Dombi Operators Research Articles

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.

A promising approach for decision modeling with single-valued neutrosophic probabilistic hesitant fuzzy Dombi operators

A combination of the single-valued neutrosophic set (SV-NS) and the probabilistic hesitant fuzzy set is the single-valued neutrosophic probabilistic hesitant fuzzy (SV-NPHF) environment (PHFS). It is intended for some unsatisfactory, ambiguous, and contradictory circumstances in which each element has a number of various values that are brought about by the situation?s actuality. The decision-maker can quickly gather and analyze the facts by employing a strategic decision-making technique. On the other hand, uncertainty will be a big part of our daily lives when we are learning. We present a decision-making strategy for the SV-NPHF context to address this data ambiguity. The fundamental operational concepts for SV-NPHF information under Dombi aggregation operators were initially developed on the basis of this study. The SV-NPHF Dombi weighted arithmetic average (SV-NPHFDWAA) operator and SV-NPHF Dombi weighted arithmetic geometric (SV-NPHFDWAG) operators are two SV-NPHF Dombi aggregation Operators that are then examined. Following that, we look into further characterizations of the proposed operators, including idempotency, boundedness, and monotonicity. For the derived operators, we additionally developed the score and accuracy functions. When using SV-NPHF data in a multi attribute decision support system (MADSS), it is necessary to compare the effectiveness of various (AOs) in order to make the best decision. In addition, it is demonstrated how to use symmetry analysis to choose the optimal social media platform for earning and learning in a practical application of SV-NPHFDWAA and SV-NPHFDWAG.

A Fuzzy Similarity Based Classification with Archimedean-Dombi Aggregation Operator

The term "classification" refers to a supervised learning technique in which samples are given class labels based on predetermined classes. Fuzzy classifiers are renowned for their ability to address the issue of outliers and deliver the performance resilience that is much needed. The major goal of this study is to provide a classification algorithm that is effective and accurate. In this work, we address Archimedean-Dombi aggregation operator by extending the similarity classifier. Earlier, Dombi operators were used to study the similarity classifier. We focus on the application of Archimedean-Dombi operators during the classifier's aggregate similarity calculation. Since Archimedean and Dombi operators are well-known for offering appropriate generalization and flexibility respectively in aggregating data, so a different version of the similarity classifier is created. One real-world medical dataset, namely Parkinson disease data set is used to test the proposed approaches. When compared to older existing operators, the new classifiers have better classification accuracy.

Interval Valued Bipolar Fuzzy Prioritized Weighted Dombi Averaging Operator Based On Multi-Criteria Decision Making Problems

In this paper, we develop to a new operator by using together IVBFS and Dombi operators. Also, the some properties of this concept are introduced like addition, scalar multiplication, scalar power, multiplication. The presented operator is Interval Valued Bipolar Fuzzy Prioritized Weighted Dombi Averaging operator (IVBFPWDA) and various properties are offered like idempotency, monotoncity, boundedness. Then, we present to score function by using similar concept to score function over (IVBFSs) [5] for ranking of aggregated values. Moreover, offered operator is applied over an investment example. The results show that our operator is reality, objective and agreement in its own. Also, a comparative analysis is given by using Interval Valued Bipolar fuzzy sets (IVBFSs) [5]. As can be seen from comparison analysis with aggregation operator over IVBFS is agreement. But our offered operator has more advantages than operators over IVBFS for example; our operator is flexible and changeable. Thus; prefer, need and requirement of decision makers can be met easily. The flexible approach is always essential because of ranking into its own.

An integrated method for evaluating the energy-saving and economic operation of power systems with interval-valued intuitionistic fuzzy numbers

Chinese population is numerous. Energy resources are limited. The ownership of per capita resource is far lower than the world average level. China is in the process of industrialization and urbanization, but energy resources are consumed and environmental pollution is serious. The energy crisis and environmental protection has restricted our country economy development and social harmony. As a source of energy consumption and environmental pollution, power industry is one of the important fields of energy saving and emission reduction. The reasonable power dispatch is the breakthrough to reduce the energy consumption and environmental pollution. In this paper, we first introduce some operations on interval-valued intuitionistic fuzzy sets, such as Heronian mean (HM) operator and Dombi operations, etc., and further develop the induced interval-valued intuitionistic fuzzy Dombi weighted Heronian mean (I-IVIFDWHM) operator. We also establish some desirable properties of this operator, such as commutativity, idempotency and monotonicity. Then, we apply the I-IVIFDWHM operator to deal with the interval-valued intuitionistic fuzzy multiple attribute decision making (MADM) problems. Finally, an illustrative example for evaluating the energy-saving and economic operation of power systems is given to verify the developed approach.

