Linguistic Aggregation Operators Research Articles

Novel Aczel-Alsina operations-based probabilistic double hierarchy linguistic aggregation operators and their applications in Blockchain performance evaluation Blockchain

The development and application of blockchain provides technical support for supply chain technological innovation and industrial innovation. Integrating the decentralized, independent, open, traceable and tamper-proof features of the blockchain into the supply chain can effectively improve the problems of unstable supply chain structure, low security, low privacy, low collaboration ability and high operating costs. Establishing probabilistic double hierarchy linguistic multi-attribute decision-making (PDHL-MADM) model to evaluate the performance of blockchain is an effective measure to optimize blockchain performance and improve supply chain stability. Therefore, this thesis first takes the processing efficiency, cost, security performance, update and improvement ability as evaluation attributes. Then the IDOCRIW weight method is used to calculate the objective weight of attributes. Based on Aczel-Alsina t-norm (AATN) and Aczel-Alsina t-conorm (AATCN), four operations of probabilistic double hierarchy linguistic term set (PDHLTS) are defined, and PDHLAAWA operator, PDHLAAOWA operator, PDHLAAHA operator, PDHLAAHM operator, PDHLAAWHM operator and their dual operators are proposed, and a series of corresponding PDHL operator models are constructed. In addition, the sensitivity and stability of this series of operator models are analyzed in depth. Finally, the new model proposed in this thesis is compared with the existing model to verify its scientific and superiority.

Decision-Making Approach Based on Bipolar Complex Fuzzy Uncertain Linguistic Aggregation Operators

Decision-Making Approach Based on Bipolar Complex Fuzzy Uncertain Linguistic Aggregation Operators

T-Spherical 2-Tuple Linguistic Aggregation Operators and Their Applications in the Decision-Making Strategy

The decision-making technique is very important and valuable and is used for evaluating the best decision from the collection of preferences. In this manuscript, we elaborated the novel concept of the T-spherical 2-tuple linguistic (TS2-TL) set and its operational laws in the consideration of t-norm and t-conorm. The theory of the TS2-TL set is more massively generalized than the fuzzy set and its extensions. Moreover, aggregating the collection of information into a singleton set is also a very challenging task for scholars; therefore, by using the TS2-TL setting, we explored the TS2-TL weighted averaging (TS2-TLWA), TS2-TL ordered weighted averaging (TS2-TLOWA), TS2-TL hybrid averaging (TS2-TLHA), TS2-TL weighted geometric (TS2-TLWG), TS2-TL ordered weighted geometric (TS2-TLOWG), and TS2-TL hybrid geometric (TS2-TLHG) operators and described their important and dominant properties. The derived operators based on TS2-TL information are the modified version of the averaging/geometric aggregation operators for fuzzy set and their extensions. Using the invented approaches, various specific terminologies are also diagnosed with the help of remarks. The elaborated operators are applied to determine and rank the manufacturing of small and medium-sized enterprises (SMEs). Finally, we utilize the sensitive analysis of the exposed approaches with various existing drawbacks in the presence of many practical examples to expose the improvements, dominance, and graphical representations of utilized approaches.

A three-way decisions approach based on double hierarchy linguistic aggregation operators of strict t-norms and t-conorms.

With the massive increase in uncertainty of linguistic information in realistic decision making, there is a great challenge for people to make decisions in the complex linguistic environment. To overcome this challenge, this paper proposes a three-way decisions method based on aggregation operators of strict t-norms and t-conorms under double hierarchy linguistic environment. By mining the double hierarchy linguistic information, strict t-norms and t-conorms are introduced to define the operation rules and their operation examples are also given. Then, the double hierarchy linguistic weighted average (DHLWA) operator and weighted geometric (DHLWG) operator are proposed based on strict t-norms and t-conorms. Besides, some of their important properties are also proved and derived, such as idempotency, boundedness and monotonicity. Next, DHLWA and DHLWG are integrated with three-way decisions to construct our three-way decisions model. Specifically, the double hierarchy linguistic decision theoretic rough set (DHLDTRS) model is constructed by incorporating the computational model of expected loss with DHLWA and DHLWG, which can consider the various decision attitudes from decision makers more adequately. Furthermore, we also propose a novel entropy weight calculation formula to improve the entropy weight method for obtaining the weights more objectively, and integrate grey relational analysis (GRA) method to calculate the conditional probability. Based on the Bayesian minimum-loss decision rules, the solving method of our model is also propounded and the corresponding algorithm is designed. Finally, an illustrative example and experimental analysis are presented, which can validate the rationality, robustness as well as superiority of our method.

