Interval-valued intuitionistic fuzzy multiple attribute decision making and their applications

In this paper, we expand the Muirhead mean (MM) operator and dual Muirhead mean (DMM) operator with interval-valued intuitionistic fuzzy numbers (IVIFNs) to propose the interval -valued intuitionistic fuzzy Muirhead mean (IVIFMM) operator, interval-valued intuitionistic fuzzy weighted Muirhead mean (IVIFWMM) operator, interval-valued intuitionistic fuzzy dual Muirhead mean (IVIFDMM) operator and interval-valued intuitionistic fuzzy weighted dual Muirhead mean (IVIFWDMM) operator. Then the MADM methods are proposed with these operators. In the end, we utilize an applicable example for green supplier selection in green supply chain management to prove the proposed methods.

Interval Valued T-Spherical Fuzzy Soft Average Aggregation Operators and Their Applications in Multiple-Criteria Decision Making

This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability and decision theory methods. Multiple-criteria decision making (MCDM) is a very effective and well-known tool to investigate fuzzy information more effectively. However, the selection of houses cannot be done by utilizing symmetry information, because enterprises do not have complete information, so asymmetric information should be used when selecting enterprises. In this paper, the notion of soft set (SftS) and interval-valued T-spherical fuzzy set (IVT-SFS) are combined to produce a new and more effective notion called interval-valued T-spherical fuzzy soft set (IVT-SFSftS). It is a more general concept and provides more space and options to decision makers (DMs) for making their decision in the field of fuzzy set theory. Moreover, some average aggregation operators like interval-valued T-spherical fuzzy soft weighted average (IVT-SFSftWA) operator, interval-valued T-spherical fuzzy soft ordered weighted average (IVT-SFSftOWA) operator, and interval-valued T-spherical fuzzy soft hybrid average (IVT-SFSftHA) operators are explored. Furthermore, the properties of these operators are discussed in detail. An algorithm is developed and an application example is proposed to show the validity of the present work. This manuscript shows how to make a decision when there is asymmetric information about an enterprise. Further, in comparative analysis, the established work is compared with another existing method to show the advantages of the present work.

Some Interval-Valued Intuitionistic Fuzzy Dombi Hamy Mean Operators and Their Application for Evaluating the Elderly Tourism Service Quality in Tourism Destination

In this paper, we expand the Hamy mean (HM) operator and Dombi operations with interval-valued intuitionistic fuzzy numbers (IVIFNs) to propose the interval-valued intuitionistic fuzzy Dombi Hamy mean (IVIFDHM) operator, interval-valued intuitionistic fuzzy weighted Dombi Hamy mean (IVIFWDHM) operator, interval-valued intuitionistic fuzzy dual Dombi Hamy mean (IVIFDDHM) operator, and interval-valued intuitionistic fuzzy weighted dual Dombi Hamy mean (IVIFWDDHM) operator. Then the MADM models are designed with IVIFWDHM and IVIFWDDHM operators. Finally, we gave an example for evaluating the elderly tourism service quality in tourism destination to show the proposed models.

Approaches to Multiple Attribute Decision Making with Interval-Valued 2-Tuple Linguistic Pythagorean Fuzzy Information

The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values. The prominent characteristic of the MSM operator is that it can capture the interrelationship among multi-input arguments. Motivated by the ideal characteristic of the MSM operator, in this paper, we expand the MSM operator, generalized MSM (GMSM), and dual MSM (DMSM) operator with interval-valued 2-tuple linguistic Pythagorean fuzzy numbers (IV2TLPFNs) to propose the interval-valued 2-tuple linguistic Pythagorean fuzzy MSM (IV2TLPFMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy weighted MSM (IV2TLPFWMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy GMSM (IN2TLPFGMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy weighted GMSM (IV2TLPFWGMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy DMSM (IN2TLPFDMSM) operator, Interval-valued 2-tuple linguistic Pythagorean fuzzy weighted DMSM (IV2TLPFWDMSM) operator. Then the multiple attribute decision making (MADM) methods are developed with these three operators. Finally, an example of green supplier selection is used to show the proposed methods.

