Dombi T-norm Research Articles

Using a fuzzy credibility neural network to select nanomaterials for nanosensors

Nanomaterials are the most important component of nanosensors, and the selection of the most desirable nanomaterial for nanosensors is a challenge for companies. The classical decision making procedure is very difficult and uncertain to select the desirable nanomaterial. Therefore, we develop a decision making model based on a fuzzy credibility neural network. In this article, we introduce a novel fuzzy credibility neural network using Dombi t-norms and co-norms and also using the score function of fuzzy credibility numbers. Further, the fuzzy credibility neural network applies to the decision making model for the selection of the best nanomaterial for nanosensors. In this approach or decision making model, we first collect data from three experts in the form of fuzzy credibility numbers and then use a neural network to aggregate the data with the help of Dombi t-norm and t-conorm. We consider the expert decision making criteria, which correspond to the input signals of the fuzzy credibility neural network, and calculate the weight of the input signal using distance measure techniques. Next, we compute the hidden layer information and the output layer information by using the fuzzy credibility neural network with the Dombi aggregation operator. The proposed approach is compared with other existing models of decision making and the results of the comparison show that the proposed technique is applicable and reliable for the decision support model.

Bipolar Neutrosophic Dombi-Based Heronian Mean Operators and Their Application in Multi-criteria Decision-Making Problems

Dombi operations based on the Dombi t-norm (TN) and t-conorm (TCN) have the advantage in terms of operational parameter flexibility in dealing with varying degrees of uncertainty and aggregation requirements. Meanwhile, Heronian mean (HM) operator is an effective technique for capturing the interrelationship between any number of inputs. Bipolar neutrosophic set (BNS) offers the ability to represent both positive and negative information as well as indeterminate information. It is beneficial in cases where there is uncertainty or insufficient information. However, the existing Dombi operator under BNS do not take into account the interrelationship between input arguments. To overcome this limitation, this study incorporates Dombi operator into HM and propose the bipolar neutrosophic Dombi Heronian mean aggregation operator. This paper introduces two type of aggregation operators namely bipolar neutrosophic Dombi-based generalized weighted Heronian mean (BND-GWHM), and bipolar neutrosophic Dombi-based improved generalized weighted Heronian mean (BND-IGWHM). The proposed operators are integrated into MCDM procedure. The influence of different parameter values on decision-making results is discussed. Finally, a comparison analysis with existing methods is also provided.

A multiple attribute group decision making model based on 2-tuple linguistic pythagorean fuzzy dombi aggregation operators for optimal selection of potential global suppliers

Multiple-Attribute Group Decision-Making (MAGDM) is a significant area of research in decision-making, and its principles and methodologies are widely implemented. A Pythagorean Fuzzy Set (PFS) is an extension of an Intuitionistic Fuzzy Set (IFS) that is highly valuable for representing uncertain information in real-world scenarios. The 2-Tuple Linguistic Pythagorean Fuzzy Number (2TLPFN) is a specific type of Pythagorean Fuzzy Number (PFN) that can be used to represent uncertainty in real-world decision making through the use of 2-Tuple Linguistic Terms (2TLTs). This paper focuses on the examination of Multiple Attribute Group Decision Making (MAGDM) using 2TLPFNs. Dombi's t-norm and t-conorm operations were commonly referred to as Dombi operations, which might have been greater degree of applicability if offered in a new form of flexibility within the general parameter. In this research, we implement Dombi operations to construct some 2-Tuple Linguistic Pythagorean Fuzzy (2TLPF) Dombi Aggregation operators. These operators include the 2TLPF Dombi Weighted Averaging (2TLPFDWA) operator, 2TLPF Dombi Ordered Weighted Averaging (2TLPFDOWA) operator, 2TLPF Dombi Weighted Geometric (2TLPFDWG) operator, and 2TLPF Dombi Ordered Weighted Geometric (2TLPFDOWA) operator. An analysis is conducted to examine the unique characteristics of these suggested operators. Subsequently, we leveraged the proposed operators to develop a model aimed at tackling the MAGDM problems in the 2TLPF environment. Eventually, a suitable instance has been demonstrated to validate the formation of the model as well as exhibit its implementation and resilience.