Generalized q-rung picture linguistic aggregation operators and their application in decision making

The q-rung picture linguistic set (q-RPLS) is an effective tool for managing complex and unpredictable information by changing the parameter ‘q’ regarding hesitancy degree. In this article, we devise some generalized operational laws of q-RPLS in terms of the Archimedean t-norm and t-conorm. Based on the proposed generalized operations, we define two types of generalized aggregation operators, namely the q-rung picture linguistic averaging operator and the q-rung picture linguistic geometric operator, and study their relevant characteristics in-depth. With a view toward applications, we discuss certain specific cases of the proposed generalized aggregation operators with a range of parameter values. Furthermore, we explore q-rung picture linguistic distance measure and its required axioms. Then we put forward a technique for q-RPLSs based on the proposed aggregation operators and distance measure to solve multi-attribute decision-making (MADM) challenges with unknown weight information. At last, a practical example is presented to demonstrate the suggested approaches’ viability and to perform the sensitivity and comparison analysis.

Decision Support System Based on Complex Fractional Orthotriple Fuzzy 2-Tuple Linguistic Aggregation Operator

In this research, we provide tools to overcome the information loss limitation resulting from the requirement to estimate the results in the discrete initial expression domain. Through the use of 2-tuples, which are made up of a linguistic term and a numerical value calculated between [0.5,0.5), the linguistic information will be expressed. This model supports continuous representation of the linguistic data within its scope, permitting it to express any information counting received through an aggregation procedure. This study provides a novel approach to develop a linguistic multi-attribute group decision-making (MAGDM) approach with complex fractional orthotriple fuzzy 2-tuple linguistic (CFOF2TL) assessment details. Initially, the concept of a complex fractional orthotriple fuzzy 2-tuple linguistic set (CFO2TLS) is proposed to convey uncertain and fuzzy information. In the meantime, simple aggregation operators, such as CFOF2TL weighted average and geometric operators, are defined. In addition, the CFOF2TL Maclaurin’s symmetric mean (CFOF2TLMSM) operators and their weighted shapes are presented, and their attractive characteristics are also discussed. A new MAGDM approach is built using the developed aggregation operators to address managing economic crises under COVID-19 with the CFOF2TL information. As a result, the effectiveness and robustness of the developed method are accompanied by an empirical example, and a comparative study is carried out by contrasting it with previous approaches.

Prioritization of Strategies of Digital Transformation of Supply Chain Employing Bipolar Complex Fuzzy Linguistic Aggregation Operators

Digitalization has addressed all parts of organizations together with supply chain management. Innovations like installed RFID, GPS, and sensors have assisted organizations with changing their current conventional supply chain framework into more spry, adaptable, open, and cooperative computerized models. A lot of organizations want to get the advantages of digitalization, particularly in the supply chain But here, the biggest problem, that the organizations are facing is the ambiguities, i.e. how to select and evaluate the best strategy for the supply chain digital transformation (SCDT), on which criteria or attribute they can assess the strategies of SCDT, etc. Multi-attribute decision-making (MADM) procedure is the finest technique to evaluate and find out the finest strategy of the SCDT. To handle these ambiguities and for making the MADM technique, this study first establishes the concept of bipolar complex fuzzy linguistic sets (BCFLSs) and its essential properties. Furthermore, we scrutinize average and geometric AOs for BCFLS such as bipolar complex fuzzy linguistic weighted averaging (BCFLWA) and bipolar complex fuzzy linguistic weighted geometric (BCFLWG) operators along with their idempotency, boundedness, and monotonicity properties. After that, to exhibit the usefulness of our established notion and AOs in real life and the selection and evaluation of the strategy of digital transformation of the supply chain, we interpret a DM technique and explore a numerical example. To exhibit the supremacy of the defined BCFLS and defined AOs we compare them with certain prevailing conceptions.

