Rung Orthopair Research Articles

Enhancing multi-criteria decision-making in smart farming using (p, q)-rung orthopair fuzzy hypersoft sets and weighted aggregation operators

Enhancing multi-criteria decision-making in smart farming using (p, q)-rung orthopair fuzzy hypersoft sets and weighted aggregation operators

MCDM model using Jaccard and cosine similarity-driven aggregation operators in (n, m)-rung orthopair fuzzy environment: a case study on government medical facilities in Indian states

MCDM model using Jaccard and cosine similarity-driven aggregation operators in (n, m)-rung orthopair fuzzy environment: a case study on government medical facilities in Indian states

A generalized interval-valued p,q Rung orthopair fuzzy Maclaurin symmetric mean and modified regret theory based sustainable supplier selection method

A novel interval valued p,q Rung orthopair fuzzy (IVPQ-ROF) multiple attribute group decision making (MAGDM) method for sustainable supplier selection (SSS) is proposed in this paper. This study mainly contains two research points: (1) tackling the interrelation between attributes; and (2) describing the psychological state and risk attitude of decision makers (DMs). For the first research point, we introduce the Archimedean operation rules for interval valued p,q Rung orthopair fuzzy sets (IVPQ-ROFSs), then the generalized interval valued p, q Rung orthopair fuzzy Maclaurin symmetric mean (GIVPQ-ROFMSM) operator and the generalized interval valued p, q Rung orthopair fuzzy weighted Maclaurin symmetric mean (GIVPQ-ROFWMSM) operator are defined to reflect the correlation between attributes. For the second research point, we introduce the positive ideal degree (PID) and negative ideal degree (NID) based on projection of IVPQ-ROFSs, and modified regret theory. Both of them consider the best alternative and worst alternative, so as to reflect the psychological state and risk attitude of DMs. Finally, a SSS problem is presented to manifest the effectiveness of the designed method. We also provide sensitivity analysis and comparative analysis to further demonstrate the rationality and validity of the proposed method.

Development of [formula omitted] quasirung orthopair fuzzy hamacher aggregation operators and its application in decision-making problems

The concept of p,q− quasirung orthopair fuzzy (p,q− QOF) sets is an advanced extension of q− rung orthopair fuzzy sets (q− ROFSs). This paper introduces the adaptation of Hamacher t-norm and t-conorm to the p,q− QOF environment. A series of Hamacher aggregation operators (AOs) and their associated properties are presented. This study extends its application to multi-criteria group decision-making (MCGDM) for practical problem-solving, illustrated through the analysis of mobile payment platforms. The influence of the aggregation operator parameters, denoted as p and q, on the outcomes of decisions is effectively showcased. Moreover, a comparative analysis is carried out to validate the credibility and authenticity of the proposed model. Finally, the advantages and limitations of the proposed model are outlined.

Multi-attribute decision-making with (p, q)-rung orthopair fuzzy sets

Multi-attribute decision-making with (p, q)-rung orthopair fuzzy sets

Novel linguistic $ q $-rung orthopair fuzzy Aczel-Alsina aggregation operators for group decision-making with applications

<p>In this article, we presented two novel approaches for group decision-making (GDM) that were derived from the initiated linguistic $ q $-rung orthopair fuzzy Aczel-Alsina weighted arithmetic (L$ q $-ROFAAWA) aggregation operator (AgOp) using linguistic $ q $-rung orthopair fuzzy numbers (L$ q $-ROFNs). To introduce these GDM techniques, we first defined new operational laws for L$ q $-ROFNs based on Aczel-Alsina $ t $-norm and $ t $-conorm. The developed scalar multiplication and addition operations of L$ q $-ROFNs addressed the limitations of operations when $ q = 1 $. The first proposed GDM methodology assumed that both experts' weights and attribute weights were fully known, while the second technique assumed that both sets of weights were entirely unknown. We also discussed properties of L$ q $-ROFNs under the L$ q $-ROFAAWA operators, such as idempotency, boundedness, and monotonicity. Furthermore, we solved problems related to environmental and economic issues, such as ranking countries by air pollution, selecting the best company for bank investments, and choosing the best electric vehicle design. Finally, we validated the proposed GDM approaches using three validity tests and performed a sensitivity analysis to compare them with preexisting models.</p>

