Triangular Cubic Hesitant Fuzzy Einstein Hybrid Weighted Averaging Operator and Its Application to Decision Making

In this paper, triangular cubic hesitant fuzzy Einstein weighted averaging (TCHFEWA) operator, triangular cubic hesitant fuzzy Einstein ordered weighted averaging (TCHFEOWA) operator and triangular cubic hesitant fuzzy Einstein hybrid weighted averaging (TCHFEHWA) operator are proposed. An approach to multiple attribute group decision making with linguistic information is developed based on the TCHFEWA and the TCHFEHWA operators. Furthermore, we establish various properties of these operators and derive the relationship between the proposed operators and the existing aggregation operators. Finally, a numerical example is provided to demonstrate the application of the established approach

Power of Continuous Triangular Norms with Application to Intuitionistic Fuzzy Information Aggregation

The paper aims to investigate the power operation of continuous triangular norms (t-norms) and develop some intuitionistic fuzzy information aggregation methods. It is proved that a continuous t-norm is power stable if and only if every point is a power stable point, and if and only if it is the minimum t-norm, or it is strict, or it is an ordinal sum of strict t-norms. Moreover, the representation theorem of continuous t-norms is used to obtain the computational formula for the power of continuous t-norms. Based on the power operation of t-norms, four fundamental operations induced by a continuous t-norm for the intuitionistic fuzzy (IF) sets are introduced. Furthermore, various aggregation operators, namely the IF weighted average (IFWA), IF weighted geometric (IFWG), and IF mean weighted average and geometric (IFMWAG) operators, are defined, and their properties are analyzed. Finally, a new decision-making algorithm is designed based on the IFMWAG operator, which can remove the hindrance of indiscernibility on the boundaries of some classical aggregation operators. The practical applicability, comparative analysis, and advantages of the study with other decision-making methods are furnished to ascertain the efficacy of the designed method

Q-rung orthopair normal fuzzy aggregation operators and their application in multi-attribute decision-making

© 2019 by the authors. Q-rung orthopair fuzzy set (q-ROFS) is a powerful tool to describe uncertain information in the process of subjective decision-making, but not express vast objective phenomenons that obey normal distribution. For this situation, by combining the q-ROFS with the normal fuzzy number, we proposed a new concept of q-rung orthopair normal fuzzy (q-RONF) set. Firstly, we defined the conception, the operational laws, score function, and accuracy function of q-RONF set. Secondly, we presented some new aggregation operators to aggregate the q-RONF information, including the q-RONF weighted operators, the q-RONF ordered weighted operators, the q-RONF hybrid operator, and the generalized form of these operators. Furthermore, we discussed some desirable properties of the above operators, such as monotonicity, commutativity, and idempotency. Meanwhile, we applied the proposed operators to the multi-attribute decision-making (MADM) problem and established a novel MADM method. Finally, the proposed MADM method was applied in a numerical example on enterprise partner selection, the numerical result showed the proposed method can effectively handle the objective phenomena with obeying normal distribution and complicated fuzzy information, and has high practicality. The results of comparative and sensitive analysis indicated that our proposed method based on q-RONF aggregation operators over existing methods have stronger information aggregation ability, and are more suitable and flexible for MADM problems

Multi-criteria decision-making method based on intuitionistic trapezoidal fuzzy prioritised owa operator

In the real decision-making, there are many multiple attribute decision-making (MADM) problems, in which there exists the prioritised relationship among decision-making attributes. In this paper, with respect to the prioritised multi-criteria decision-making problems under intuitionistic trapezoidal fuzzy information, a new decision-making method on the basis of the intuitionistic trapezoidal fuzzy prioritised ordered weighted aggregation operator has been proposed. Firstly, the definitions, operational rules and characteristics of intuitionistic trapezoidal fuzzy numbers and POWA operator have been introduced. Then, intuitionistic trapezoidal fuzzy prioritised ordered weighted aggregation (ITFPOWA) operator has been defined as well as the computational method of associated weight, and some properties have been studied and proved. Furthermore, based on the ITFPOWA operator, an approach to the multi-criteria decision-making with intuitionistic trapezoidal fuzzy numbers has been established. Finally, an illustrative example has been given to prove the evaluation procedures of the developed approach and to demonstrate its practicality and validity

Development of q-Rung Orthopair Trapezoidal Fuzzy Einstein Aggregation Operators and Their Application in MCGDM Problems

Compared to previous extensions, the q-rung orthopair fuzzy sets are superior to intuitionistic ones and Pythagorean ones because they allow decision-makers to use a more extensive domain to present judgment arguments. The purpose of this study is to explore the multicriteria group decision-making (MCGDM) problem with the q-rung orthopair trapezoidal fuzzy (q-ROTrF) context by employing Einstein t-conorms and t-norms. Firstly, some arithmetical operations for q-ROTrF numbers, such as Einstein-based sum, product, scalar multiplication, and exponentiation, are introduced based on Einstein t-conorms and t-norms. Then, Einstein operations-based averaging and geometric aggregation operators (AOs), viz., q-ROTrF Einstein weighted averaging and weighted geometric operators, are developed. Further, some prominent characteristics of the suggested operators are investigated. Then, based on defined AOs, a MCGDM model with q-ROTrF numbers is developed. In accordance with the proposed operators and the developed model, two numerical examples are illustrated. The impacts of the rung parameter on decision results are also analyzed in detail to reflect the suitability and supremacy of the developed approach

Some operators with IVGSVTrN-numbers and their applications to multiple criteria group decision making

Interval valued generalized single valued neutrosophic trapezoidal number (IVGSVTrN-number), which permits the membership degrees of an element to a set expressed with intervals rather than exact numbers, is considered to be very useful to describe uncertain information for analyzing multiple criteria decision making (MCDM) problems. In this paper, we firstly introduced the concept of IVGSVTrN-number with some operations based on neutrosophic number. Then, we presented some aggregation and geometric operators. Finally, we developed a approaches for multiple criteria group decision making problems based on the proposed operators and we applied the method to a numerical example to illustrate proposed approach