Multiattribute Group Decision Making with Unknown Decision Expert Weights Information in the Framework of Interval Intuitionistic Trapezoidal Fuzzy Numbers

The aim of this paper is to investigate an approach to multiattribute group decision making with interval intuitionistic trapezoidal fuzzy numbers, in which the decision expert weights are unknown. First, we introduce a distance measure between two interval intuitionistic trapezoidal fuzzy matrixes, and based on the distance between individual matrix and extreme matrix, as well as the average matrix, we obtain the decision expert weights. Second, we utilize the interval intuitionistic trapezoidal fuzzy weighted geometric (IITFWG) operator and the interval intuitionistic trapezoidal fuzzy ordered weighted geometric (IITFOWG) operator to aggregate all individual interval intuitionistic trapezoidal fuzzy decision matrices into a collective interval intuitionistic trapezoidal fuzzy decision matrix and then derive the group overall evaluation values of the given alternatives. Finally, an illustrative example of emergency alternatives selection is given to demonstrate the effectiveness and superiority of the proposed method

A new similarity function for generalized trapezoidal fuzzy numbers

Numerous authors have proposed functions to quantify the degree of similarity between two fuzzy numbers using various descriptive parameters, such as the geometric distance, the distance between the centers of gravity or the perimeter. However, these similarity functions have drawback for specific situations. We propose a new similarity measure for generalized trapezoidal fuzzy numbers aimed at overcoming such drawbacks. This new measure accounts for the distance between the centers of gravity and the geometric distance but also incorporates a new term based on the shared area between the fuzzy numbers. The proposed measure is compared against other measures in the literature

Nearest symmetric trapezoidal approximation of fuzzy numbers

Abstract Many authors analyzed triangular and trapezoidal approximation of fuzzy numbers. But, to best of our knowledge, there is no method for symmetric trapezoidal fuzzy number approximation of fuzzy numbers. So, in this paper, we try to convert any fuzzy number into symmetric trapezoidal fuzzy number by using metric distance. This approximation helps us to avoid the computational complexity in the process of decision making problems. Moreover, we investigate some reasonable properties of this approximation. An application of this new method is also provided

A New Similarity Measure of Generalized Trapezoidal Fuzzy Numbers and Its Application on Rotor Fault Diagnosis

Fault diagnosis technology plays a vital role in the variety of critical engineering applications. Fuzzy approach is widely employed to cope with decision-making problems because it is in the simplest and most used form. This paper proposed a new similarity measure of generalized trapezoidal fuzzy numbers used for fault diagnosis. The presented similarity measure combines concepts of the geometric distance, the center of gravity point, the perimeter, and the area of the generalized trapezoidal fuzzy numbers for calculating the degree of similarity between generalized trapezoidal fuzzy numbers. This method is proposed to deal with both standardized and nonstandardized generalized trapezoidal fuzzy numbers. Some properties of the proposed similarity measure have been proved, and 12 sets of generalized fuzzy numbers have been used to compare the calculation results of the proposed similarity measures with the existing similarity measures. Comparison results indicate that the proposed similarity measure can overcome the drawbacks of existing similarity measures. Finally, a fault diagnosis experiment is carried out in laboratory based on multifunctional flexible rotor experiment bench. Experimental results demonstrate that the proposed similarity measure is more effective than other methods in terms of rotor fault diagnosis

Trapezoidal Intuitionistic Fuzzy Multiattribute Decision Making Method Based on Cumulative Prospect Theory and Dempster-Shafer Theory

With respect to decision making problems under uncertainty, a trapezoidal intuitionistic fuzzy multiattribute decision making method based on cumulative prospect theory and Dempster-Shafer theory is developed. The proposed method reflects behavioral characteristics of decision makers, information fuzziness under uncertainty, and uncertain attribute weight information. Firstly, distance measurement and comparison rule of trapezoidal intuitionistic fuzzy numbers are used to derive value function under trapezoidal intuitionistic fuzzy environment. Secondly, the value function and decision weight function are used to calculate prospect values of attributes for each alternative. Then considering uncertain attribute weight information, Dempster-Shafer theory is used to aggregate prospect values for each alternative, and overall prospect values are obtained and thus the alternatives are sorted consequently. Finally, an illustrative example shows the feasibility of the proposed method

A new approach for trapezoidal approximation of fuzzy numbers using WABL distance

In this paper, we present a new approach to obtain trapezoidal approximation of fuzzy numbers with respect to weighted distance proposed by Nasibov [5] which the main property of this metric is flexibility in the decision maker's choice. Also, we prove some properties of the proposed method such as translation invariance, scale invariance and identity. Finally, we illustrate the efficiency of proposed method by solving some numerical examples

Revisiting the interval and fuzzy topsis methods: Is euclidean distance a suitable tool to measure the differences between fuzzy numbers?

Euclidean distance (ED) calculates the distance between n-coordinate points that n equals the dimension of the space these points are located. Some studies extended its application to measure the difference between fuzzy numbers (FNs).This study shows that this extension is not logical because although an n-coordinate point and an FN are denoted the same, they are conceptually different. An FN is defined by n components; however, n is not equal to the dimension of the space where the FN is located. This study illustrates this misapplication and shows that the ED between FNs does not necessarily reflect their difference. We also revisit triangular and trapezoidal fuzzy TOPSIS methods to avoid this misapplication. For this purpose, we first defuzzify the FNs using the center of gravity (COG) method and then apply the ED to measure the difference between crisp values. We use an example to illustrate that the existing fuzzy TOPSIS methods assign inaccurate weights to alternatives and may even rank them incorrectly

Novel Distance Measure in Fuzzy TOPSIS for Supply Chain Strategy Based Supplier Selection

In today’s highly competitive environment, organizations need to evaluate and select suppliers based on their manufacturing strategy. Identification of supply chain strategy of the organization, determination of decision criteria, and methods of supplier selection are appearing to be the most important components in research area in the field of supply chain management. In this paper, evaluation of suppliers is done based on the balanced scorecard framework using new distance measure in fuzzy TOPSIS by considering the supply chain strategy of the manufacturing organization. To take care of vagueness in decision making, trapezoidal fuzzy number is assumed for pairwise comparisons to determine relative weights of perspectives and criteria of supplier selection. Also, linguistic variables specified in terms of trapezoidal fuzzy number are considered for the payoff values of criteria of the suppliers. These fuzzy numbers satisfied the Jensen based inequality. A detailed application of the proposed methodology is illustrated