Some Aggregation Operators Based on Dombi t-norm (TN) and t-co-norm (TCN) Operations: Applications in Economic Corridor Prospective

Some Aggregation Operators Based on Dombi t-norm (TN) and t-co-norm (TCN) Operations: Applications in Economic Corridor Prospective

Modeling challenges for Industry 4.0 implementation in new energy systems towards carbon neutrality: Implications for impact assessment policy and practice in emerging economies

New energy systems (NESs) in a circular economy (CE) perspective may contribute significantly to achieving emerging economies’ carbon peaking and neutrality goals. However, CE-based NESs in developing countries towards carbon peaking and neutrality remain unexplored in scientific research and development. Additionally, challenges for I4.0 implementation in the CE context for NESs are still under research gaps in emerging economies. The previous research mainly focused on qualitative discussions on carbon neutrality, I4.0 challenges, and opportunities for renewable energy generation from waste biomass. Therefore, this scientific work, for the first time, offered an innovative decision support model integrating qualitative management tool OGSM (Objective, Goals, Strategies, and Measures), Dombi t-norm and Dombi t-conorm operator based Interval-valued Fermatean fuzzy number (IVFFN) Delphi and IVFFN-Decision Making Trial and Evaluation Laboratory (DEMATE) as a new extension of DEMATEL for assessing interactions among I4.0 implementing challenges in a CE context for NESs towards carbon neutrality which can handle border scale of uncertainty and ambiguity. The findings indicated that out of fifteen I4.0 challenges, nine were identified as causal challenges and the rest as effect group challenges, suggesting that improving causal challenges can notably enhance the effect group challenges. “Lack of aptitude to integrate sophisticated I4.0 infrastructure for NESs” has been identified as the top priority causal challenge that significantly impacts the effect group challenges. Further, based on the findings of IVFFN-DEMATEL, short-, mid-, and long-term action plans are proposed for real-time decision-makers to improve the existing situations. The output of the study may contribute robustly to the real-time scenarios of NESs by supporting decision-makers, researchers, government authorities, and stakeholders towards developing sustainable CE-based NESs by integrating I4.0 technologies, which will help to achieve a carbon-neutral economy in emerging economies.

A novel study of spherical fuzzy soft Dombi aggregation operators and their applications to multicriteria decision making

In many decision-making situations, we are not restricted to two kinds of aspects, such as membership degree or nonmembership degree, and sometimes we need to include the abstinence degree (AD). However, many fuzzy set theories fail to cover issues, such as an intuitionistic fuzzy soft set, Pythagorean fuzzy soft set and q-rung orthopair fuzzy soft set. All the above notions can only consider membership degree and a nonmembership degree in their structures. The spherical fuzzy soft set compensates for these drawbacks in its structure. Moreover, the Dombi t-norm and Dombi t-conorm are the fundamental apparatuses to generalize the basic operational laws of sum and product. Therefore, in this article, based on the dominant features of spherical fuzzy soft sets and valuable features of the Dombi t-norm and Dombi t-conorm, we initially developed the basic Dombi operational laws for spherical fuzzy soft numbers. Moreover, based on these newly developed operational laws, we introduced aggregation operators called spherical fuzzy soft Dombi average (weighted, ordered weighted, hybrid) aggregation operators. We discussed the basic properties of these aggregation operators. Additionally, we have developed a multiple criteria decision making (MCDM) approach using an explanatory example via our approach to show its effective utilization. Furthermore, a comparative study of our approach shows the superiority of our introduced notions.

