Intuitionistic Uncertain Linguistic Information Research Articles

Intuitionistic uncertain linguistic prioritized aggregation operators and their application to multi-criteria decision making

The intuitionistic uncertain linguistic information aggregation problems considering different priority levels of criteria are investigated. Firstly, we extended the prioritized averaging (PA) operator to intuitionistic uncertain linguistic environment, defined two new prioritized aggregation operators called the intuitionistic uncertain linguistic prioritized weighted average (IULPWA) operator and the intuitionistic uncertain linguistic prioritized weighted geometric (IULPWG) operator, and established various desirable properties of the proposed operators. Secondly, we developed a multi-criteria decision making (MCDM) approach based on the IULPWA operator (or the IULPWG operator) to deal with the MCDM problems in which the criterion values take the form of intuitionistic uncertain linguistic numbers (IULNs) and the criteria are in different priority levels. Finally, an example is given to illustrate the feasibility and effectiveness of the proposed method, and a comparison analysis is conducted to make clear the differences among the IULPWA operator, the IULPWG operator, the intuitionistic uncertain linguistic number weighted averaging (IULNWA) operator and the intuitionistic uncertain linguistic weighted geometric average (IULWGA) operator.

Model for evaluating the enterprise financial performance with interval-valued intuitionistic uncertain linguistic information

With the development of market economy, Mergers and Acquisitions has become a trend in the development of company. How to effectively analyze and evaluate the financial performance of the listed companies which implemented Mergers and Acquisitions, h

A Novel Integrated Approach for Green Supplier Selection with Interval-Valued Intuitionistic Uncertain Linguistic Information: A Case Study in the Agri-Food Industry

With strengthening global consciousness of environmental protection, green supply chain management plays an increasingly important role in modern enterprise production operation management. A critical means to implement green supply chain management is incorporating environmental requirements into the supplier selection practices. In this paper, we put forward a novel integrated approach by using interval-valued intuitionistic uncertain linguistic sets (IVIULSs) and grey relational analysis (GRA)-technique for order preference by similarity to ideal solution (TOPSIS) method for the evaluation and selection of green suppliers. First, various qualitative assessments of alternatives provided by decision makers are described by the IVIULSs. Then, the GRA-TOPSIS method is extended and employed to prioritize the alternative suppliers. The proposed model can handle the uncertainty and fuzziness of decision makers’ subjective evaluations more easily and get a more realistic and accurate ranking of green suppliers. Finally, an illustrative example in the agri-food industry is presented to verify the proposed green supplier selection model and demonstrate its practicality and effectiveness.

Correlation Coefficient of Interval-Valued Intuitionistic Uncertain Linguistic Sets and Its Application

ABSTRACTWith respect to multiattribute group decision-making with interval-valued intuitionistic uncertain linguistic information, correlation and correlation coefficient are defined. To obtain the optimal weight vector, models based on the introduced correlation coefficient are constructed. Furthermore, two aggregation operators called the interval-valued intuitionistic uncertain linguistic Shapley averaging operator and the interval-valued intuitionistic uncertain linguistic Shapley geometric operator are defined, which are used to aggregate the interval-valued intuitionistic uncertain linguistic information. Moreover, an approach to multiattribute group decision-making under interval-valued intuitionistic uncertain linguistic environment is developed. Finally, an illustrative example is selected to verify the practicality and feasibility of the proposed procedure.

