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 nearest trapezoidal fuzzy number to a fuzzy number, with respect to a well-known metric and preserving the expected interval, was determined in recent articles. In the present paper the properties of additivity and continuity of the trapezoidal approximation operator are studied. Keywords— Additivity, Approximation, Continuity, Fuzzy number, Trapezoidal fuzzy number.

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 pr...

In this paper, we prove new distance properties between a fuzzy number and its trapezoidal approximation preserving the expected interval. Then, we find the best Lipschitz constant of the trapezoidal approximation operator preserving the expected interval. Finally, we use this result in finding within a reasonable error the trapezoidal approximation of a fuzzy number preserving the expected int...

The problem to find the nearest trapezoidal approximation of a fuzzy number with respect to a well-knownmetric, which preserves the expected interval of the fuzzy number, is completely solved. The previously proposed approximation operators are improved so as to always obtain a trapezoidal fuzzy number. Properties of this new trapezoidal approximation operator are studied. © 2007 Elsevier B.V. ...

Abstract The well-known Karush-Kuhn-Tucker theorem can be used, as in the fuzzy case, to find the trapezoidal approximation of a given intuitionistic fuzzy number. The method is quite technical such that obtaining the trapezoidal approximation of an intuitionistic fuzzy numbers from the trapezoidal approximation of a fuzzy number is proposed in the present paper. Among the advantages of this me...

P-normGeneralizedTrapezoidalIntuitionisticFuzzyNumberisthemostgeneralizedformofFuzzy aswellasIntuitionisticFuzzyNumber.Ithasahugeapplicationwhilesolvingvariousproblemsin impreciseenvironment.Inthispapertheauthorshavediscussedsomebasicarithmeticoperationsof p-normGeneralizedTrapezoidalIntuitionisticFuzzyNumbersusingtwodifferentmethods(extensio...

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...

Ranking of fuzzy numbers plays a very important role in linguistic decision making and some other fuzzy application systems. Several strategies have been proposed for ranking of fuzzy numbers. Each of these techniques has been shown to produce nonintuitive results in certain cases. In this paper, some new approaches for ranking of trapezoidal fuzzy numbers are introduced. Keywords— Magnitude of...

The emergency service facilities location is one of the most important issues in the emergency management. This study focused on the location set covering problem (LSCP) for emergency service facilities under fuzzy environment. On the basis of defining the signed distance of trapezoidal fuzzy number, the ranking rules of trapezoidal fuzzy number are defined, the model of emergency service facil...