Intuitionistic fuzzy credibility Dombi aggregation operators and their application of railway train selection in Pakistan

<abstract><p>The degree of credibility of the fuzzy assessment value demonstrates its significance and necessity in the fuzzy decision making problem. The fuzzy assessment values should be closely related to their credibility measures in order to increase the credibility levels and degrees of fuzzy assessment values. This will increase the abundance and the credibility of the assessment information. As a new extension of the intuitionistic fuzzy concept, this study suggests the idea of an intuitionistic fuzzy credibility number (IFCN). So, based on Dombi norms, we proposed some new operational laws for intuitionistic fuzzy credibility numbers. Different intuitionistic fuzzy credibility aggregation operators are defined using Dombi t-norm and t-conorm operations. i.e., intuitionistic fuzzy credibility Dombi weighted averaging (IFCDWA), intuitionistic fuzzy credibility Dombi ordered weighted averaging (IFCDOWA), intuitionistic fuzzy credibility Dombi hybrid weighted averaging (IFCDHWA) operators. Next, we defined multiple criteria group decisions (MCGDM) approach. To ensure that their results are reliable and applicable, we also gave an example of railway train selection and discussed comparative result analysis.</p></abstract>

Dombi Bonferroni Mean Operators Under Bipolar Complex Fuzzy Environment and Their Applications in Internet World

Internet is almost a necessary facility and tool to solve daily life problems in every field life. Whether at the individual level or national and international level sale purchase of any kind of object has always been of much importance, especially after Corona Pandemic, when online business is at its peak. Because of the enhancement of online sales and purchases, various businessmen are looking for suitable internet websites for their businesses, and the selection of the most suitable internet websites is one of the multi-attribute decision-making (MADM) dilemmas. Thus, in this script, we take benefits of three various concepts that are Bonferroni mean (BM) operator which is a significant technique to catch the interrelatedness among any number of inputs, Dombi operations which are based on Dombi t-norm and t-conorm and the ability to create an aggregation procedure more flexible because of the parameter, bipolar complex fuzzy set (BCFS) which is an outstanding model for tackling two-dimensional information with negative aspect and interpret bipolar complex fuzzy (BCF) Dombi Bonferroni mean (BCFDBM), BCF weighted Dombi Bonferroni mean (BCFWDBM), BCF Dombi geometric Bonferroni mean (BCFDGBM), and BCF weighted Dombi geometric Bonferroni mean (BCFWDGBM) operators. After ward, in this script, for tackling MADM dilemmas in the setting of BCFS, we investigate a MADM procedure based on the investigated operators and solve a MADM dilemma (selection of a suitable internet website for businessmen). Further, to display the superiority and efficiency of our work, we compare our approach and operators with a few current approaches and operators.

Case study for hospital-based Post-Acute Care-Cerebrovascular Disease using Sine Hyperbolic q-rung orthopair fuzzy Dombi aggregation operators

The Sine Hyperbolic q-rung orthopair fuzzy sets (sinh-q-ROFSs) are the important concept of accepting more uncertainty than the q-rung orthopair fuzzy sets (q-ROFSs). The well-known sine hyperbolic function preserves the origin’s periodicity and symmetric existence, and so fulfills the expert’s expectations for the multi-time process’ parameters. The aim of this study is to offer some robust sine hyperbolic Dombi operation laws (sinhDOLs) for q-ROFSs in order to preserve these qualities and the significance of sinh-q-ROFSs. Score and accuracy functions for the sinh-q-ROFSs’ are also defined. We define a number of new averaging/geometric aggregation operators (AOs) based on Dombi t-norm and conorm operations. The fundamental properties of the defined operators were discussed. Then, using defined AOs, we provide a group decision-making (DM) approach for solving DM problems. We demonstrate a numerical example to verify the defined method.