Q- rung orthopair probabilistic hesitant fuzzy hybrid aggregating operators in multi-criteria decision making problems

With the increase of complex information in applications of decision making problems, the use of probabilistic hesitant fuzzy set structure has expanded. Therefore, this paper aims to present two new operators namely q-rung orthopair probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric (q-ROPHHWAG) operator and q-rung orthopair probabilistic hesitant fuzzy hybrid ordered weighted arithmetic and geometric (q-ROPHHOWAG) operator for q>0. The presented operators are better than existing operators in many respects as adding a new parameter, having more flexible structure and presenting comparative analysis in its own. Moreover, we mention from some properties of the proposed operators. In addition to, we give an algorithm and example to indicate effective, reality and flexible of presented method and operators. Then, we solve an example over Pythagorean probabilistic hesitant fuzzy sets with our operators and the results are agreement and the offered operators have superior effect than other operators.

Bidirectional normalized $$q$$-rung orthopair fuzzy projection and extended TOPSIS approach to multiattribute group decision making

Bidirectional normalized $$q$$-rung orthopair fuzzy projection and extended TOPSIS approach to multiattribute group decision making

Cosine Similarity Measures of (m, n)-Rung Orthopair Fuzzy Sets and Their Applications in Plant Leaf Disease Classification

A fuzzy set is a powerful tool to handle uncertainty and ambiguity, and generally, the notions of symmetry and similarity are also exhibited in the fuzzy set theory. The class of (m, n)-rung orthopair fuzzy sets through two universes are more flexible and efficient than the q-rung orthopair fuzzy sets when discussing the symmetry and similarity between multiple objects. This research article comprehensively investigates ten similarity measures that employ cosine and cotangent functions for comparing (m, n)-rung orthopair fuzzy sets, which are a superclass of q-rung orthopair fuzzy sets. Moreover, the proposed weighted similarity measures are applied to real-world problems in building material analysis. A comparative analysis is conducted between the proposed measures and the existing cosine and cotangent measures of q-rung orthopair fuzzy sets, showing that the proposed measures are more efficient than existing ones. Additionally, a numerical example demonstrates the practical and scientific applications of these similarity measures in classifying plant leaf diseases. The sensitivity analysis shows that the existing measures cannot be applied to (m, n)-fuzzy data for distinct values of m and n. The results are supported by graphical interpretations, further illustrating the efficacy of the proposed measures.

Schweizer‐Sklar operations based hybrid aggregation operator to dual hesitant q‐rung orthopair fuzzy set and its application on MCGDM

AbstractDual hesitant q‐rung orthopair fuzzy (DHq‐ROF) set appears as a powerful tool in compare to other variants of fuzzy sets to deal with uncertainties associated with available information in various real‐life decision‐making cases. In order to make DHq‐ROF aggregation information process flexible, at first some operations viz., addition, multiplication, scalar multiplication, exponential laws based on Schweizer‐Sklar class of t‐conorms and t‐norms are defined. Subsequently, using these operations, weighted average and geometric operators and ordered weighted average and geometric operators are introduced. But weighted average or geometric operators and ordered weighted average or geometric operators consider only the weight of the opinions and the weight of the ordered position of each given opinion respectively. To resolve weights of the arguments, hybrid aggregation operators viz., DHq‐ROF Schweizer‐Sklar hybrid averaging, DHq‐ROF Schweizer‐Sklar hybrid geometric operators are developed and their properties are discussed. Afterwards, a new method to deal with multicriteria group decision making problems under DHq‐ROF environment is framed. To illustrate the proposed method a decision making problem related to investment company selection is considered and solved. To show the advantages of the proposed study, a comparative analysis among the developed and existing studies is discussed.