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.

Exploring factors affecting airport selection during the COVID-19 pandemic from air cargo carriers’ perspective through the triangular fuzzy Dombi-Bonferroni BWM methodology

The COVID-19 pandemic has created unexpected demand for air cargo in terms of rapid mobility of critical basic needs. Air cargo carriers aim to maximize their profits by taking advantage of the current demand and using their limited capacity in the right place. At this point, some of the qualifications of the airports in the places where demand plays a crucial role in this decision of the carriers. Thus, evaluating the factors considered in the airport selection for air cargo carriers during the COVID-19 period is curious. This study proposes a triangular fuzzy Dombi-Bonferroni best-worst method (BWM) framework with vast flexibility to establish the priority preferences of factors considered in selecting airports. The fuzzy BWM model becomes a superior decision support system by combining the Bonferroni mean operator's ability to consider interrelationships between attributes and the flexibility of the Dombi operator. In this sense, we highlight eighteen criteria based on five airport aspects: location, physical features, performance, costs, and reputation. Findings reveal that the foremost aspects are location and costs, whereas the most crucial factors are airport charges and handling charges. The study suggests that airports should follow a low-price policy for airport-related charges without compromising their sustainability to have a share of the increasing number of air cargo flights, especially during the COVID-19 period, when airline passenger flights are decreased. The study is crucial in deciding the strategy and policy of air cargo carriers and airports during the pandemic period.

Multi-attribute decision making for power Dombi operators under Pythagorean fuzzy information with MABAC method

Multi-attribute decision making for power Dombi operators under Pythagorean fuzzy information with MABAC method

Dombi operations for linguistic T-spherical fuzzy number: an approach for selection of the best variety of maize

Dombi operations for linguistic T-spherical fuzzy number: an approach for selection of the best variety of maize

A Novel Approach of Linguistic Picture Fuzzy Dombi Heronian Mean Operators and their Application to Emergency Program Selection

ABSTRACT In decision support systems, linguistic fuzzy information played an important role and the linguistic fuzzy aggregation operators (AOs) worked in group decision support systems. Recently, we proposed the linguistic picture fuzzy (LPF) sets, which is the extension of the linguistic intuitionist fuzzy sets, to reflect the ambiguity and vagueness of knowledge in decision-making (DM) problem. The goal of this research work is to define a new family of LPF AOs through the use of Dombi operations and Heronian mean (HM) operator. In addition to fusing individual attribute values, the evolved operators are good ability to handle the common association between the attributes, making them more appropriate to effectively solve difficult multi-attribute DM (MADM) problems. Therefore, we developed an approach for MADM problem based on LPF Dombi HM operators and solved an emergency programme selection problem. The comparison section provides the effectiveness, reliability and practicality.

Dombi weighted aggregation operators of neutrosophic Z-numbers for multiple attribute decision making in equipment supplier selection

Advances in multiple attribute decision making (MADM) require the development of information aggregation operations flexible enough to deal with neutrosophic Z-number (NZN) information. In this situation, new operations of NZNs are needed to aggregate NZNs with different values of operational parameter and to realize the MADM flexibility. Motivated by the Dombi operations, this study proposes the Dombi operations and some Dombi weighted aggregation operators of NZNs to solve a gap of flexible MADM in the setting of NZNs. Thus, the main aims of this article are (i) to propose several Dombi operations of NZNs, (ii) to present the NZN Dombi weighted arithmetic averaging (NZNDWAA) and NZN Dombi weighted geometric averaging (NZNDWGA) operators for aggregating NZN information and their properties, (iii) to establish a MADM approach based on the NZNDWAA and NZNDWGA operators for solving MADM problems under the environment of NZNs, and (iv) to give a MADM example and related comparative analysis on the issue of equipment supplier selection for indicating the applicability and efficiency of the developed MADM approach. However, the proposed MADM approach is more flexible for the selection of decision makers’ preferences and the actual requirements in MADM applications.