Q-Rung orthopair fuzzy soft aggregation operators based on Dombi t-norm and t-conorm with their applications in decision making

Recently, some improvement has been made in the dominant notion of fuzzy set that is Yager investigated the generalized concept of fuzzy set, Intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS) and called it q-rung orthopair fuzzy (q-ROF) set (q-ROFS). The aim of this manuscript is to present the concept of q-ROF soft (q-ROFSt) set (q-ROFStS) based on the Dombi operations. Since Dombi operational parameter possess natural flexibility with the resilience of variability. Some new operational laws are defined based on hybrid study of soft sets and q-ROFS. The advantage of Dombi operational parameter is very important to express the experts’ attitude in decision making. In this paper, we present q-ROFSt Dombi average (q-ROFSt DA) aggregation operators including q-ROFSt Dombi weighted average (q-ROFSt DWA), q-ROFSt Dombi ordered weighted average (q-ROFSt DOWA) and q-ROFSt Dombi hybrid average (q-ROFSt DHA) operators. Moreover, we investigate q-ROFSt Dombi geometric (q-ROFSt DG) aggregation operators including q-ROFSt Dombi weighted geometric (q-ROFSt DWG), q-ROFSt Dombi ordered weighted geometric (q-ROFSt DOWG), and q-ROFSt Dombi hybrid geometric (q-ROFSt DHG) operators. The basic properties of these operators are presented with detail such us Idempotency, Boundedness, Monotonicity, Shift invariance, and Homogeneity. Thus from the analysis and advantages of proposed model, it is clear that the investigated q-ROFSt DWA operator is the generalized form of IF St DWA, PFSt DWA and q-ROFDWA operators. Similarly, the investigated q-ROFSt DWG operator is the generalized form of IF St DWG, PFSt DWG and q-ROFDWG operators. By applying the develop approach, this manuscript contains the technique and algorithm for multicriteria decision making (MCDM). Further a numerical example is developed to illustrate the flexibility and applicability of the developed operators.

An Approach for the Analysis of Energy Resource Selection Based on Attributes by Using Dombi T-Norm Based Aggregation Operators

Dombi t-norm (DTN) and t-conorm (TCN) are among the most effective triangular norms in fuzzy systems for aggregation purposes. The environment of interval-valued intuitionistic fuzzy (IVIF) set gives us precision in expressing uncertain information by using a membership grade (MG) and non-membership grade (NMG) in the form of closed subintervals of 0, 1. The goal of this paper is to introduce DTN-based aggregation operators (AOs) for IVIF numbers (IVIFNs) and study their performance in the evaluation of the worth of energy recourses to be opted in Pakistan to deal with the energy crises situation. We first introduced some DTN and TCN-based operations for IVIFNs and developed two new AOs known as IVIF Dombi weighted averaging (IVIFDWA) and IVIF Dombi weighted geometric (IVIFDWG) operators. The validity and fitness of the proposed operators are tested. A case study is presented where the energy resources of Pakistan are discussed and the problem of the selection of sustainable energy resources in the context of Pakistan is investigated. The sensitivity analysis of the proposed IVIFDWA and IVIFDWG operators is studied and a comparative analysis of the current work with previous studies is established.

Novel Decision-Making Techniques in Tripolar Fuzzy Environment with Application: A Case Study of ERP Systems.

The intuitionistic fuzzy set (IFS) and bipolar fuzzy set (BFS) are all effective models to describe ambiguous and incomplete cognitive knowledge with membership, non-membership, negative membership, and hesitancy sections. But in daily life problems, there are some situations where we cannot apply the ordinary models of IFS and BFS, separately. Hence, there is a need to combine both the models of IFS and BFS into a single one. A tripolar fuzzy set (TFS) is a generalization of IFS and BFS. In circumstances where BFS and IFS models cannot be used individually, a tripolar fuzzy model is more dependable and efficient. Further, the IFS and BFS models are reduced to corollaries due to the proposed model of TFS. For this purpose in this article, we first consider some novel operations on tripolar fuzzy information. These operations are formulated on the basis of well-known Dombi T-norm and T-conorm, and the desirable properties are discussed. By applying the Dombi operations, arithmetic and geometric aggregation operators of TFS are proposed, and we introduce the concepts of a TF-Dombi weighted average (TFDWA) operator, a TF-Dombi ordered weighted average (TFDOWA) operator, and a TF-Dombi hybrid weighted (TFDHW) operator and explore their fundamental features including idempotency, boundedness, monotonicity, and others. In the second part, we propose TF-Dombi weighted geometric (TFDWG) operator, TF-Dombi ordered weighted geometric (TFDOWG) operator, and TF-Dombi hybrid geometric (TFDHG) operator. The features and specific cases of the mentioned operators are examined. Enterprise resource planning (ERP) is a management and integration approach that organizations employ to manage and develop many aspects of their operations. The study's primary contribution is to employ TFS to create certain decision-making strategies for the selection of optimal ERP systems. The proposed operators are then used to build several techniques for solving multiattribute decision-making (MADM) issues with TF information. Finally, an example of ERP system selection is investigated to demonstrate that the techniques suggested are trustworthy and realistic.

