Linguistic Intuitionistic Fuzzy Information Research Articles

A personalized individual semantics model for computing with linguistic intuitionistic fuzzy information and application in MCDM

This paper develops a personalized individual semantics (PISs) model for computing with linguistic intuitionistic fuzzy information and applies to evaluate different brands of mobile phones. First, considering that a linguistic term means different things to different decision-makers, a consistency-driven optimization model for checking the additive consistent linguistic intuitionistic fuzzy preference relations (LIFPRs) is constructed by considering the PISs model. Besides, several optimization models are built to determine the PISs of linguistic terms with LIFPRs and obtain the acceptable additive consistent LIFPRs. Second, a new definition of Hamming distance for measuring linguistic intuitionistic fuzzy numbers (LIFNs) is developed by considering the PISs model, and several desirable properties are discussed. Then, the method of deriving the weight vectors of criteria is calculated based on the proposed distance measure. Subsequently, a framework of group decision-making (GDM) process with LIFPRs is offered, and the application of the proposed method is illustrated by using a multi-criteria decision-making (MCDM) problem about evaluating different brands of mobile phones. Finally, the comparative analysis is conducted to show the feasibility of proposed method.

On three perspectives for deriving three-way decision with linguistic intuitionistic fuzzy information

The determination of both thresholds in decision-theoretic rough sets is an important problem of study that has aroused widespread attention in recent years. Although many related methods have been proposed, they may need a substantial amount of computation in model solving even not capture the thresholds in some cases. In this paper, we introduce linguistic intuitionistic fuzzy numbers (LIFNs) into loss functions due to LIFNs integrating the advantages of linguistic terms and intuitionistic fuzzy numbers, and propose a single optimization model-based, threshold-determined method to derive three-way decision. First, we define a novel measure for ranking LIFNs, verify its properties, analyze the relationships between loss functions with LIFNs and establish linguistic intuitionistic fuzzy decision-theoretic rough sets with a novel measure for LIFNs. Second, we investigate linguistic intuitionistic fuzzy, three-way decision methods from three perspectives, especially from the third perspective. We construct a single optimization model for capturing the thresholds that can overcome the shortcomings of the methods from two other perspectives, and the uniqueness of the optimal solution of this model is proven with the aid of the Karush-Kuhn-Tucker (KKT) condition. Third, a single model-based perspective method and its corresponding algorithm are designed to determine the thresholds for linguistic intuitionistic fuzzy information. Last, an illustrative example and simulated experiments are conducted to show the validity of our method.

Group decision making for internet public opinion emergency based upon linguistic intuitionistic fuzzy information

With the wide use of network, the outbreak of network public opinion emergencies has changed from single to multiple. The goal of the current study is to construct the emergency group decision-making (EGDM) model for multiple network public opinion emergencies under the linguistic intuitionistic environment. First of all, we introduce a new version of Copula and Co-copula named extended Copula (EAC) and extended Co-Copula (EACC), respectively, which can be used to capture the relation of attributes (indexes) in the group decision making problems of network public opinion emergencies; Some special cases of EAC and EACC are gained to manage intuitionistic fuzzy information (IFI). Besides, the novel operational rules of linguisitic intuitionistic fuzzy numbers (LIFNs) based upon EAC and EACC are also defined under linguistic intuitionistic environment. What’s more, by integrating the Choquet integral and the proposed operational rules of LIFNs, the linguistic intuitionistic fuzzy Choquet-Copula aggregation operators (LIFCCA) are proposed together with their properties are also investigated; whilst, five specific forms of LIFCCA are obtained when EAC and EACC take different generators. Last but not least, an EGDM approach is constructed based upon proposed LIFCCA; Consequently, the validities and merits of the proposed EGDM approach are shown by comparing with existing approaches.

A Linguistic Intuitionistic Cloud Decision Support Model with Sentiment Analysis for Product Selection in E-commerce

Online product reviews significantly impact the online purchase decisions of consumers. However, extant decision support models have neglected the randomness and fuzziness of online reviews and the interrelationships among product features. This study presents an integrated decision support model that can help customers discover desirable products online. This proposed model encompasses three modules: information acquisition, information transformation, and integration model. We use the information acquisition module to gather linguistic intuitionistic fuzzy information in each review through sentiment analysis. We also apply the information transformation module to convert the linguistic intuitionistic fuzzy information into linguistic intuitionistic normal clouds (LINCs). The integration module is employed to obtain the overall LINCs for each product. A ranked list of alternative products is determined. A case study on Taobao.com is then provided to illustrate the effectiveness and feasibility of the proposal, along with sensitivity and comparison analyses, to verify its stability and superiority. Finally, conclusions and future research directions are suggested.