Some novel q‐rung orthopair fuzzy similarity measures and entropy measures with their applications

AbstractIn this paper, we have introduced some new similarity measures for ‐rung orthopair fuzzy sets and discussed their various features. These similarity measures have been constructed with the help of t‐conorms. The suggested similarity measures are more effective than the available ones in computing the similarity between distinct ‐rung orthopair fuzzy sets. With the help of these suggested similarity measures, we have also developed some novel entropy measures for ‐rung orthopair fuzzy sets. The newly proposed entropy measures are more effective than the existing ones in handling linguistic hedges. The applicability of the suggested similarity measures has been demonstrated in pattern analysis and the findings have been found to be better than due to existing ones. The traditional decision‐making method namely, the technique for order preference by similarity to the ideal solution gives us a compromise solution that is either closest to the positive ideal solution and farthest from the negative ideal solution but not both. So, to overcome this major drawback, we suggest a novel multi‐attribute decision‐making method in the ‐rung orthopair fuzzy environment and apply it to a decision‐making problem.

Weighted dual hesitant $$q$$-rung orthopair fuzzy sets and their application in multicriteria group decision making based on Hamacher operations

Weighted dual hesitant $$q$$-rung orthopair fuzzy sets and their application in multicriteria group decision making based on Hamacher operations

A novel structure of $ q $-rung orthopair fuzzy sets in ring theory

<abstract><p>The q-rung orthopair fuzzy atmosphere is an innovative approach for handling unclear circumstances in a range of decision making problems. As compare to intuitionistic fuzzy sets, this one is more appropriate and adaptable because it evaluates the significance of ring theory while retaining the features of q-rung orthopair fuzzy sets. In this study, we characterize $ q $-rung orthopair fuzzy subring as a modification of the pythagorean fuzzy subring. We introduce the novel idea of $ q $-rung orthopair fuzzy subring and investigate the algebraic characteristics for the $ q $-rung orthopair fuzzy subrings. Furthermore, we establish the concept of $ q $-rung orthopair fuzzy quotient ring and $ q $-rung orthopair fuzzy left and right ideals. Also, we describe the $ q $-rung orthopair fuzzy level subring and associate axioms. Finally, we investigate how ring homomorphism influences the q-rung orthopair fuzzy subring and investigate there pre-images homomorphism on $ q $-ROFSR and different aspects of images.</p></abstract>

A novel decision model with Einstein aggregation approach for garbage disposal plant site selection under $ q $-rung orthopair hesitant fuzzy rough information

<abstract><p>Environmental science and pollution research has benefits around the globe. Human activity produces more garbage throughout the day as the world's population and lifestyles rise. Choosing a garbage disposal site (GDS) is crucial to effective disposal. In illuminated of the advancements in society, decision-makers concede a significant challenge for assessing an appropriate location for a garbage disposal site. This research used a multi-attribute decision-making (MADM) approach based on $ q $-rung orthopair hesitant fuzzy rough ($ q $-ROHFR) Einstein aggregation information for evaluating GDS selection schemes and providing decision-making (DM) support to select a suitable waste disposal site. In this study, first, q-ROHFR Einstein average aggregation operators are integrated. Some intriguing characteristics of the suggested operators, such as monotonicity, idempotence and boundedness were also explored. Then, a MADM technique was established using the novel concept of $ q $-ROHFR aggregation operators under Einstein t-norm and t-conorm. In order to help the decision makers (DMs) make a final choice, this technique aims to rank and choose an alternative from a collection of feasible alternatives, as well as to propose a solution based on the ranking of alternatives for a problem with conflicting criteria. The model's adaptability and validity are then demonstrated by an analysis and solution of a numerical issue involving garbage disposal plant site selection. We performed a the sensitivity analysis of the proposed aggregation operators to determine the outcomes of the decision-making procedure. To highlight the potential of our new method, we performed a comparison study using the novel extended TOPSIS and VIKOR schemes based on $ q $-ROHFR information. Furthermore, we compared the results with those existing in the literature. The findings demonstrate that this methodology has a larger range of information representation, more flexibility in the assessment environment, and improved consistency in evaluation results.</p></abstract>

Averaging aggregation operators under the environment of <i>q</i>-rung orthopair picture fuzzy soft sets and their applications in MADM problems