A novel approach on decision support system based on triangular linguistic cubic fuzzy Dombi aggregation operators

The triangular linguistic cubic fuzzy sets (TLCFSs) can express the fuzzy data easily and is also very useful in modeling of uncertain data in decision making (DM) problems. First of all, on the basis of Dombi t-norm and t-conorm (DTT), we propose novel operational rules of triangular linguistic cubic fuzzy numbers (TLCFNs). We propose some new aggregation operators of TLCFNs based on the newly developed operations, i.e., triangular linguistic cubic fuzzy Dombi weighted averaging (TLCFDWA), triangular linguistic cubic fuzzy Dombi weighted geometric (TLCFDWG), triangular linguistic cubic fuzzy Dombi order weighted averaging (TLCFDOWA), triangular linguistic cubic fuzzy Dombi order weighted geometric (TLCFDOWG), triangular linguistic cubic fuzzy Dombi hybrid weighted averaging (TLCFDHWA), and triangular linguistic cubic fuzzy Dombi hybrid weighted geometric (TLCFDHWG) operators. Furthermore, a new method is proposed with the help of the proposed operators to solve the decision making problem. Finally, a numerical example is provided to illustrate the effectiveness of the new method. Comparative analysis is used to demonstrate the proposed method’s superiority.

Entropy based extended TOPOSIS method for MCDM problem with fuzzy credibility numbers

<abstract><p>Due to the vagueness and uncertainty of human cognition/judgments as related to complicated decision-making problems, existing fuzzy decision-making approaches merely signal fuzzy assessment values and lack degrees/levels of credibility for the fuzzy assessment values in alternatives over attributes. As a result, the fuzzy evaluative value's credibility degree highlights its significance and importance in the fuzzy decision-making problem. To improve the degrees/levels of credibility of fuzzy evaluation values, the fuzzy assessment values should be tightly linked to their credibility measures, which would result in more abundant and reliable assessment information. The major goal of this research was to describe new procedures for credible fuzzy numbers based on the Dombi t-norm and Dombi t-conorm. Dombi operations can benefit from the operational parameter's best tractability. These operations are more generalized for credibility fuzzy numbers. Furthermore, using the basic operational laws of Dombi t-norm and Dombi t-conorm, we develop a series of fuzzy credibility Dombi aggregation operators, like the fuzzy credibility Dombi geometric aggregation operator, fuzzy credibility Dombi ordered geometric aggregation operator and fuzzy credibility Dombi hybrid geometric aggregation operator. To handle this sort of decision-making problem, an extended TOPSIS (technique for order of preference by similarity to ideal solution) is proposed. Finally, we present an example, along with a discussion of the comparative results to check the accuracy and validation of the proposed methods, to confirm that their results are credible and feasible.</p></abstract>

Decision support system based on fuzzy credibility Dombi aggregation operators and modified TOPSIS method

<abstract><p>The operational law plays an important role in the aggregation operator for group decision system. The aggregation information has high influence in aggregating group decision information. Therefore, the main objective of the proposed work is to develop some operational laws as aggregation operator for fuzzy credibility numbers based on Dombi norms. Dombi operations can benefit from the best operational parameter flexibility. To the best of our knowledge, Dombi operations have so far not been used in for fuzzy credibility numbers (FCNs). Using these Dombi t-norm and t-conorm to define some different fuzzy credibility aggregation operators. i.e., fuzzy credibility Dombi weighted averaging (FCDWA) operator, fuzzy credibility Dombi ordered weighted averaging (FCDOWA) operator, fuzzy credibility Dombi hybrid weighted averaging (FCDHWA) operator. Next, we used TOPSIS method procedure for multi-attribute grouped decision-making (MAGDM). Finally, we provided an example, as well as a discussion of the comparative result analysis, to ensure that their findings are credible and practical.</p></abstract>