Some interactive uncertain linguistic aggregation operators based on Shapley function and their application

In this paper, two uncertain linguistic aggregation operators named the induced uncertain linguistic hybrid Shapley arithmetical averaging (IULHSAA) operator and the induced uncertain linguistic hybrid Shapley geometric mean (IULHSGM) operator are defined. These operators do not only globally consider the importance of the elements and their ordered positions but overall reflect the correlations between them, respectively. Furthermore, to reduce the complexity of solving a fuzzy measure, the induced uncertain linguistic hybrid 2-additive Shapley arithmetical averaging (IULHASAA) operator and the induced uncertain linguistic hybrid 2-additive Shapley geometric mean (IULHASGM) operator are defined. Moreover, if the weight information of experts and attributes is incompletely known, models for the optimal fuzzy measures are established. Meanwhile, an approach to multi-attribute group decision making under uncertain linguistic environment is developed, which considers the correlative characteristics between experts as well as between attributes. Finally, a numerical example is provided to illustrate the developed procedure.

A Two-Sided Matching Decision-Making Approach with Correlative Criteria Under Probabilistic Linguistic Environment

Two-sided matching decision-making (TSMDM) problems widely exist in human being’s life. In practical TSMDM problems, subjects who are being matched with usually tend to provide linguistic evaluations for convenience. Owing to the fuzziness of decision-making environment, subjects may provide several linguistic terms associated with their probabilities as the evaluations, which can be described as the probabilistic linguistic term sets (PLTSs). To model such scenarios, this paper proposes a TSMDM approach with probabilistic linguistic evaluations. The probabilistic linguistic evaluations are firstly normalized with the preservation of ignored probabilities. The normalized evaluations are then aggregated into the comprehensive evaluations by using the defined Choquet integral-based probabilistic linguistic aggregation (CIPLA) operator. Thereafter, the satisfaction degrees of two sides of subjects are calculated based on the closeness coefficient in TOPSIS method. On the basis of this, a multi-objective TSMDM model aiming to maximize the comprehensive satisfaction degree is built and transformed into a single-objective TSMDM model considering the weights of two sides. To solve the single-objective TSMDM model is to determine the optimal matching result. An illustrative example of matching enterprises and knowledge-sender universities is introduced to validate the proposed approach and compare it with other existing TSMDM approaches. The results illustrate that the proposed approach can not only avoid information loss, but also effectively integrate PLTSs with correlative criteria.

An integrated approach for service quality evaluation of online health communities based on q-rung orthopair fuzzy linguistic aggregation operators

Online health communities (OHCs) have emerged as a significant platform for people communicating health information and self-healthcare management. In recent, the researches focusing on its performance measurement and the service quality evaluation have drawn intensive attention. Although some qualitative methods have made evaluation and analyses for the OHCs performance, the studies based on fuzzy multi-attribute decision making theory are rarely developed in the service quality evaluation of OHCs. In view of the complexity and uncertainty of evaluation mission, this paper develops an integrated evaluation approach of the OHC service quality based on the q-rung orthopair fuzzy linguistic aggregation operators. Firstly, we propose the cross-entropy of q-rung orthopair fuzzy numbers, which is applied in solving the optimal weight of indicators by a linear programming model. Next, the q-rung orthopair fuzzy linguistic power average (q-ROFLPA) and q-rung orthopair fuzzy linguistic partitioned dual Maclaurin symmetric mean (q-ROFLPDMSM) operators are developed for aggregating the assessment information and ranking the OHCs. Based on the proposed aggregation operators, the evaluation indicator system and an evaluation framework are constructed to accomplish the service quality evaluation of OHCs. Finally, a practical evaluation case of OHCs is provided to demonstrate the reliability and advantages of the proposed approach.