Intuitionistic uncertain linguistic partitioned Bonferroni means and their application to multiple attribute decision-making

ABSTRACTThe Bonferroni mean (BM) was originally introduced by Bonferroni and generalised by many other researchers due to its capacity to capture the interrelationship between input arguments. Nevertheless, in many situations, interrelationships do not always exist between all of the attributes. Attributes can be partitioned into several different categories and members of intra-partition are interrelated while no interrelationship exists between attributes of different partitions. In this paper, as complements to the existing generalisations of BM, we investigate the partitioned Bonferroni mean (PBM) under intuitionistic uncertain linguistic environments and develop two linguistic aggregation operators: intuitionistic uncertain linguistic partitioned Bonferroni mean (IULPBM) and its weighted form (WIULPBM). Then, motivated by the ideal of geometric mean and PBM, we further present the partitioned geometric Bonferroni mean (PGBM) and develop two linguistic geometric aggregation operators: intuitionistic uncertain linguistic partitioned geometric Bonferroni mean (IULPGBM) and its weighted form (WIULPGBM). Some properties and special cases of these proposed operators are also investigated and discussed in detail. Based on these operators, an approach for multiple attribute decision-making problems with intuitionistic uncertain linguistic information is developed. Finally, a practical example is presented to illustrate the developed approach and comparison analyses are conducted with other representative methods to verify the effectiveness and feasibility of the developed approach.

Model for evaluating the management performance of the sport grounds with interval-valued intuitionistic uncertain linguistic information

Our country's education got big development in these days. For its future's more durative and healthy development, the research on all educational resources in our country's education is recognized. The sports grounds of National Education System which is one of the most important educational resources are the key ensurance and material basis for the smooth development of our country's school sport. The data of Fifth National Sport-Site Investigation show the sports grounds of National Education System take percentage of 65.6 in all of our country's sports grounds. As a result, the development situation of sports grounds in National Education System not only has direct effect on our country's school sport, but also on our country's other sports career. This paper introduced some operations of interval-valued intuitionistic uncertain linguistic sets, and further developed the induced interval-valued intuitionistic uncertain linguistic correlated geometric (I-IVIULCG) operator. We also establish some desirable properties of this operator, such as commutativity and monotonicity. Then, we apply the induced interval-valued intuitionistic uncertain linguistic correlated geometric (I-IVIULCG) operator to deal with the multiple attribute decision making problems for evaluating the management performance of the sport grounds. Finally, an illustrative example for evaluating the management performance of the sport grounds is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Model for evaluating the design patterns of the Micro-Air vehicle under interval-valued intuitionistic uncertain linguistic environment

The problem for evaluating the design patterns of the Micro-Air vehicle is the multiple attribute decision making problems. In this paper, we introduce the concept of interval-valued intuitionistic uncertain linguistic sets and propose the induced interval-valued intuitionistic uncertain linguistic ordered weighted average (I-IVIULOWA) operator on the basis of the interval-valued intuitionistic uncertain linguistic ordered weighted average (IVIULOWA) operator and IOWA operator. We also study some desirable properties of the proposed operator, such as commutativity, idempotency and monotonicity. Then, we utilize the induced interval-valued intuitionistic uncertain linguistic ordered weighted average (IIVIULOWA) operator to solve the multiple attribute decision making problems with interval-valued intuitionistic uncertain linguistic information. Finally, an illustrative example for evaluating the design patterns of the Micro-Air vehicle is given.

An approach to evaluating the knowledge management performance with interval-valued intuitionistic uncertain linguistic information

In this paper, we first introduce some operations on interval-valued intuitionistic uncertain linguistic sets, and further develop the induced interval-valued intuitionistic uncertain linguistic ordered weighted geometric (I-IVIULOWG) operator. We also establish some desirable properties of this operator, such as commutativity, idempotency and monotonicity. Then, we apply the induced interval-valued intuitionistic uncertain linguistic ordered weighted geometric (I-IVIULOWG) operator to deal with the interval-valued intuitionistic uncertain linguistic multiple attribute decision making problems. Finally, an illustrative example for evaluating the knowledge management performance is given to verify the developed approach and to demonstrate its practicality and effectiveness.