Application of Choquet integral in interval type‐2 Pythagorean fuzzy sustainable supply chain management under risk

The purpose of this study is to offer requisite models for unravelling the complex issues that arise in a supplier selection-order allocation problem by soothing the risk and disturbances. To do this, a new uncertain environment, interval type-2 Pythagorean fuzzy set (IT2PFS) is introduced to assist the experts for assuring secure and reliable outcomes in hesitant situations. The operational laws on IT2PFS under Dombi t-norm and t-conorm are defined, which are further utilized to develop geometric Bonferroni mean and Bonferroni mean operators based on Choquet integral (CI) under IT2PFS. The aggregation operators can ennoble the pliability of the information blending process through the adjustment of several parameters and can make good interactions among the criteria with their weights. Thereafter, to determine the weights of the criteria, an empirical method, namely the decision making trial and evaluation laboratory (DEMATEL) is amplified by conjoining CI and IT2PFS into it. A multicriteria decision making method, namely, the multiattribute border approximation area comparison (MABAC) and subsequently the CI based grey relational analysis method are then employed to classify the suppliers and derive their corresponding weights with reference to the sustainable criteria. Over and above, a new multiobjective optimization model is exhibited to uphold the purchasing managers for assembling suppliers keeping in mind the sustainability aspects and overall risk of suppliers by following Markowitz portfolio theory. A real-life supply chain management problem is demonstrated to elucidate the aptness and efficiency of the proposed work. Furthermore, the effectiveness and importance of the study are validated via the comparative analysis with existing approaches. The main contribution of the study is in handling the difficulty and confusion that arise during information gathering, information aggregation, suppliers evaluation and order allocation phases.

Novel Dombi Aggregation Operators in Spherical Cubic Fuzzy Information with Applications in Multiple Attribute Decision-Making

The notion of spherical fuzzy sets (SFSs) is one of the most effective ways to model the fuzzy information in decision-making processes. The sum of squares of membership, neutral, and nonmembership degrees in SFSs lies in the interval [0, 1] and accommodates more uncertainties. Henceforth, in this article, the idea of spherical cubic fuzzy sets (SCFSs) is introduced, which is the generalization of SFSs. Spherical cubic fuzzy set is the combination of spherical fuzzy sets and interval-valued spherical fuzzy sets. The membership, neutral, and nonmembership degrees in an SCFS are cubic fuzzy numbers (CFNs). Consequently, this set outperforms the pre-existing structures of fuzzy set theory. Moreover, some fundamental operations for the comparison of two spherical CFNs are defined such as score function and accuracy function. Further, several new operations through Dombi t-norm and Dombi t-conorms are characterized to get the best results during the decision criteria. Furthermore, spherical cubic fuzzy Dombi weighted averaging (SCFDWA), SCFD ordered weighted averaging (SCFDOWA), SCFD hybrid weighted averaging (SCFDHWA), SCFD weighted geometric (SCFDWG), SCFD ordered weighted geometric (SCFDOWG), and the SCFD hybrid weighted geometric (SCFDHWG) aggregated operators are discussed, and their characteristics are examined. In addition, some of the operational laws of these operators are defined. Also, a decision-making approach based on these operators is proposed. Since the proposed methods and operators are the generalizations of the existing methods and operators, therefore, these techniques produce more general, accurate, and precise results as compared with existing ones. Finally, a descriptive example is given in order to describe the validity, practicality, and effectiveness of the proposed methods.

