AA product, AA scalar multiplication, and AA exponentiation, by virtue of which we generate a few useful SVN AOs, for instance, the SVN AA weighted average (SVNAAWA) operator, SVN AA order weighted average (SVNAAOWA) operator, and SVN AA hybrid average (SVNAAHA) operator. Next, we create distinct features for such operators, group numerous exceptional cases together, and study the relationships between them. Following that, we created a way for “multiple attribute decision making (MADM)” in the SVN context using the SVNAAWA operator. We provided an illustration to substantiate the appropriateness and, additionally, the productiveness of the produced operators and strategy. Besides this, we contrasted the suggested strategy to the given procedures and conducted a comprehensive analysis of the new framework.
The motivation of this paper is to build up a new technique to manage multi-attribute decision-making (MADM) issues with interval-valued Pythagorean fuzzy (IVPF) set according to the concepts of ...Hamacher
t
-norm and
t
-conorm, and give its application in MADM problems. To begin with, we integrate the Hamacher operations on IVPF sets. Then, in view of these operations, we formulate a few IVPF aggregation operators, for example, IVPF Hamacher weighted average operator, IVPF Hamacher order weighted average operator, IVPF Hamacher hybrid average operator, IVPF Hamacher weighted geometric operator, IVPF Hamacher order weighted geometric operator, and IVPF Hamacher hybrid geometric operator. We investigate the distinguished features of these suggested operators. Moreover, we carry out the proposed aggregation operators to produce a method for solving MADM issues under IVPF data. We present an example of the emerging software system selection to elaborate on its practicality and effectiveness. We investigate the impact of the parameter for different values on decision-making outcomes. The main advantage of utilizing the suggested operator lies in the fact that this operator provides an increasingly complete perspective on the issue to the decision-makers. The technique suggested in this study gives progressively broad, improve the accuracy and exact outcomes when contrasted with the existing related methods. Therefore, this technique performs an important function in real-life MADM issues.
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.
The multi-attribute decision-making (MADM) has really become widely utilized in many domains, including management, economics, and other disciplines. It plays a significant role in mainstream ...decision science. Its main process is the ranking of choices available and selecting the optimal option out of a group of options based on a set of attribute values. Aggregation operators (AOs) play a significant role in MADM techniques to aggregate uncertain and vague information. Aczel Alsina AOs are recently introduced to handle with ambiguous or uncertain information and has their significance. This article aims to generalize the concept "Aczel Alsina AOs of Pythagorean fuzzy sets" (PyFSs) to interval-valued Pythagorean fuzzy (IVPyF) information by utilizing the Aczel-Alsina t-norm (AA-TNM) and t-conorm (AA-TCNM). We developed a series of Aczel-Alsina AOs such as "IVPyF Aczel-Alsina weighted averaging" (IVPyFAAWA), "IVPyF Aczel-Alsina ordered weighted averaging" (IVPyFAAOWA), and "IVPyF Aczel-Alsina hybrid weighted averaging" (IVPyFAAHWA) operators. We also studied the "IVPyF Aczel-Alsina weighted geometric" (IVPyFAAWG) operator. We interpreted certain characteristics of our invented approaches. To check the effectiveness and reliability of our proposed approaches, we establish an illustrative numerical example for the selection of research scientist. The sensitivity analysis of the parameters is also established and their impact on ranking results is analyzed. We illustrated a realistic comparison in which we compare outcomes of exiting methodologies with the consequences of current discussed approaches.
Energy Supplier Selection is vital for sustainable energy management. Optimal supplier choices reduce environmental impact and promote resource efficiency per green principles. However, A decision ...model for Energy Supplier Selection is crucial in making informed choices for sustainable and efficient energy management. A complex fuzzy set (CFS) is the generalization of the fuzzy set (FS). It is a vital tool to deal with uncertain situations, especially when an object is to be described as a part of a real-life scenario. CFS represents the belongingness of anything to a real-life system with the help of two terms. Furthermore, a rough set (RS) is another tool to reduce uncertainty using approximations. The primary goal of this article is to develop a technique for selecting energy suppliers based on multiple attributes. Complex fuzzy rough sets (CFRS) are created by first making a bridge between CFS and RS. CFRS is not any new theory but is obtained by applying the idea of the roughness of CFS. Hence, CFRS is the framework that deals with uncertainty more accurately than the CFS and RS. With the development of the CFRS, we also need the operators that should deal with the information in the form of the CFRS. So, complex fuzzy rough weighted averaging (CFRWA) and complex fuzzy rough weighted geometric (CFRWG) operators are developed to deal with the information in the form of complex fuzzy rough values (CFRVs). Some basic properties of these operators are discussed and verified. Finally, the developed operators are applied to the real-life problem of multi-attribute decision-making (MADM) by using the technique for order of preference by similarity to the ideal solution (TOPSIS) method.
