Search

In view of the multi-attribute decision problem in which the value of attribute was in the form of Pythagorean 2-tuple linguistic numbers, considering the bounded rational behavior of decision maker, this paper proposed the decision making method of the preference ranking organization method for enrichment evaluations (PROMETHEE) based on prospect theory. Firstly, this paper introduced the related concepts of the Pythagorean 2-tuple linguistic set, improved the existing distance of P2TLN, and defined the improved distance by use of the score function and the exact function of P2TLN, and verified the properties of the improved distance. Secondly, in order to reflect the risk preference of decision makers when comparing decision information, it constructed the priority function of P2TLN by combining the prospect value function. Then, it compared the alternatives in pairs by use of the priority function, and ranked the alternatives by calculating the net flow of each scheme. Finally, this paper gave an example about the evaluation of logistics companies to show the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Pythagorean hesitant fuzzy set as a new generalization of Pythagorean fuzzy and hesitant fuzzy set can handle fuzzy information more flexibly in multiple attribute decision making. In view of the important role of aggregation operator in multiple attribute decision making and under the condition of the imperfect aggregation operator in Pythagorean hesitant fuzzy decision environment, this paper systematically investigated Pythagorean hesitant fuzzy aggregation operators. It defined some Pythagorean hesitant fuzzy aggregation operators based on the operational laws of Pythagorean hesitant fuzzy numbers, including Pythagorean hesitant fuzzy ordered weighted average operator ( PHFOWA), generalized ordered weighted average operator (GPHFOWA), hybrid average operator ( PHFHA), Pythagorean hesitant fuzzy ordered weighted geometric average operator ( PHFOWG),generalized ordered weighted geometric average operator( GPHFOWG) and hybrid geometric average operator ( PHFHG). It gave the mathematical expression of these operators by derivation and discussed in detail some desirable properties such as boundedness, monotonicity and commutativity. Finally, this paper proposed a decision making method based on Pythagorean hesitant fuzzy aggregation operators, and used an applied example lo illustrate the feasibility and applicability of the proposed method. [ABSTRACT FROM AUTHOR]

Aiming at the information integration problem in the multi-attribute decision making problem of Pythagorean fuzzy environment, the attributes of the schemes were related to each other, this paper proposed a multi-attribute decision-making method based on Pythagorean fuzzy Heronian operators. Combining Pythagorean fuzzy numbers with Heronian operators, it proposed Pythagorean fuzzy Heronian operators and Pythagorean fuzzy weighted Heronian operators, discussed the properties of these operators, and corresponding proof. On this basis, it proposed a multi-attribute decision making method based on Pythagorean fuzzy Heronian operator. Finally, this paper applied it in the service quality evaluation of four domestic airlines. The result shows the effectiveness and feasibility of the operator. [ABSTRACT FROM AUTHOR]

Due to the complexity of the actual decision-making problem, most indicators have the characteristics of mutual dependence. Therefore, for the multi-attribute decision-making problem with correlation between indicators under uncertain environment, a decision method with hierarchical structure as the framework and cloud model twofold integral (C-TI) as the aggregation operator is proposed. Firstly, in order to reflect the uncertain thinking of decision makers in determining the index weights, a cloud model fuzzy measure is proposed. Secondly, the cloud model twofold integral operator is constructed on the basis of cloud model fuzzy measure, which takes the cloud model as the representation of decision information, fully reflects the fuzzy and random nature of decision information. And twofold integral combining the advantages of Choquet integral and Sugeno integral is applied to aggregating the index values, which can not only effectively deal with the interaction problem between indexes, but also take into account the focus relationship between the index value and the weight. Subsequently, the theorems and properties of the cloud model twofold integral operator and the variation form of specific conditions are then discussed and the corresponding proofs are given. Finally, a hierarchical multi- attribute decision making method for cloud model twofold integral operator is constructed and applied to the corporate social responsibility assessment problem. Compared with other models, it is further shown that the method constructed in this paper is suitable for dealing with fuzzy and stochastic uncertainty problems and can take into account the overall decision effect while the indicators are correlated. [ABSTRACT FROM AUTHOR]

For multi-attribute group decision-making(MAGDM) problem, this paper used Pythagorean fuzzy linguistic numbers as input information which could make decision maker evaluate the options effectively with more flexible values. First, this paper created Pythagorean fuzzy linguistic distance measure based on the distance measure of Pythagorean fuzzy sets and linguistic sets this paper and gave its properties. Then, using this distance measure in power average(PA) operator, it created the Pythagorean fuzzy linguistic power weighted average(PFLPWA) operator to aggregate a collection of Pythagorean fuzzy linguistic numbers(PFLNs), and considered the differences of the decision makers in this aggregation process. Finally, it built a group decision making method on the basis of PFLPWA operator and gave a numerical example to demonstrate its effectiveness and feasibility. [ABSTRACT FROM AUTHOR]

An automated method for aggregating depth contour based on triangulation is proposed. Firstly, an automatic method to detect aggregating contours is proposed, which doesn't need to reco-gnize the submarine topography features. Secondly, triangles to construct the bridge areas are filtered, and the bridge areas are expanded and related "holes" are filled. Next, the bend areas to generalize are detected. Then generalized areas are derived by merging the bride areas and generalizing bend areas, and then the aggregated result contours are achieved by conducting symmetric difference calculation on the boundary of generalized areas and the aggregating contours. Test results show that the method proposed in this paper can detect the aggregating contours correctly, and the aggregated results not only can guarantee navigation safety but also can achieve a legible and smooth depth contour. [ABSTRACT FROM AUTHOR]

With respect to the limitations in existing papers, the new arithmetic operations of intuitionistic trapezoidal fuzzy numbers are defined. Then some aggregation operators of intuitionistic trapezoidal fuzzy numbers as well as their properties are proposed. The proposed aggregation operators are applied into the group decision making problems and a solution method is developed. In the end, a numerical example is illustrated to show the proposed decision making method's effectiveness and rationality. [ABSTRACT FROM AUTHOR]