A q-rung orthopair fuzzy multiple attribute group decision making method based on generalized Maclaurin symmetry mean and Dombi t-norm and t-conorm

Generalized Maclaurin symmetry mean (GMSM) operator is an effective tool in the process of multi-attribute group decision making (MAGDM) with the characteristic of capturing the interrelationships between multiple arguments. at the same time, q-rung orthopair fuzzy set (q-ROFS) is a good tool to describe uncertainty and fuzziness. To effectively aggregate q-rung orthopair fuzzy information based on the extension of Dombi operations, some novel operators and ideal properties of the proposed operators are put forward in this study. Further, this research present a novel method to MAGDM based on the proposed operators. Finally, the applicability of new method can be proved by a numerical experiment. A detailed parametric analysis and a comparative analysis are also discussed to highlight the flexibility and superiority of the method proposed in this paper.

Some new hybrid hesitant fuzzy weighted aggregation operators based on Archimedean and Dombi operations for multi-attribute decision making

Hesitant fuzzy set (HFS) is more flexible and general tool in comparison to fuzzy set theory. There is not yet reported an aggregation operator (AO) which can provide desirable generality, flexibility and compatibility in adjusting risk preferences while aggregating attribute values under hesitant fuzzy (HF) environment, although based on algebraic t-norm and t-conorm, Einstein t-norm and t-conorm, Hammacher t-norm and t-conorm, Dombi t-norm and t-conorm and Frank t-norm and t-conorm; weighted AOs have been developed earlier to attempt to meet above such eventualities. So, the primary objective of this paper is to develop some general, flexible as well as compatible AOs that can be exploited to solve MADM problems with HF information. From this perspective, at the very beginning, we develop new operations between HFEs by uniting the features of Archimedean and Dombi operations. Next, based on these operations, we develop HF Archimedean-Dombi weighted arithmetic and geometric AOs, HF Archimedean-Dombi ordered weighted arithmetic and geometric AOs and HF Archimedean-Dombi hybrid arithmetic and geometric AOs. We have shown that the existing HF-algebraic weighted AOs, HF-Einstein weighted AOs and HF-Hammacher weighted AOs are special cases of our developed AOs. We discuss in detail some intriguing properties of the proposed AOs. Next, we establish a procedure of MADM endowed by the proposed operators under HF environment. Then, we present a practical example concerning the personnel selection to gloss the decision steps of the proposed method. We also conduct a validity test to show that our proposed AOs are authentic and legal. Moreover, we exhibit a sensitivity investigation with diverse criteria weight sets to examine the stability of our proposed intriguing approach. Also, we draw attention toward a comparison between the existing decision-making methods with the proposed method to prove the superiority of our model.

Extensions of Dombi Aggregation Operators for Decision Making under m-Polar Fuzzy Information

An m-polar fuzzy set is a powerful mathematical model to analyze multipolar, multiattribute, and multi-index data. The m-polar fuzzy sets have appeared as a useful tool to portray uncertainty in multiattribute decision making. The purpose of this article is to analyze the aggregation operators under the m-polar fuzzy environment with the help of Dombi norm operations. In this article, we develop some averaging and geometric aggregation operators using Dombi t-norm and t-conorm to handle uncertainty in m-polar fuzzy (mF, henceforth) information, which are mF Dombi weighted averaging (mFDWA) operator, mF Dombi ordered weighted averaging (mFDOWA) operator, mF Dombi hybrid averaging (mFDHA) operator, mF Dombi weighted geometric (mFDWG) operator, mF Dombi weighted ordered geometric operator, and mF Dombi hybrid geometric (mFDHG) operator. We investigate properties, namely, idempotency, monotonicity, and boundedness, for the proposed operators. Moreover, we give an algorithm to solve multicriteria decision-making issues which involve mF information with mFDWA and mFDWG operators. To prove the validity and feasibility of the proposed model, we solve two numerical examples with our proposed models and give comparison with mF-ELECTRE-I approach (Akram et al. 2019) and mF Hamacher aggregation operators (Waseem et al. 2019). Finally, we check the effectiveness of the developed operators by a validity test.