A comparative analysis of score functions for multiple criteria decision making in intuitionistic fuzzy settings

Cumulative prospect theory integrated CRITIC and TOPSIS methods for intuitionistic fuzzy multiple attribute group decision making

The purpose of this paper is to provide an efficient multiple attribute group decision making (MAGDM) method to better serve the decision-makers(DMs), considering the real psychological state and preferences of the DMs when facing different risks. In real life, MAGDM is a very complex and uncertain problem, which needs to be considered from many aspects. In view of this, the intuitionistic fuzzy TOPSIS method on the basis of cumulative prospect theory (IF-CPT-TOPSIS) is proposed in this paper, which can effectively solve the above problems, cater to the expectations of DMs, and make the decision results more objective and more reliable. The originality of this paper comes from three aspects. First, the new score function is combined with CRITIC method to calculate the weight of attributes, which eliminates the influence of Subjective preference of DMs and makes the primary information more reasonable. Furthermore, the use of the new score function can effectively avoid the exception conditions in the IFS problems. Secondly, applying the distance measurement formula of IFSs to determine the degree of approaching the ideal solution, so that the decision model can reflect the environmental changes more quickly. Thirdly, calculate the relative profit loss ratio of each scheme. Hence, each scheme is ranked and the optimal one is selected. Finally, in order to demonstrate the effectiveness of the model, a specific example is given and comparative analysis with the existing methods. The results show that the improved IF-CPT-TOPSIS method is useful and can be widely adapted for complex MAGDM problems.

Research on service quality evaluation of sports clubs with Pythagorean fuzzy information

In this paper, considering the traditional geometric operation laws and Pythagorean fuzzy information, a varies of new distance measures of Pythagorean fuzzy set are proposed, such as generalized Pythagorean fuzzy ordered geometric distance (GPFOWGD) measures and generalized Pythagorean fuzzy hybrid weighted geometric distance (GPFHWGD) measures. Besides, some special issues including Hamming distance, Euclidean distance and Hausdorff distance of these raised geometric distance measures are investigated. To testify the valid of these new presented distance measures, a decision-making model is built and illustrated by a mathematical calculation example to evaluate the service quality of sports clubs using Pythagorean fuzzy information. The results display that the approach is uncomplicated, valid and simple to compute. The example illustrates that the method presented in the paper can be used to deal with problems of uncertainty such as dynamic multiple attribute decision making.

Limit properties in the metric semi-linear space of picture fuzzy numbers

The picture fuzzy set (PFS) just appeared in 2014 and was introduced by Cuong, which is a generalization of intuitionistic fuzzy sets (Atanassov in Fuzzy Sets Syst 20(1):87–96, 1986) and fuzzy sets (Zadeh Inf Control 8(3):338–353, 1965). The picture fuzzy number (PFN) is an ordered value triple, including a membership degree, a neutral-membership degree, a non-membership degree, of a PFS. The PFN is a useful tool to study the problems that have uncertain information in real life. In this paper, the main aim is to develop basic foundations that can become tools for future research related to PFN and picture fuzzy calculus. We first establish a semi-linear space for PFNs by providing two new definitions of two basic operations, addition and scalar multiplication, such that the set of PFNs together with these two operations can form a semi-linear space. Moreover, we also provide some important properties and concepts such as metrics, order relations between two PFNs, geometric difference, multiplication of two PFNs. Next, we introduce picture fuzzy functions with a real domain that is also known as picture fuzzy functions with time-varying values, called geometric picture fuzzy function (GPFFs). In this framework, we give definitions about the limit of GPFFs and sequences of PFN. The important limit properties are also presented in detail. Finally, we prove that the metric semi-linear space of PFNs is complete, which is an important property in the classical mathematical analysis.

Using Fuzzy AHP-PROMETHEE for Market Risk Assessment of New-Build River Cruises on the Yangtze River

Cruise tourism on the Yangtze River Basin has developed rapidly in recent years. However, it is still facing such challenges as homogenization of itinerary and shore attraction arrangement, as well as aging cruise ships and simplification of service facilities, while it is also difficult to satisfy hierarchical and personalized tourist needs. To change such circumstances, new-build river cruise ships are inevitable. Complexity of market supply and demand environment, together with variability of tourist preferences, have increased market uncertainties of new-build cruise products. This study aims to assess market risks of new-build river cruise ships first by identifying risk factors, from the perspective of supply and demand under the actual conditions of the Yangtze River cruise market, then by evaluating potential impacts, caused by risk factors based on multi-criteria decision-making considerations. Fuzzy AHP-PROMETHEE was employed to prioritize the risk factors. The results reveal that among the most significant market risk factors are the following, in sequence: backwardness of support facilities; sudden security crisis; homogenization of cruise products; simplification of tourism route design; and inadequate management of the tourism market. Such findings will provide beneficial insights for strategic and sustainable development of river cruises on the Yangtze River.