A novel linguistic decision-making method based on the voting model for large-scale linguistic decision making

The notable characteristic of large-scale linguistic decision-making problems is that there are so many decision makers who provide linguistic assessments by using fuzzy linguistic representation models. In real-world applications, fuzzy linguistic terms mean different things for different people, and linguistic assessments based on different linguistic representation models may be simultaneous in the same large-scale linguistic decision-making problems. To this end, a novel linguistic decision-making method based on the voting model is proposed in the paper to deal with multi-linguistic assessments provided by decision makers. In large-scale linguistic decision process, evaluation-based voting is defined and multi-linguistic decision matrix is designed to represent multi-linguistic assessments provided by decision makers by using different linguistic representation models, and properties of the decision matrix are analyzed to show that linguistic assessments based on different linguistic representation models can be simultaneously represented. Based on multi-linguistic decision matrix, a new linguistic decision-making framework is developed to deal with large-scale linguistic decision-making problems with multi-linguistic assessments, in which normalization of multi-linguistic decision matrix and trust degrees of linguistic terms are contained, and more important, based on trust degrees of linguistic terms and 2-tuple fuzzy linguistic aggregation operators, an uniform fusion method of multi-linguistic assessments is proposed to aggregate multi-linguistic assessments of large-scale linguistic decision-making problems. Finally, user experiences of shared bikes, which are a large-scale linguistic decision-making problem in real-world applications, are employed to show the new decision-making framework and the uniform fusion method of multi-linguistic assessments, and furthermore, compared with existing linguistic decision-making methods analyzed in the example, it seems that multi-linguistic decision matrix and the uniform fusion method are useful and effective tools to deal with large-scale linguistic decision-making problems with multi-linguistic assessments.

An Approach of Interval-Valued Picture Fuzzy Uncertain Linguistic Aggregation Operator and Their Application on Supplier Selection Decision-Making in Logistics Service Value Concretion

With respect to multiple criteria group decision-making (MCGDM) problems in which both the criteria weights and the expert weights take the form of crisp numbers and attribute values take the form of interval-valued picture fuzzy uncertain linguistic numbers, some new group decision-making analysis methods are developed. Firstly, some operational laws, expected value, and accuracy function of interval-valued picture fuzzy uncertain linguistic numbers are introduced. Then, an interval-valued picture fuzzy uncertain linguistic averaging and geometric aggregation operators are developed. Furthermore, some desirable properties of the developed operators, such as commutativity, idempotency, and monotonicity, have been studied. Based on these operators, an approach to multiple criteria group decision-making with interval-valued picture fuzzy uncertain linguistic information has been proposed. Finally, a practical example of 3PL supplier selection in logistics service value concretion is taken to test the defined method and to expose the effectiveness of the defined model.

Some self-evaluation models of enterprise’s credit based on some probabilistic double hierarchy linguistic aggregation operators

Probabilistic double hierarchy linguistic term set (PDHLTS) can not only express the complex linguistic information that the probabilistic linguistic term set (PLTS) cannot express, but also reflect the frequency or importance of linguistic term set (LTS)that cannot be reflected by the double hierarchy linguistic term set (DHLTS). It is an effective tool to deal with multiple attribute group decision making (MAGDM) problems. Therefore, in this paper, we propose several aggregation operators which can aggregate PDHLTS information and apply them to MAGDM problems. Firstly, the basic notion of PDHLTS is reviewed, and the distance formula and algorithm of PDHLTS are defined; then, extant weighted averaging (WA) operator, weighted geometric(WG) operator and power weighted averaging (PWA) operator, power weighted geometric(PWG) operator to PDHLTS, and establish probability double hierarchy linguistic weighted averaging (PDHLWA) operator, probability double hierarchy linguistic weighted geometric (PDHLWG) operator, probability double hierarchy linguistic power weighted averaging (PDHLPWA) operator, probability double hierarchy linguistic power weighted geometric (PDHLPWG) operator; in addition, The idempotency, boundedness and monotonicity of these aggregation operators are studied; what’s more, those aggregation operators are proposed to establish the enterprise credit self-evaluation model; Finally, compared with the available probabilistic double hierarchy linguistic MAGDM methods, the defined model is proved to be scientific and effective.

