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In this paper, we extend MM operator and dual MM (DMM) operator to process the interval-valued Pythagorean fuzzy numbers (IVPFNs) and then to solve the MADM problems. Firstly, we develop some interval-valued Pythagorean fuzzy Muirhead mean operators by extending MM and DMM operators to IVPFNs. Then, we prove some properties and discuss some special cases with respect to the parameter vector. Moreover, we present some new methods to deal with MADM problems with the IVPFNs based on the proposed MM and DMM operators. Finally, we verify the validity and reliability of our methods by using an application example for green supplier selections, and analyse the advantages of our methods by comparing it with other existing methods. [ABSTRACT FROM AUTHOR]

For this article, we shall expand the TODIMmodel to the MADM with the picture fuzzy numbers (PFNs). Firstly, the concept, comparative method and distance of PFNs are introduced and the traditional TODIMmodel is presented. Then, the expanded TODIMmodel is developed to solve MADMproblems with PFNs. Finally, a numerical example is given to verify the proposed approach. [ABSTRACT FROM AUTHOR]

The picture fuzzy set is characterized by three functions expressing the degree of membership, the degree of neutral membership and the degree of non-membership. It was proposed as a generalization of an intuitionistic fuzzy set in order to deal with indeterminate and inconsistent information. In this work, we shall present some novel Dice similarity measures of picture fuzzy sets and the generalized Dice similarity measures of picture fuzzy sets and indicate that the Dice similarity measures and asymmetric measures (projection measures) are the special cases of the generalized Dice similarity measures in some parameter values. Then, we propose the generalized Dice similarity measures-based patterns recognition models with picture fuzzy information. Then, we apply the generalized Dice similarity measures between picture fuzzy sets to building material recognition. Finally, an illustrative example is given to demonstrate the efficiency of the similarity measures for building material recognition. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the multiple attribute decision making problems with picture fuzzy information. Then, we utilize arithmetic and geometric operations to develop some picture fuzzy aggregation operators: picture fuzzy weighted average (PFWA) operator, picture fuzzy weighted geometric (PFWG) operator, picture fuzzy ordered weighted average (PFOWA) operator, picture fuzzy ordered weighted geometric (PFOWG) operator, picture fuzzy hybrid average (PFHA) operator and picture fuzzy hybrid geometric (PFHG) operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the picture fuzzy multiple attribute decision making problems. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

Hamacher product is a t-norm and Hamacher sum is a t-conorm. They are good alternatives to algebraic product and algebraic sum, respectively. Nevertheless, it seems that most of the existing hesitant fuzzy aggregation operators are based on the algebraic operations. In this paper, we utilize Hamacher operations to develop some hesitant Pythagorean fuzzy aggregation operators: hesitant Pythagorean fuzzy Hamacher weighted average (HPFHWA) operator, hesitant Pythagorean fuzzy Hamacher weighted geometric (HPFHWG) operator, hesitant Pythagorean fuzzy Hamacher ordered weighted average (HPFHOWA) operator, hesitant Pythagorean fuzzy Hamacher ordered weighted geometric (HPFHOWG) operator, hesitant Pythagorean fuzzy Hamacher hybrid average (HPFHHA) operator and hesitant Pythagorean fuzzy Hamacher hybrid geometric (HPFHHG) operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the hesitant Pythagorean fuzzy multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

The stock investment selection could be deemed as a classic multiple attribute group decision making (MAGDM) problem involving multiple conflicts and interleaved qualitative and quantitative attributes. Spherical fuzzy sets (SFSs) can excavate the potential vagueness and intricacy in MAGDM more effectively and deeply. This article we propose an integrated decision support system (IDSS) based on SFSs, prospect theory (PT), distance from average solution (EDAS) method and the MEthod based on the Removal Effects of Criteria (MEREC). The proposed IDSS, called SF-PT-EDAS-MEREC model, uses SFSs to describe the uncertain and obscure assessment information of DMs. The combination of PT and EDAS (PT-EDAS) method adequately captures DMs' psychological behavior characteristics to execute more reasonable alternative evaluation. The MEREC is utilized to efficaciously obtain unknown attribute weights. In addition, this paper also presents a novel score function to compare spherical fuzzy numbers (SFNs) more directly and efficiently. Eventually, in order to illustrate the practicability of the proposed IDSS, two numerical examples of stock investment selection are employed to achieve this. Meanwhile, the comparative study with existing approach further demonstrates the effectiveness and superiority of SF-PT-EDAS-MEREC model. [ABSTRACT FROM AUTHOR]

Probabilistic dual hesitant fuzzy set (PDHFS) is a more powerful and important tool to describe uncertain information regarded as generalization of hesitant fuzzy set (HFS) and dual HFS (DHFS), not only reflects the hesitant attitude of decision-makers (DMs), but also reflects the probability information of DMs. Score function of fuzzy number and weighting method are very important in multi-attribute group decision-making (MAGDM) issues. In many fuzzy environments, the score function and entropy measure have been proposed one after another. Firstly, based on the detailed analysis of the existed score function of PDHF element (PDHFE) and with the help of previous references, we build a novel score function for PDHFE. Secondly, a combined weighting method is built based on the minimum identification information principle by fusing PDHF entropy and Criteria Importance Through Intercriteria Correlation (CRITIC) method. Thirdly, a novel PDHF MAGDM approach (PDHF-EDAS) is built by extending evaluation based on distance from average solution (EDAS) approach to the PDHF environment to solve the issue that the decision attribute information is PDHFE. Finally, the practicability and effectiveness of the PDHF MAGDM technique is verified by suppliers selection (SS) and comparing analysis with existing methods. [ABSTRACT FROM AUTHOR]