<abstract><p><italic>q</italic>-Rung orthopair fuzzy soft set handles the uncertainties and vagueness by membership and non-membership degree with attributes, here is no information about the neutral degree so to cover this gap and get a generalized structure, we present hybrid of picture fuzzy set and <italic>q</italic>-rung orthopair fuzzy soft set and initiate the notion of <italic>q</italic>-rung orthopair picture fuzzy soft set, which is characterized by positive, neutral and negative membership degree with attributes. The main contribution of this article is to investigate the basic operations and some averaging aggregation operators like <italic>q</italic>-rung orthopair picture fuzzy soft weighted averaging operator and <italic>q</italic>-rung orthopair picture fuzzy soft order weighted averaging operator under the environment of <italic>q</italic>-rung orthopair picture fuzzy soft set. Moreover, some fundamental properties and results of these aggregation operators are studied, and based on these proposed operators we presented a stepwise algorithm for MADM by taking the problem related to medical diagnosis under the environment of <italic>q</italic>-rung orthopair picture fuzzy soft set and finally, for the superiority we presented comparison analysis of proposed operators with existing operators.</p></abstract>

Interval Valued q- Rung Orthopair Hesitant Fuzzy Choquet Aggregating Operators in Multi-Criteria Decision Making Problems

Abstract: In this paper, we introduce Interval valued q- Rung Orthopair Hesitant fuzzy sets (IVq-ROHFS) with motivation of Interval valued pythagorean Hesitant fuzzy sets [44] as a new concept. Then, we give some basic operations as complement, union, intersection, addition, scalar multiplication, scalar power. Also, we combine to (IVq-ROHFS) and choquet integral , together with aggregating operators, and develop to Interval valued q- rung orthopair hesitant fuzzy Choquet averaging operator (IVq-ROHCA) and Interval valued q- rung orthopair hesitant fuzzy Choquet geometric operator (IVq-ROHCG). Then, we offer to indicate soft approach of proposed IVq-ROHCA and IVq-ROHCG an example adopted from Interval-valued intuitionistic hesitant fuzzy Choquet integral based TOPSIS (IVIHCI) [43]. The obtained results are agreement with IVIHCI but presented IVq-ROHCA and IVq-ROHCG have more advantages than existing structures as Interval-valued intuitionistic hesitant fuzzy sets (IVIHFS), interval-valued Pythagorean Hesitant fuzzy sets (IVPHFS) with reasons changing according to need, requirement, prefer of decision makers and moreover, being IVIHFS and IVPHFS are special cases of IVq-ROHFS. It is open from comparative analysis that the while some of offered approaches are giving no solution for some values, our operators present to needed results.

Ranking products through online reviews considering the mass assignment of features based on BERT and [formula omitted]-rung orthopair fuzzy set theory

A product ranking method is an effective tool that can analyze a significant number of online product reviews to recommend suitable products to consumers. However, existing product ranking methods have two main limitations: (1) the high manual annotation costs and (2) the inability to express consumers’ purchasing decisions because the information is limited to a single feature of each product. To overcome the limitations, this paper proposes a novel product ranking method considering the mass assignment of features based on bidirectional encoder representations using transformers (BERT) and q-rung orthopair fuzzy set theory. First, BERT is adopted to identify sentiment orientations of online product reviews and product features from online product reviews. Subsequently, the product features are clustered into groups and the relative frequencies of product features are obtained. Second, the relative frequencies of product features are transformed into q-rung orthopair fuzzy numbers based on mass assignment theory. Third, the q-rung orthopair fuzzy numbers are aggregated by the q-rung orthopair fuzzy generalized weighted Heronian mean operator to rank the products. Finally, we implement the method using a case study of six different phones to verify its feasibility. Using the case study, we also perform comparisons and sensitivity analyses, which demonstrate the superiority of our method.

Approach to multi-attribute decision-making problems based on neutrality aggregation operators of T-spherical fuzzy information