Hesitant T-spherical Dombi fuzzy aggregation operators and their applications in multiple criteria group decision-making

A hesitant fuzzy (HF) set is an extension of the fuzzy sets and a T-spherical fuzzy set (T-SFS) is a generalization of the spherical fuzzy set (SFS). HF set has a significant role for modelling disagreements of the decision-makers over membership degree of an element. Also, T-SFS is quite effective in the modelling of the uncertainty for decision-making (DM) problems. In this paper, we define the concept of hesitant T-spherical fuzzy (HT-SF) set (HT-SFS) by combining concepts of HF set and T-SFS, and present some set-theoretical operations of HT-SFSs. We also develop the Dombi operations on HT-SFSs. We present some aggregation operators based on Dombi operators, including hesitant T-spherical Dombi fuzzy weighted arithmetic averaging operator, hesitant T-spherical Dombi fuzzy weighted geometric averaging operator, hesitant T-spherical Dombi fuzzy ordered weighted arithmetic averaging operator, and hesitant T-spherical Dombi fuzzy ordered weighted geometric averaging operator, and investigate some properties of them. In addition, we give a multi-criteria group decision-making method and algorithm of the proposed method under the hesitant T-spherical fuzzy environment. To show the process of proposed method, we present an example related to the selection of the most suitable person for the assistant professorship position in a university. Besides this, we present a comparative analysis with existing operators to reveal the advantages and authenticity of our technique.

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.

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>

A Study of Complex Dombi Fuzzy Graph With Application in Decision Making Problems

A complex fuzzy set (CFS) is a generalization of a fuzzy set (FS) in which a limit of degrees occurs on the complex plane with unit disc. The averaging operators are a key part of turning all the data into one value. Dombi operators have exceptional flexibility with operating factors, and they are particularly efficient in decision-making problems. In this paper, we establish complex dombi fuzzy graph (CDFG). We implement dombi operators on CFSs to extend graph nomenclature. We define the complement of CDFG with an example. The idea of self-complementary in CDFG is discussed. The concepts of homomorphism, isomorphism, weak isomorphism, and co-weak isomorphism of two CDFGs are discussed. We define regular and entirely regular graphs with sufficient elaboration and examine their key properties. Furthermore, significant characteristics are used to explain the edge regularity of CDFG. Lastly, we establish an application of CDFG in decision making problem.

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>

Interval‐Valued q‐Rung Orthopair Fuzzy QUALIFLEX Decision Analysis Method with Dombi Operators

As a new and useful decision tool, interval‐valued q‐rung orthopair fuzzy set (IVq‐ROFS), has strong ability to address uncertain or imprecision information in practical decision‐making processes. This paper develops a new interval‐valued q‐rung orthopair fuzzy QUALIFLEX decision analysis method with Dombi operators for handling the group decision‐making problems with IVq‐ROFSs data. We also conduct a case study on the health management of hypertensive patients for demonstrating the feasibility and superiority of the developed method. The main contributions of this paper are as follows: (1) we first propose interval‐valued q‐rung orthopair fuzzy Dombi operational laws and investigate their desirable properties; (2) using the developed Dombi operational laws, we develop an interval‐valued q‐rung orthopair fuzzy Dombi weighted average (IVq‐ROFDWA) operator, and we prove that the IVq‐ROFDWA operator satisfies the properties of idempotency, commutativity, boundedness, and monotonicity; (3) we introduce the concept of interval‐valued q‐rung orthopair fuzzy ideal group opinions with the help of IVq‐ROFDWA operator and propose a new weight‐determining method for identifying the weights of experts; (4) we develop a new interval‐valued q‐rung orthopair fuzzy distance measure. With the help of the developed distance measure, we calculate interval‐valued q‐rung orthopair fuzzy concordance/discordance index under each permutation, and then a new interval‐valued q‐rung orthopair fuzzy QUALIFLEX decision analysis method is developed for addressing the complex multiattribute group decision‐making problems with IVq‐ROFSs.