Linguistic Intuitionistic Fuzzy Group Decision Making Based on Aggregation Operators

This paper researches decision making with linguistic intuitionistic fuzzy variables. Several linguistic intuitionistic fuzzy operations are first defined. Then, several linguistic intuitionistic fuzzy aggregation operators are provided, including the linguistic intuitionistic fuzzy hybrid weighted arithmetical averaging operator, and the linguistic intuitionistic fuzzy hybrid weighted geometric mean operator. Considering the interactive characteristics between the weights of elements in a set, several linguistic intuitionistic fuzzy Shapley aggregation operators are presented, including the linguistic intuitionistic fuzzy hybrid Shapley arithmetical averaging operator, and the linguistic intuitionistic fuzzy hybrid Shapley geometric mean operator. To ensure the application reasonably, several desirable properties are discussed. When the weighting information is incompletely known, models for the optimal fuzzy and additive measures are constructed. After that, an approach to multi-criteria group decision making with linguistic intuitionistic fuzzy information is performed. Finally, a practical example about evaluating different types of engines is provided to illustrate the developed procedure.

Linguistic intuitionistic fuzzy Hamacher aggregation operators and their application to group decision making

Linguistic intuitionistic fuzzy variables (LIFVs) can efficiently denote the qualitative preferred and non-preferred cognitions of decision makers. This paper researches group decision making with linguistic intuitionistic fuzzy information. To do this, several Hamacher operational laws on LIFVs are defined. To derive the comprehensive evaluating values of alternatives, several linguistic intuitionistic fuzzy Hamacher aggregation operators are proposed, including the linguistic intuitionistic fuzzy Hamacher weighted average operator, the linguistic intuitionistic fuzzy Hamacher weighted geometric mean operator, the linguistic intuitionistic fuzzy Hamacher ordered weighted average operator, the linguistic intuitionistic fuzzy Hamacher ordered weighted geometric mean operator, the linguistic intuitionistic fuzzy Hamacher hybrid weighted average operator, and the linguistic intuitionistic fuzzy Hamacher hybrid weighted geometric mean operator. Then, several of their desirable properties are researched to guarantee the rationality. Methods for determining the weights of criteria, decision makers as well as the ordered positions are offered, respectively. After that, a procedure for group decision making with linguistic intuitionistic fuzzy information is provided. Finally, a group decision-making problem is offered to illustrate the application of the new results.

Partitioned Heronian means based on linguistic intuitionistic fuzzy numbers for dealing with multi-attribute group decision making

Heronian mean (HM) operator has the advantages of considering the interrelationships between parameters, and linguistic intuitionistic fuzzy number (LIFN), in which the membership and non-membership are expressed by linguistic terms, can more easily describe the uncertain and the vague information existing in the real world. In this paper, we propose the partitioned Heronian mean (PHM) operator which assumes that all attributes are partitioned into several parts and members in the same part are interrelated while in different parts there are no interrelationships among members, and develop some new operational rules of LIFNs to consider the interactions between membership function and non-membership function, especially when the degree of non-membership is zero. Then we extend PHM operator to LIFNs based on new operational rules, and propose the linguistic intuitionistic fuzzy partitioned Heronian mean (LIFPHM) operator, the linguistic intuitionistic fuzzy weighted partitioned Heronian mean (LIFWPHM) operator, the linguistic intuitionistic fuzzy partitioned geometric Heronian mean (LIFPGHM) operator and linguistic intuitionistic fuzzy weighted partitioned geometric Heronian mean (LIFWPGHM) operator. Further, we develop two methods to solve multi-attribute group decision making (MAGDM) problems with the linguistic intuitionistic fuzzy information. Finally, we give some examples to verify the effectiveness of two proposed methods by comparing with the existing

Multiattribute Group Decision Making Methods Based on Linguistic Intuitionistic Fuzzy Power Bonferroni Mean Operators

This paper focuses on the multiattribute group decision making problems with linguistic intuitionistic fuzzy information. Firstly the concept of linguistic intuitionistic fuzzy numbers (LIFNs) is introduced, and then based on the LIFNs, some new aggregation operators based on Bonferroni mean and power operator are proposed, such as linguistic intuitionistic fuzzy power Bonferroni mean (LIFPBM) operator, linguistic intuitionistic fuzzy weighted power Bonferroni mean (LIFWPBM) operator, linguistic intuitionistic fuzzy geometric power Bonferroni mean (LIFGPBM) operator, and linguistic intuitionistic fuzzy weighted geometric power Bonferroni mean (LIFWGPBM) operator. Then, some properties are proved such as idempotency, permutation, and boundedness. Besides, some special situations of the operators are explored. After that, an approach based of the LIFWGPBM and LIFWGPBM operators is proposed. Finally an example is used to illustrate the validity of the developed method.

Linguistic Intuitionistic Fuzzy Sets and Application in MAGDM

To better deal with imprecise and uncertain information in decision making, the definition of linguistic intuitionistic fuzzy sets (LIFSs) is introduced, which is characterized by a linguistic membership degree and a linguistic nonmembership degree, respectively. To compare any two linguistic intuitionistic fuzzy values (LIFVs), the score function and accuracy function are defined. Then, based ont-norm andt-conorm, several aggregation operators are proposed to aggregate linguistic intuitionistic fuzzy information, which avoid the limitations in exiting linguistic operation. In addition, the desired properties of these linguistic intuitionistic fuzzy aggregation operators are discussed. Finally, a numerical example is provided to illustrate the efficiency of the proposed method in multiple attribute group decision making (MAGDM).