An extended TODIM method for multiple attribute group decision making based on intuitionistic uncertain linguistic variables

The intuitionistic uncertain linguistic variables are the good tools to express the fuzzy information, and the TODIM (an acronym in Portuguese of Interactive and Multicriteria Decision Making) method can consider the bounded rationality of decision makers based on the prospect theory. However, the classical TODIM method can only process the multiple attribute decision making (MADM) problems where the attribute values take the form of crisp numbers. In this paper, we will extend the TODIM method to the multiple attribute group decision making (MAGDM) with intuitionistic uncertain linguistic information. Firstly, the definition, characteristics, expectation, comparison method and distance of intuitionistic uncertain linguistic variables are briefly introduced, and the steps of the classical TODIM method for MADM problems are presented. Then, on the basis of the classical TODIM method, the extended TODIM method is proposed to deal with MAGDM problems with intuitionistic uncertain linguistic variables, and its significant characteristic is that it can fully consider the decision makers' bounded rationality which is a real action in decision making. Finally, an illustrative example is proposed to verify the developed approach.

Some new intuitionistic linguistic aggregation operators based on Maclaurin symmetric mean and their applications to multiple attribute group decision making

With respect to multiple attribute group decision making (MAGDM) problems in which the attributes are dependent and the attribute values take the forms of intuitionistic linguistic numbers and intuitionistic uncertain linguistic numbers, this paper investigates two novel MAGDM methods based on Maclaurin symmetric mean (MSM) aggregation operators. First, the Maclaurin symmetric mean is extended to intuitionistic linguistic environment and two new aggregation operators are developed for aggregating the intuitionistic linguistic information, such as the intuitionistic linguistic Maclaurin symmetric mean (ILMSM) operator and the weighted intuitionistic linguistic Maclaurin symmetric mean (WILMSM) operator. Then, some desirable properties and special cases of these operators are discussed in detail. Furthermore, this paper also develops two new Maclaurin symmetric mean operators for aggregating the intuitionistic uncertain linguistic information, including the intuitionistic uncertain linguistic Maclaurin symmetric mean (IULMSM) operator and the weighted intuitionistic uncertain linguistic Maclaurin symmetric mean (WIULMSM) operator. Based on the WILMSM and WIULMSM operators, two approaches to MAGDM are proposed under intuitionistic linguistic environment and intuitionistic uncertain linguistic environment, respectively. Finally, two practical examples of investment alternative evaluation are given to illustrate the applications of the proposed methods.

INTUITIONISTIC UNCERTAIN LINGUISTIC POWERED EINSTEIN AGGREGATION OPERATORS AND THEIR APPLICATION TO MULTI-ATTRIBUTE GROUP DECISION MAKING

The intuitionistic uncertain fuzzy linguistic variable can easily express the fuzzy information, and the power average (PA) operator is a useful tool which provides more versatility in the information aggregation procedure. At the same time, Einstein operations are a kind of various t-norms and <i>t</i>-conorms families which can be used to perform the corresponding intersections and unions of intuitionistic fuzzy sets (IFSs). In this paper, we will combine the PA operator and Einstein operations to intuitionistic uncertain linguistic environment, and propose some new PA operators. Firstly, the definition and some basic operations of intuitionistic uncertain linguistic number (IULN), power aggregation (PA) operator and Einstein operations are introduced. Then, we propose intuitionistic uncertain linguistic fuzzy powered Einstein averaging (IULFPEA) operator, intuitionistic uncertain linguistic fuzzy powered Einstein weighted (IULFPEWA) operator, intuitionistic uncertain linguistic fuzzy Einstein geometric (IULFPEG) operator and intuitionistic uncertain linguistic fuzzy Einstein weighted geometric (IULFPEWG) operator, and discuss some properties of them in detail. Furthermore, we develop the decision making methods for multi-attribute group decision making (MAGDM) problems with intuitionistic uncertain linguistic information and give the detail decision steps. At last, an illustrate example is given to show the process of decision making and the effectiveness of the proposed method.