Methods for evaluating the computer network security with fuzzy number intuitionistic fuzzy dual Hamy mean operators

The concept of fuzzy number intuitionistic fuzzy sets (FNIFSs) is designed to effectively depict uncertain information in decision making problems which fundamental characteristic of the FNIFS is that the values of its membership function and non-membership function are depicted with triangular fuzzy numbers (TFNs). The dual Hamy mean (DHM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this paper, we used the dual Hamy mean (DHM) operator and dual weighted Hamy mean (WDHM) operator with fuzzy number intuitionistic fuzzy numbers (FNIFNs) to propose the fuzzy number intuitionistic fuzzy dual Hamy mean (FNIFDHM) operator and fuzzy number intuitionistic fuzzy weighted dual Hamy mean (FNIFWDHM) operator. Then the MADM methods are proposed along with these operators. In the end, we utilize an applicable example for computer network security evaluation to prove the proposed methods.

Power Average Operators of Trapezoidal Cubic Fuzzy Numbers and Application to Multi-attribute Group Decision Making

Trapezoidal cubic fuzzy numbers (TzCFNs) are an extraordinary cubic fuzzy set on a real number set. TzCFNs are useful for dealing with well-known quantities in decision data and decision making problems themselves. This paper is about multi-attribute group decision making problems in which the attribute values are stated with TzCFNs, which are solved by developing a new decision method based on power average operators of TzCFNs. The new operation laws for TzCFNs are given. Hereby, the power average operator of real numbers is extended to four kinds of power average operators of TzCFNs, involving the power average operator of TzCFNs, the weighted power average operator of TzCFNs, the power ordered weighted average operator of TzCFNs, and the power hybrid average operator of TzCFNs. In the proposed group decision method, the individual overall evaluation values of alternatives are generated by using the power average operator of TzCFNs. Applying the hybrid average operator of TzCFNs, the specific general evaluation standards of alternatives are then combined into the collective ones, which are used to rank the alternatives. The example analysis shows the practicality and effectiveness of the proposed method.

Some Hesitant Fuzzy Hamacher Power-Aggregation Operators for Multiple-Attribute Decision-Making

As an extension of the fuzzy set, the hesitant fuzzy set is used to effectively solve the hesitation of decision-makers in group decision-making and to rigorously express the decision information. In this paper, we first introduce some new hesitant fuzzy Hamacher power-aggregation operators for hesitant fuzzy information based on Hamacher t-norm and t-conorm. Some desirable properties of these operators is shown, and the interrelationships between them are given. Furthermore, the relationships between the proposed aggregation operators and the existing hesitant fuzzy power-aggregation operators are discussed. Based on the proposed aggregation operators, we develop a new approach for multiple-attribute decision-making problems. Finally, a practical example is provided to illustrate the effectiveness of the developed approach, and the advantages of our approach are analyzed by comparison with other existing approaches.

Diagram Illustrations of Aggregation Operations for the Intuitionistic Fuzzy Values

Atanassov (Intuitionistic fuzzy set, Fuzzy Sets and Systems 20 (1986) 87–96) proposed the intuitionistic fuzzy set (A-IFS) that is a generalization of Zadeh's fuzzy set. The essential elements of an A-IFS are intuitionistic fuzzy values (IFVs), each of which is depicted by a membership degree and a non-membership degree. The existing literature only gives the explanation of the meaning and the aggregation operators of IFVs, which is very hard and non-visualized for us to comprehend. To overcome the above shortcomings, this paper puts forward the diagram method to analyze the structures of the basic aggregation operations of IFVs. In addition, this paper utilizes the diagram method which is similar to joint probability distribution to describe the components of aggregation operations of IFVs, and each IFV depicts a 3-dimensional vector which is regarded as the marginal distributions of the joint probability distribution.