We propose a generalization of trapezoidal fuzzy numbers based on modal interval theory, which we name “modal interval trapezoidal fuzzy numbers”. In this generalization, we accept that the alpha cuts associated with a trapezoidal fuzzy number can be modal intervals, also allowing that two interval modalities can be associated with a trapezoidal fuzzy number. In this context, it is difficult to...

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...

Standard intuitionistic fuzzy arithmetic operations have certain problems in division and subtraction operations. Ezzati et al. (2014) defined a new operation on symmetric trapezoidal intuitionistic fuzzy numbers in which the properties ≈ 1 and ≈ 0 are satisfied. In this paper, the new operations according to Ezzati et al. (2014) are extended to symmetric trapezoidal intuitionistic fuzzy number...

An approach for solving a matrix game whose pay off elements are symmetric trapezoidal fuzzy numbers is proposed. P.Grzegorzewski’s theorem[1]has been used to transform symmetric trapezoidal fuzzy numbers to interval fuzzy number such that length of all intervals are different.Acceptability index has been defined and ordering of fuzzy numbers has been established.

Ranking fuzzy numbers are an important aspect of decision making in a fuzzy environment. Since their inception in 1965, many authors have proposed different methods for ranking fuzzy numbers. However, there is no method which gives a satisfactory result to all situations. Most of the methods proposed so far are nondiscriminating and counterintuitive. This paper proposes a new method for ranking...

A b s t r a c t . 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 drawbacks for specific situations. We propose a new similarity measure for generalized trapezoidal fuz...

The similarity measure of fuzzy numbers is very important in many research fields such as pattern recognition [[5],[6]] and risk analysis in fuzzy environment [[1],[3],[15]]. Some methods have been presented to calculate the degree of similarity between fuzzy numbers [[1][4],[8],[15]]. In [16], Wen presented A modified similarity measure of generalized fuzzy numbers. Pandey et al.,[7] proposed ...

Methods for aggregating intuitionistic trapezoidal fuzzy information are investigated. Some operational laws of intuitionistic trapezoidal fuzzy numbers are introduced. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy ordered weighted averaging (ITFOWA) operator and intuitionistic trapezoidal fuzzy hybrid aggregation (ITFHA) operator, are p...

In this paper, we want to represent a method for ranking of two exponential trapezoidal fuzzy numbers. In this study a new Cardinality between exponential trapezoidal fuzzy numbers is proposed. Cardinality in this method is relatively simple and easier in computation and ranks various types of exponential fuzzy numbers. For the validation the results of the proposed approach are compared with d...

Fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is discussed. New algorithms for calculating the proper trapezoidal approximation of fuzzy numbers with respect to the distance based on bi-symmetrical weighted functions are proposed. It is shown that the adequate approximation operator is chosen with respect both to the global spread of a fuzzy numbe...