A Revised Picture Fuzzy Linguistic Aggregation Operator and Its Application to Group Decision-Making

The complexity of decision environments poses challenges for individuals engaged in decision-making proceedings. Picture fuzzy linguistic sets (PFLSs) are an effective tool for depicting the inherent subjective nature of human cognition. Aiming for the promotion of a general theory on PFLSs, we conduct a critical research to identify some limitations of a recent publication in Cognitive Computation [2018, 10(2), 242–259]. This published article is a meaningful and interesting study that initiates the PFLS as well as introduces the corresponding operations and the Archimedean picture fuzzy linguistic weighted arithmetic averaging operator. Unfortunately, we have carefully analyzed these operations and found that they may not be appropriate to all situations within picture fuzzy linguistic environment, which would result in the violation of human cognition. To eliminate this limitation, we explore and suggest novel operational laws and an aggregation operator for PFLSs from a modified version, so as to support further study on picture fuzzy linguistic group decision-making. Furthermore, a comparative and illustrative example is presented to validate the advantages of our modified operations. Towardly , the research outcome will be of significant benefit to promoting the development of picture fuzzy linguistic decision-making theory. Accordingly, our contribution to improving the current research on PFLSs makes their application in solving realistic problems feasible and practical.

Multi-criteria group decision-making framework for offshore wind farm site selection based on the intuitionistic linguistic aggregation operators

Offshore wind farms have been rapidly proposed owing to the promotion of sustainable development policies. Site selection contributes to the success of offshore wind farm projects and is a complex multi-criteria group decision-making problem. This paper proposes a multi-criteria group decision-making method based on the intuitionistic linguistic aggregation operators and applies it to the site selection decision-making process of offshore wind farm. To begin with, the intuitionistic linguistic numbers are introduced to deal with the uncertainty and fuzziness in decision-making. An optimization weighting model that comprehensively considers subjective and objective factors is then established, which can effectively reflect the correlations among the criteria. Furthermore, in view of the limited rational behavior of the decision-makers, an extended intuitionistic linguistic aggregation operator is defined, according to which the criteria values can be aggregated into a numerical value for comparison. Finally, a case study in China is conducted to verify the rationality and effectiveness of this method. The research results show that the offshore wind farm located in Laizhou, Dongying is the optimal site, and the ranking results of the alternatives are sensitive to the absolute risk aversion coefficient.

Fudge: Fuzzy ontology building with consensuated fuzzy datatypes

An important problem in Fuzzy OWL 2 ontology building is the definition of fuzzy membership functions for real-valued fuzzy sets (so-called fuzzy datatypes in Fuzzy OWL 2 terminology). In this paper, we present a tool, called Fudge, whose aim is to support the consensual creation of fuzzy datatypes by aggregating the specifications given by a group of experts. Fudge is freeware and currently supports several linguistic aggregation strategies, including the convex combination, linguistic OWA, weighted mean and fuzzy OWA, and easily allows to build others in. We also propose and have implemented two novel linguistic aggregation operators, based on a left recursive form of the convex combination and of the linguistic OWA.

Hesitant Fuzzy Linguistic Hamy Mean Aggregation Operators and Their Application to Linguistic Multiple Attribute Decision-Making

Linguistic aggregation operator is a paramount appliance to fix linguistic multiple attribute decision-making (MADM) issues. In the article, the Hamy mean (HM) operator is utilized to fuse hesitant fuzzy linguistic (HFL) information and several novel HFL aggregation operators including the hesitant fuzzy linguistic Hamy mean (HFLHM) operator, weighted hesitant fuzzy linguistic Hamy mean (WHFLHM) operator, hesitant fuzzy linguistic dual Hamy mean (HFLDHM) operator, and weighted hesitant fuzzy linguistic dual Hamy mean (WHFLDHM) operator are proposed. Besides, several paramount theorems and particular cases of these aggregation operators are investigated in detail, and then a novel MADM approach is presented by using the proposed aggregation operators. Ultimately, a practical example is utilized to manifest the effectiveness and practicability of the propounded method.

