The degree of similarity or dissimilarity between the objects under study plays an important role. In vector space, especially, the cosine similarity measure is often used in information retrieval, citation analysis, and automatic classification. However, it scarcely deals with trapezoidal fuzzy information and multicriteria decision-making problems. For this purpose, a cosine similarity measur...

In many real life problems, the parameters used to characterize the uncertainty or vagueness or impreciseness in information are either triangular or trapezoidal fuzzy numbers. But it is not always possible to restrict the membership function to either triangular or trapezoidal form. In this paper, a new form of non-normal fuzzy number named as Heptagonal fuzzy number is introduced and its arit...

Cviklovič V., Hrubý D., Olejár M., Lukáč O., 2011. Comparison of numerical integration methods in strapdown inertial navigation algorithm. Res. Agr. Eng., 57 (Special Issue): S30–S34. The numerical mathematical theory provides a few ways of numerical integration with different errors. It is necessary to make use of the most exact method with respect to the computing power for a majority of micr...

Time-integration for lumped parameter systems obeying implicit Bingham-Kelvin constitutive models is studied. The governing system of equations describing the lumped parameter system is a non-linear differential-algebraic equation and needs to be solved numerically. The response of this system is non-smooth and the kinematic variables can not be written in terms of the dynamic variables, explic...

We have presented trapezoidal intuitionistic fuzzy number. Arithmetic operations of trapezoidal intuitionistic fuzzy number is presented based on (α, β)-cuts. We have presented intuitionistic fuzzy fault tree analysis using trapezoidal intuitionistic fuzzy number. In application of intuitionistic fuzzy fault tree analysis, we have computed failure of fire protection system taking failure of eac...

The Electromagnetic transients progr am and its variants all use the “trapezoidal rule” numerical integration method. The trapezoidal rule is a second order numerical integration technique that is simple to implement. However, it is also susceptible to numerical oscillations when differentiat ing step changes in voltage and current. The program user should be aware of the potential for these os...

As an extension of the intuitionistic fuzzy set, intuitionistic trapezoidal fuzzy set is an invaluable mathematical theory to express uncertain phenomenon in our real word. In this article, the aggregation methods of the intuitionistic trapezoidal fuzzy information are chief researched. Firstly, the generalized aggregation operator is introduced for aggregating intuitionistic trapezoidal fuzzy ...

This paper describes a fault tree technique based on generalized fuzzy numbers to a possibility distribution of reliability indices for power systems. Due to uncertainty in the collected data, all the failure probabilities are represented by generalized trapezoidal fuzzy number. In this paper, the fault-tree incorporated with the generalized trapezoidal fuzzy number and minimal cut sets approac...

The Assignment Problem is one of the most studied, well known and important problem in mathematics and is used very often in solving problems of engineering and management sciences. In this problem denotes the cost for assigning the job to the person. This cost is usually deterministic in nature. In this paper has been considered to be generalized trapezoidal intuitionistic fuzzy numbers denote...

This paper focuses on modelling fuzzy numbers with meaningful membership functions. More precisely, it proposes a method to construct trapezoidal fuzzy number approximations from raw discrete data. In many applications, input information is numerical, and therefore, particular fuzzy sets, such as fuzzy numbers, hold great interest and relevance in managing data imprecision and vagueness. The pr...