Comparative analysis of MCDM methods for the assessment of mortality in patients with acute coronary syndrome

Sałabun, Wojciech; Piegat, Andrzej

doi:10.1007/s10462-016-9511-9

Cited by 101 publications

(40 citation statements)

References 33 publications

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“…[7,12]) and B = ( [1,30] , [15,17]). Both A and B are proper trapezoidal fuzzy numbers, that is, trapezoidal fuzzy numbers in the classical sense.…”

Section: Corollary 2 Under the Above Conditions Of Theoremmentioning

confidence: 99%

“…Both A and B are proper trapezoidal fuzzy numbers, that is, trapezoidal fuzzy numbers in the classical sense. The solution of the equation ([0, 20] , [7,12]) + X = ( [1,30] , [15,17]) is X = ( [1,30] , [15,17]) − dual ([0, 20] , [7,12]) = ( [1,10] , [8,5]) .…”

Section: Corollary 2 Under the Above Conditions Of Theoremmentioning

confidence: 99%

“…Next, let us consider the fuzzy equation A + X = B, where A is the MITFN P P , A = ( [2,9] , [6,7]) and B is the MITFN P I , B = ( [15,10] , [9,14]) . The solution for X is: 15,10] , [9,14]) − dual ( [2,9] , [6,7]) = ( [13,1] , [3,7]) , which is an MITFN P I (see Figure 6).…”

Section: Corollary 2 Under the Above Conditions Of Theoremmentioning

confidence: 99%

“…The solution for X is: 15,10] , [9,14]) − dual ( [2,9] , [6,7]) = ( [13,1] , [3,7]) , which is an MITFN P I (see Figure 6). The transition modality value for X is α 0 X = 3 4 = 0.75 and the transition modality value for B is α 0 B = 1 2 = 0.5; thus, the interpretation of the calculus A + X = B is:…”

Section: Corollary 2 Under the Above Conditions Of Theoremmentioning

confidence: 99%

“…Nowadays, we can find applications of fuzzy sets in the most part of scientific disciplines, such as decision-making [2][3][4], probability [5], control theory [6], medical sciences [7], characterization of complex systems [8], among others.…”

Section: Introductionmentioning

confidence: 99%

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A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory

Jorba

Adillon

2017

Symmetry

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Abstract: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 maintain the traditional graphic representation of trapezoidal fuzzy numbers and we must use the interval plane in order to represent our modal interval trapezoidal fuzzy numbers graphically. Using this representation, we can correctly reflect the modality of the alpha cuts. We define some concepts from modal interval analysis and we study some of the related properties and structures, proving, among other things, that the inclusion relation provides a lattice structure on this set. We will also provide a semantic interpretation deduced from the modal interval extensions of real continuous functions and the semantic modal interval theorem. The application of modal intervals in the field of fuzzy numbers also provides a new perspective on and new applications of fuzzy numbers.

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“…[7,12]) and B = ( [1,30] , [15,17]). Both A and B are proper trapezoidal fuzzy numbers, that is, trapezoidal fuzzy numbers in the classical sense.…”

Section: Corollary 2 Under the Above Conditions Of Theoremmentioning

confidence: 99%