A Group Decision Making Approach Based on Interval-Valued Intuitionistic Uncertain Linguistic Aggregation Operators

This paper investigates group decision making problems in which the criterion values take the form of interval-valued intuitionistic uncertain linguistic numbers (IIULNs). First, some additive operational laws of IIULNs are defined. Subsequently, some new arithmetic aggregation operators, such as the interval-valued intuitionistic uncertain linguistic weighted averaging (IIULWA) operator, interval-valued intuitionistic uncertain linguistic ordered weighted averaging (IIULOWA) operator and interval-valued intuitionistic uncertain linguistic hybrid aggregation (IIULHA) operator, are proposed which are based on the operational laws. Furthermore, an approach to group decision making with interval-valued intuitionistic uncertain linguistic information is developed, which is based on the IIULWA and IIULHA operators. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the proposed method.

INTUITIONISTIC UNCERTAIN LINGUISTIC WEIGHTED BONFERRONI OWA OPERATOR AND ITS APPLICATION TO MULTIPLE ATTRIBUTE DECISION MAKING

With respect to multiple attribute decision making (MADM) problems, in which attribute values take the form of intuitionistic uncertain linguistic information, a new decision-making method based on the intuitionistic uncertain linguistic weighted Bonferroni OWA operator is developed. First, the score function, accuracy function, and comparative method of the intuitionistic uncertain linguistic numbers are introduced. Then, an intuitionistic uncertain linguistic Bonferroni OWA (IULBOWA) operator and an intuitionistic uncertain linguistic weighted Bonferroni OWA (IULWBOWA) operator are developed. Furthermore, some properties of the IULBOWA and IULWBOWA operators, such as commutativity, idempotency, monotonicity, and boundedness, are discussed. At the same time, some special cases of these operators are analyzed. Based on the IULWBOWA operator, the multiple attribute decision-making method with intuitionistic uncertain linguistic information is proposed. Finally, an illustrative example is given to illustrate the decision-making steps and to demonstrate its practicality and effectiveness.

Some geometric aggregation operators based on interval intuitionistic uncertain linguistic variables and their application to group decision making

With respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of crisp numbers, and attribute values take the form of interval-valued intuitionistic uncertain linguistic variables, some new group decision making analysis methods are developed. Firstly, some operational laws, expected value and accuracy function of interval-valued intuitionistic uncertain linguistic variables are introduced. Then, an interval-valued intuitionistic uncertain linguistic weighted geometric average (IVIULWGA) operator and an interval-valued intuitionistic uncertain linguistic ordered weighted geometric (IVIULOWG) operator have been developed. Furthermore, some desirable properties of the IVIULWGA operator and the IVIULOWG operator, such as commutativity, idempotency and monotonicity, have been studied, and an interval-valued intuitionistic uncertain linguistic hybrid geometric (IVIULHG) operator which generalizes both the IVIULWGA operator and the IVIULOWG operator, was developed. Based on these operators, an approach to multiple attribute group decision making with interval-valued intuitionistic uncertain linguistic information has been proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.

Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making

With respect to multiple attribute group decision making (MAGDM) problems in which the attribute weights and the expert weights take the form of real numbers and the attribute values take the form of intuitionistic uncertain linguistic variables, new group decision making methods have been developed. First, operational laws, expected value definitions, score functions and accuracy functions of intuitionistic uncertain linguistic variables are introduced. Then, an intuitionistic uncertain linguistic weighted geometric average (IULWGA) operator and an intuitionistic uncertain linguistic ordered weighted geometric (IULOWG) operator are developed. Furthermore, some desirable properties of these operators, such as commutativity, idempotency, monotonicity and boundedness, have been studied, and an intuitionistic uncertain linguistic hybrid geometric (IULHG) operator, which generalizes both the IULWGA operator and the IULOWG operator, was developed. Based on these operators, two methods for multiple attribute group decision making problems with intuitionistic uncertain linguistic information have been proposed. Finally, an illustrative example is given to verify the developed approaches and demonstrate their practicality and effectiveness.