Contrasting Correlation Coefficient with Distance Measure in Interval Valued Intuitionistic Trapezoidal Fuzzy MAGDM Problems

In this paper, Multiple Attribute Group Decision Making (MAGDM) problems in which the data is of the form of Interval Valued Intuitionistic Trapezoidal Fuzzy Numbers (IVITzFNs) is presented. Some operational laws of IVITzFNs are introduced. Then some new aggregation operators including interval valued Intuitionistic Trapezoidal Fuzzy Weighted Averaging (IVITzFWA) operator, interval valued Intuitionistic Trapezoidal Fuzzy Ordered Weighted Averaging (IVITzFOWA) operator and Interval Intuitionistic Trapezoidal Fuzzy Hybrid Averaging (IVITzFHA) operator, are proposed and some desirable properties of these operators are studied, such as Commutativity, Idempotency and Monotonicity. A new distance function and correlation coefficient are proposed for IVITzFNs which will be utilized for ranking the alternatives in MAGDM problems. Finally, numerical illustrations are given to verify the developed approach and to demonstrate its practicality and effectiveness.

Contrasting Correlation Coefficient with Distance Measure in Interval Valued Intuitionistic Trapezoidal Fuzzy MAGDM Problems

In this paper, Multiple Attribute Group Decision Making (MAGDM) problems in which the data is of the form of Interval Valued Intuitionistic Trapezoidal Fuzzy Numbers (IVITzFNs) is presented. Some operational laws of IVITzFNs are introduced. Then some new aggregation operators including interval valued Intuitionistic Trapezoidal Fuzzy Weighted Averaging (IVITzFWA) operator, interval valued Intuitionistic Trapezoidal Fuzzy Ordered Weighted Averaging (IVITzFOWA) operator and Interval Intuitionistic Trapezoidal Fuzzy Hybrid Averaging (IVITzFHA) operator, are proposed and some desirable properties of these operators are studied, such as Commutativity, Idempotency and Monotonicity. A new distance function and correlation coefficient are proposed for IVITzFNs which will be utilized for ranking the alternatives in MAGDM problems. Finally, numerical illustrations are given to verify the developed approach and to demonstrate its practicality and effectiveness.

Some Aggregation Operators Based on Einstein Operations under Interval-Valued Dual Hesitant Fuzzy Setting and Their Application

We investigate the multiple attribute decision making (MADM) problems in which attribute values take the form of interval-valued dual hesitant fuzzy information. Firstly, some operational laws for interval-valued dual hesitation fuzzy elements (IVDHFEs) based on Einstein operations are developed. Then we develop some aggregation operators based on Einstein operations: the interval-valued dual hesitant fuzzy Einstein weighted averaging (IVDHFEWA) operator, interval-valued dual hesitant fuzzy Einstein ordered weighted averaging (IVDHFEOWA) operator, interval-valued dual hesitant fuzzy Einstein hybrid averaging (IVDHFEHA) operator, interval-valued dual hesitant fuzzy Einstein weighted geometric (IVDHFEWG) operator, interval-valued dual hesitant fuzzy Einstein ordered weighted geometric (IVDHFEOWG) operator, and interval-valued dual hesitant fuzzy Einstein hybrid geometric (IVDHFEHG) operator. Furthermore, we discuss some desirable properties of these operators, and investigate the relationship between the developed operators and the existing ones. Based on the IVDHFEWA operator, an approach to MADM problems is proposed under the interval-valued dual hesitant fuzzy environment. Finally, a numerical example is given to show the application of the developed method, and a comparison analysis is conducted to demonstrate the effectiveness of the proposed approach.

THE MULTI-ATTRIBUTE GROUP DECISION MAKING METHOD BASED ON THE INTERVAL GREY LINGUISTIC VARIABLES WEIGHTED HARMONIC AGGREGATION OPERATORS

With respect to the characteristics of fuzziness, complexity and uncertainty for many group-decision making problems in real world, the paper proposes a novel method based on the interval grey linguistic variables hybrid weighted harmonic aggregation operators to solve the multiple attribute group decision making problems in which the attribute values and the weights take the form of the interval grey linguistic variables. In the approach, the relative concepts and the operation rules of interval grey linguistic variables are defined, and some operators (such as interval grey linguistic weighted harmonic aggregation (IGLWHA) operator, interval grey linguistic ordered weighted harmonic aggregation (IGLOWHA) operator, and interval grey linguistic hybrid weighted harmonic aggregation (IGLHWHA) operator) are proposed to solve the group decision making problems. The computational results from an illustrative example have shown that the proposed approach is feasible and effective for the group-decision making problems.