•First time application of TOPSIS with Complex Fuzzy Rough Information.•Introducing a novel decision model for Energy Supplier Selection.•Leveraging CFRS, a powerful tool for handling uncertain situations.•Introducing CFRWA and CFRWG operators to process CFRVs.
In this paper, the concept of intuitionistic fuzzy translation to intuitionistic fuzzy subalgebras and ideals in B-algebras are introduced with several related properties investigated. Examples are ...also given to illustrate results. The notion of intuitionistic fuzzy extensions and intuitionistic fuzzy multiplications of intuitionistic fuzzy subalgebras and ideals are introduced. Relationships are investigated between intuitionistic fuzzy translations, intuitionistic fuzzy extensions and intuitionistic fuzzy multiplications of intuitionistic fuzzy subalgebras and ideals.
The power Bonferroni mean (PBM) is a combined networking system that can benefit both the power average (PA) operator, which might attenuate the effects of irrational data provided by the prejudiced ...decision-makers (DMs), and the BM operator, which may incorporate the interconnections between any two attributes. In this paper, we defined the aggregation operators (AOs), such as the power average (PA) operator and the power Bonferroni mean (PBM) operator, based on the Aczel-Alsina (AA) operational rules under the environment of the q-Rung Orthopair fuzzy set (q-ROFS), and provided their specific characteristics for the solution of numerical problems. We extend the power Bonferroni mean (PBM) operator under the framework of q-ROFVs to establish the q-Rung Orthopair Fuzzy Aczel-Alsina power Bonferroni mean (q-ROFAAPBM) operator and the q-Rung Orthopair Fuzzy Aczel-Alsina weighted power Bonferroni mean (q-ROFAAWPBM) operator and discuss a few of the most useful properties of these AOs. After that, the q-ROFAAWPBM operator is used to solve the multi-attribute decision-making steps for q-ROFVs. The disease is diagnosed with the MADM method, which shows its usefulness and effectiveness. Finally, the comparison of our developed approach has been demonstrated to be superior and more effective than the existing literature, and we can conclude the result.
When dealing with the haziness that is intrinsic in decision analysis-driven decision making procedures, interval-valued intuitionistic fuzzy sets (IVIFSs) can be quite effective. Our approach to ...solving the multiple attribute decision making (MADM) difficulties, where all of the evidence provided by the decision-makers is demonstrated as interval-valued intuitionistic fuzzy (IVIF) decision matrices, in which all of the components are distinguished by an IVIF number (IVIFN), is based on Aczel–Alsina operational processes. We begin by introducing novel IVIFN operations including the Aczel–Alsina sum, product, scalar multiplication, and exponential. We may then create IVIF aggregation operators, such as the IVIF Aczel–Alsina weighted geometric operator, the IVIF Aczel–Alsina ordered weighted geometric operator, and the IVIF Aczel–Alsina hybrid geometric operator, among others. We present a MADM approach that relies on the IVIF aggregation operators that have been developed. A case study is used to demonstrate the practical applicability of the strategies proposed in this paper. By contrasting the newly developed technique with existing techniques, the method is capable of demonstrating the advantages of the newly developed approach. A key result of this work is the discovery that some of the current IVIF aggregation operators are subsets of the operators reported in this article.
In this paper, the notion of closed cubic intuitionistic ideals, cubic intuitionistic
-ideals and cubic intuitionistic
-ideals in
-algebras are introduced, and several related properties are ...investigated. Relations between cubic intuitionistic subalgebras, closed cubic intuitionistic ideals, cubic intuitionistic
-ideals, cubic intuitionistic
-ideals and cubic intuitionistic
-ideals are discussed. Conditions for a cubic intuitionistic ideal to be a cubic intuitionistic
-ideal are provided. Characterizations of a cubic intuitionistic
-ideal are considered. The cubic intuitionistic extension property for a cubic intuitionistic
-ideal is established.
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