In the process of decision-making, uncertain information is always challenging to deal with. T-spherical fuzzy set (TSFS) operates vagueness of data by analysing three independent functions, namely membership, non-membership, and abstinence function. The TSFS provides us robust scheme with parameter qge 1 to handle the countless opportunities. Hence, this set proves its superiority over the existing picture fuzzy set (PFS) and spherical fuzzy set (SFS). Now a day, decision-makers usually assign impartial values throughout the assessment. This manuscript demonstrates some new operational laws by fusing the neutral characteristics of the degrees of membership and using the probability sum (PS) function. Meanwhile, we determine several aggregation operators (AOs) including weighted averaging neutral, ordered weighed neutral, and hybrid averaging neutral AOs to aggregate the data under T-spherical fuzzy (TSF) environment. As it came to the notice that weighted neutral averaging aggregation operators of the Pythagorean fuzzy set (PyFS), single-valued neutrosophic fuzzy set (SVNFS), and q-rung orthopair fuzzy set (q-ROFS) have some restrictions during the decision-making problems. So, to overcome this, we introduce a new multi-attribute group decision-making method (MAGDM) based on proposed AOs. Lastly, we provide various numerical instances to explain the method and exhibit its supremacy. Furthermore, a comparative analysis is conducted to compare the potential of proposed AOs with some other existing methods.

Loss Function Information Fusion and Decision Rule Deduction of Three-Way Decision by Constructing Interval-Valued $q$-Rung Orthopair Fuzzy Integral

Three-way decision is consistent with human cognitive processes and applied to different information systems. However, since the real world is more imprecision, hesitation, and ambiguity, experts can select interval fuzzy information to represent their evaluations. In the evaluation process, experts sometimes may not guarantee the interval fuzzy information satisfy the constraint between membership and nonmembership, which further impacts make decisions. Interval-valued <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> -rung orthopair fuzzy set (IVq-ROFS) are proposed to improve the fault-tolerant ability and ensure the experts’ evaluation make sense. In this case, this article generalizes IVq-ROFS to three-way decision, which consists of the construction of three-way decision and the aggregation of interval continuity of IVq-ROFS. For considering the aggregation of interval continuity of IVq-ROFS, we first investigate the IVq-ROFS integral to aggregate continuous IVq-ROFSs by developing simplified interval-valued <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> -rung orthopair fuzzy set. Particularly, in order to obtain integrable region, we design <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> -amendment to amend integral region of IVq-ROFS for removing unmeaning point in advance. To simplify the calculation, we further utilize Taylor series of the integral function to replace the complicated integral function. Second, a new equivalence class method is constructed to support three-way decision. Third, with the aid of the integral of IVq-ROFS and equivalence class method, we availably fuse the loss functions of the equivalence class and obtain the classifying rules of three-way decision by comparing the expected losses. Finally, we elaborate three-way decision by using a case of medical diagnosis about nephropathy and prove the validity of the investigated model.

Models for MAGDM with dual hesitant q-rung orthopair fuzzy 2-tuple linguistic MSM operators and their application to COVID-19 pandemic.

In this article, we introduce dual hesitant -rung orthopair fuzzy 2-tuple linguistic set (DHq-ROFTLS), a new strategy for dealing with uncertainty that incorporates a 2-tuple linguistic term into dual hesitant -rung orthopair fuzzy set (DHq-ROFS). DHq-ROFTLS is a better way to deal with uncertain and imprecise information in the decision-making environment. We elaborate the operational rules, based on which, the DHq-ROFTL weighted averaging (DHq-ROFTLWA) operator and the DHq-ROFTL weighted geometric (DHq-ROFTLWG) operator are presented to fuse the DHq-ROFTL numbers (DHq-ROFTLNs). As Maclaurin symmetric mean (MSM) aggregation operator is a useful tool to model the interrelationship between multi-input arguments, we generalize the traditional MSM to aggregate DHq-ROFTL information. Firstly, the DHq-ROFTL Maclaurin symmetric mean (DHq-ROFTLMSM) and the DHq-ROFTL weighted Maclaurin symmetric mean (DHq-ROFTLWMSM) operators are proposed along with some of their desirable properties and some special cases. Further, the DHq-ROFTL dual Maclaurin symmetric mean (DHq-ROFTLDMSM) and weighted dual Maclaurin symmetric mean (DHq-ROFTLWDMSM) operators with some properties and cases are presented. Moreover, the assessment and prioritizing of the most important aspects in multiple attribute group decision-making (MAGDM) problems is analysed by an extended novel approach based on the proposed aggregation operators under DHq-ROFTL framework. At long last, a numerical model is provided for the selection of adequate medication to control COVID-19 outbreaks to demonstrate the use of the generated technique and exhibit its adequacy. Finally, to analyse the advantages of the proposed method, a comparison analysis is conducted and the superiorities are illustrated.