Harmonic Aggregation Operator with Trapezoidal Picture Fuzzy Numbers and Its Application in a Multiple-Attribute Decision-Making Problem

Picture fuzzy sets (PFSs) can be used to handle real-life problems with uncertainty and vagueness more effectively than intuitionistic fuzzy sets (IFSs). In the process of information aggregation, many aggregation operators under PFSs are used by different authors in different fields. In this article, a multi-attribute decision-making (MADM) problem is introduced utilizing harmonic mean aggregation operators with trapezoidal fuzzy number (TrFN) under picture fuzzy information. Three harmonic mean operators are developed namely trapezoidal picture fuzzy weighted harmonic mean (TrPFWHM) operator, trapezoidal picture fuzzy order weighted harmonic mean (TrPFOWHM) operator and trapezoidal picture fuzzy hybrid harmonic mean (TrPFHHM) operator. The related properties about these operators are also studied. At last, an MADM problem is considered to interrelate among these operators. Furthermore, a numerical instance is considered to explain the productivity of the proposed operators.

TOPSIS method for spherical fuzzy MAGDM based on cumulative prospect theory and combined weights and its application to residential location

Nowadays, how to choose a comfortable and relatively satisfactory residence is one of the multiple attribute group decision making (MAGDM) issues which people are paying more and more attention. However, since the inaccuracy and fuzziness of the information are given by decision makers (DMs) in practical decision-making and psychological factors of DMs should be considered in the decision-making process, this paper presents TOPSIS approach based on cumulative prospect theory (CPT) to deal with the MAGDM issues under the spherical fuzzy environment. Furthermore, considering the objective relationship between the attributes, the combined weights are used to get attribute weights in spherical fuzzy sets (SFSs). Finally, an example of residential location is introduced to prove the validity of our proposed approach by comparing with spherical fuzzy TOPSIS(SF-TOPSIS) method and spherical fuzzy WASPAS (SF-WASPAS) method.

Picture fuzzy MABAC method based on prospect theory for multiple attribute group decision making and its application to suppliers selection

In the garment manufacturing industry, purchasing management is an important link. The materials of making clothes often need high cost. In addition, customers put forward a request in the quality of clothes. Thus, choosing an optimal supplier is an essential part of job. Reaching cooperation with an optimal supplier not only can help garment manufacturer improve the quality of clothes but also is benefit to reduce the cost of producing. Most importantly, it can improve the competitiveness of manufacture enterprises. So, it is important for managers to find an optimal supplier and make a cooperation with it. In this paper, we analysis an issue about choosing an optimal supplier during four different suppliers. With analyzing this problem, we can introduce an extended method under picture fuzzy environment to evaluate and choose an optimal supplier. In this article, we describe some basic knowledges about picture fuzzy sets (PFSs) and picture fuzzy numbers (PFNs). Then, we introduce the extension of MABAC method which is on the basis of prospect theory (PT) with picture fuzzy numbers (PF-PT-MABAC) and utilize the PF-PT-MABAC model to evaluate different suppliers to choose an optimal supplier. Finally, we compare the result of PF-PT-MABAC with the result of traditional MABAC, PFWG operators and traditional TODIM method to test the efficiency of PF-PT-MABAC model.

Combinatorial Design of the MAUT and PAMSSEM II Methods for Multiple Attributes Group Decision Making with Probabilistic Linguistic Information

This paper considers the application of probabilistic linguistic term sets (PLTS) in multiple-attribute group decision-making (MAGDM) when the weights can’t be determined. First, as an improvement of the PROMETHEE method, the PAMSSEM method can not only handle missing evaluations, but also proposes a rejection threshold to calculate the overall consistency of the plan, so as to rank the plan more reasonably. At the same time, the MAUT uses the marginal utility function to reallocate the attribute values of the alternatives in the interval , and then calculate the total utility to sort them. Because the utility function is beneficial in expressing consumer satisfaction, we combine the MAUT method and PAMSSEM II method and apply it to solve decision-making problems under probabilistic linguistic environment. Secondly the coefficient of variation method, entropy method and analytic hierarchy process are used to calculate the weights in a combination. In the process of data processing, we use the transfer function to convert the PLTS into the hesitant probabilistic fuzzy set (HPFS) for calculation. Finally, the PL-MAUT-PAMSSEM II method, PROMRTHE method, TOPSIS method and ARAS method are compared with each other.

The Compromise Ratio Method With Intuitionistic Fuzzy Distance for FMAGDM

The compromise ratio method (CRM) is an effective method to solve multiple attribute group decision making (MAGDM). Distance measure of intuitionistic fuzzy (IF) numbers (IFNs) is important for CRM. In this paper, according to the IF distance of IFNs, an extended compromise ratio method (CRM) is developed for (MAGDM) problems which attribute weights and evaluation values of alternatives on attributes are expressed in linguistic variables parameterized using TIFNs. Finally, the effectiveness and practicability of the extended CRM with IF distance are demonstrated by solving a software selection problem.

Approaches to Multiple Attribute Decision-Making with Fuzzy Number Intuitionistic Fuzzy Information and Their Application to English Teaching Quality Evaluation

Many experts and scholars focus on the Maclaurin symmetric mean (MSM) operator, which can reflect the interrelationship among the multi-input arguments. It has been generalized to different fuzzy environments and put into use in various actual decision problems. The fuzzy number intuitionistic fuzzy numbers (FNIFNs) could well depict the uncertainties and fuzziness during the English teaching quality evaluation. And the English teaching quality evaluation is frequently viewed as the multiple attribute decision-making (MADM) issue. We expand the MSM equation with FNIFNs to propose the fuzzy number intuitionistic fuzzy MSM (FNIFMSM) equation and fuzzy number intuitionistic fuzzy weighted MSM (FNIFWMSM) equation in this study. A few MADM tools are developed with FNIFWMSM equation. Finally, taking English teaching quality evaluation as an example, this paper illustrates the depicted approach.