An Integrated Decision Support Framework Using Single-Valued-MEREC-MULTIMOORA for Low Carbon Tourism Strategy Assessment

In this paper, globally existing low-carbon tourism strategies (LCTSs) are recognized and then ranked over fourteen different indicators relevant to SEE analysis (social (S), economic (E), and environmental (E) aspects) of sustainability. A comprehensive framework is proposed in which decision experts (DEs) are capable to assess linguistic values to give their decisions and contribute in the decision-making needs to rank the SEE aspects that affect the sustainable perspective of LCTSs. This paper therefore proposes an integrated decision-making framework considering the various conflicting indicators and SEE aspects of sustainability. In addition, treating of uncertainty and inconsistency for data, we consider a neutrosophic setting with the use of single-valued neutrosophic numbers (SVNNs). First, the MEREC (Method based on the removal effects of criteria) weighting procedure is applied to recognize the relative significance of the SEE aspects and their indicators. Second, the generalized Dombi operators are proposed and their elegant properties are discussed to obtain aggregated information of SVNNs. Third, MULTIMOORA method is used to prioritize alternatives. A case study considering six LCTSs is taken to approve the practicality of the introduced methodology, and comparison discussion is made to illustrate the benefits of the developed methodology. Sensitivity investigation is done to evidence the rationality and permanence of the proposed methodology with variations in indicators’ weights. The outcomes of the study offer valuable facts for low-carbon tourism experts and the outcomes of the case study specify that the LCTS-I is the optimum sustainable LCTSs with overall assessment degree of 0.208 after that LCTS-II with utility degree of 0.172.

A new similarity-based classifier with Dombi aggregative operators

• A new classification method using Dombi aggregation operators is proposed and tested on real world datasets. • The most suitable Dombi operator for aggregation in each data set is determined. • The new classifier is efficient in classifying samples from both large and small datasets. • Classification accuracies obtained indicate an improvement compared to benchmark classifiers. In this paper we extend the similarity classifier to cover Dombi aggregation operators. The similarity classifier was earlier studied with the ordered weighted averaging (OWA) operator, the generalized mean, and other operators. We concentrate on the use of Dombi operators during aggregation of similarities within the classifier. Four Dombi aggregation operators applied here include: conjunctive, disjunctive, weighted conjunctive, and the product operator. From each of these operators, we form a variant of the similarity classifier. The proposed methods were tested on four real world medical datasets which include: fertility, lung cancer, Haberman’s survival, and liver disorder. The new classifiers achieved improved classification accuracies compared with earlier methods. Compared with the classifier using the generalized mean, the proposed method achieved an improvement of 17.80 % on fertility, 5.88 % on lung cancer, 0.65 % on Haberman’s survival, and 0.29 % on liver disorder datasets.

Probabilistic linguistic q‐ rung orthopair fuzzy Generalized Dombi and Bonferroni mean operators for group decision‐making with unknown weights of experts

In this paper, we develop a multicriteria group decision-making methodology with probabilistic linguistic q-rung orthopair fuzzy sets (PLqROFSs). The benefit of choosing PLqROFSs is that they consider the simultaneous occurrence of stochastic and nonstochastic uncertainty and so are superior to probabilistic hesitant fuzzy sets, linguistic intuitionistic fuzzy sets, and linguistic Pythagorean fuzzy sets. To develop the methodology, we first propose two types of operators, namely, probabilistic linguistic q-rung orthopair fuzzy weighted Generalized Dombi operator which gives the flexibility of choosing the parameter values and probabilistic linguistic q-rung orthopair fuzzy weighted Generalized Dombi Bonferroni mean operator which can consider the interrelationships between criteria. Since both the subjective and objective weights of experts are hardly considered in the current PLqROFSs-based research, so in our proposed methodology, we deploy the thought of consistency and similarity between the experts to calculate the subjective and objective weights, respectively, of the experts and as a result the evaluation results do not get malformed. For measuring the weights of criteria, the gray correlation coefficient of the assessment value of criteria is used to reflect the similarity between the criteria and its reference value. To exhibit the applicability of the proposed operators, we provide a case study on biomass feedstock selection. Moreover, to make sure that our model is stable, we have investigated a sensitivity analysis of parameters. At the end, we make a comparison of our approach to different existing schemes.