Probabilistic linguistic information fusion: A survey on aggregation operators in terms of principles, definitions, classifications, applications, and challenges

The probabilistic linguistic term set is a flexible and efficient tool to represent the cognitive complex information of experts. It has attracted many scholars’ attention since it was proposed. Information fusion over the cognitive complex information is a significant issue for decision-making problems. Over the past years, more than 40 aggregation operators have been proposed to fuse the probabilistic linguistic term sets. The aim of this paper is to survey the existing probabilistic linguistic aggregation operators from the perspectives of principles, definitions, classifications, and applications. To do so, first, we summarize the present normalization techniques and operations of probabilistic linguistic term sets. Afterward, this study classifies the existing probabilistic linguistic aggregation operators into 12 kinds. Then, the application areas of these probabilistic linguistic aggregation operators are outlined. Future research directions with interests are proposed to tackle present challenges.

The q-Rung Orthopair Hesitant Fuzzy Uncertain Linguistic Aggregation Operators and Their Application in Multi-Attribute Decision Making

This paper combines the q-rung orthopair hesitant fuzzy sets (q-ROHFSs) with the uncertain linguistic variables, and proposes the q-rung orthopair hesitant fuzzy uncertain linguistic sets (q-ROHFULSs). In addition, the Schweizer-Sklar T-norm is introduced, and a multi-attribute decision-making method based on the q-rung orthopair hesitant fuzzy uncertain linguistic Schweizer-Sklar aggregation operators is established. Firstly, based on the Schweizer-Sklar T-norm, the operational properties of q-rung orthopair hesitant fuzzy uncertain linguistic elements are defined, and the score function, accuracy function and ranking method of the q-rung orthopair hesitant fuzzy uncertain linguistic elements are proposed. Secondly, the q-rung orthopair hesitant fuzzy uncertain linguistic Schweizer-Sklar Bonferroni mean (BM) operator and geometric Bonferroni mean (GBM) operator, Maclaurin symmetric mean (MSM) operator and dual Maclaurin symmetric mean (DMSM) operator, Maclaurin mean (MM) operator and dual Maclaurin mean (DMM) operator are defined. The calculation formulas of the operators are given, the related properties are studied, and the special forms of the operators are discussed. Finally, a multi-attribute decision-making model based on the q-rung orthopair hesitant fuzzy uncertain linguistic aggregation operators is established, and the feasibility and effectiveness of the decision-making method are demonstrated through calculation examples and comparative analyses.

Analysis of Decision Support System Based on 2-Tuple Spherical Fuzzy Linguistic Aggregation Information

The aim of this paper is to propose the 2-tuple spherical fuzzy linguistic aggregation operators and a decision-making approach to deal with uncertainties in the form of 2-tuple spherical fuzzy linguistic sets. 2-tuple spherical fuzzy linguistic operators have more flexibility than general fuzzy set. We proposed a numbers of aggregation operators, namely 2-tuple spherical fuzzy linguistic weighted average, 2-tuple spherical fuzzy linguistic ordered weighted average, 2-tuple spherical fuzzy linguistic hybrid average, 2-tuple spherical fuzzy linguistic weighted geometric, 2-tuple spherical fuzzy linguistic ordered geometric, and 2-tuple spherical fuzzy linguistic hybrid geometric operators. The distinguishing feature of these proposed operators is studied. At that point, we have used these operators to design a model to deal with multiple attribute decision-making issues under the 2-tuple spherical fuzzy linguistic information. Then, a practical application for best company selection for feeds is given to prove the introduced technique and to show its practicability and effectiveness. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantage of our method. Results indicate that the proposed method is suitable and effective for decision making problems.