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Estimation of missing values in fuzzy matrices (FM) and interval-valued fuzzy matrices (IVFM)
Life Cycle Reliability and Safety Engineering, 2020In real-life problems, uncertainty also occurs due to loss of information, which ultimately results in incomplete information. There are many other reasons which also cause incompleteness, e.g., erroneous data measure, insufficient data collection, lack of evidence, etc.
D. S. Hooda, M. S. Barak
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On fuzzy idempotent matrices of T-type
Information Sciences, 1994It is proved that idempotent fuzzy matrices satisfying a diagonal dominance condition \((T\)-type) have adjoints which are idempotent.
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Hamacher Operations on Pythagorean Fuzzy Matrices and Fermatean Fuzzy Matrices
Annals of Pure and Applied MathematicsThis study aims to extend Pythagorean and Fermatean fuzzy matrices within the framework of Hamacher operations. This paper introduces the concepts of Pythagorean fuzzy matrices and Hamacher operations for Fermatean fuzzy matrices and discusses several desirable properties of these operations, including commutativity, idempotency, and monotonicity ...
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An Introduction to Fuzzy Matrices
2020Fuzzy matrices are successfully used when fuzzy uncertainty occurs in a problem. Fuzzy matrices have become popular in the last two decades. In this chapter, two new binary fuzzy operators, ⊕ and ⨀, for fuzzy matrices are introduced. Several properties on ⊕ and ⨀ are presented here.
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Fuzzy Sets and Systems, 1992
A matrix \(M\) is called controllable if for some permutation matrix \(P\), \(PMP^ T\) has \((i,j)\) entry at least as large as \((j,i)\) entry for \(i\) greater than \(j\). The author gives an algorithm to reduce controllable matrices to canonical form.
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A matrix \(M\) is called controllable if for some permutation matrix \(P\), \(PMP^ T\) has \((i,j)\) entry at least as large as \((j,i)\) entry for \(i\) greater than \(j\). The author gives an algorithm to reduce controllable matrices to canonical form.
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2007
In this paper, some elementary operations on triangular fuzzy numbers (TFNs) are defined. We also define some operations on triangu- lar fuzzy matrices (TFMs) such as trace and triangular fuzzy determinant (TFD). Using elementary operations, some important properties of TFMs are presented.
Shyama, Amiya Kumar l, Pal, Madhumangal
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In this paper, some elementary operations on triangular fuzzy numbers (TFNs) are defined. We also define some operations on triangu- lar fuzzy matrices (TFMs) such as trace and triangular fuzzy determinant (TFD). Using elementary operations, some important properties of TFMs are presented.
Shyama, Amiya Kumar l, Pal, Madhumangal
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On the min-max composition of fuzzy matrices
Fuzzy Sets and Systems, 1995The paper examines the min-max product \[ (A*B)_{ij} = \min_{1\leq k\leq n} \max (a_{ik}, b_{kj}), \quad i=1, \dots, m,\;j=1, \dots,p \] of matrices \(A,B\) over the semiring \(([0,1], \min, \max)\) [cf. e.g. Chapter 3 in: \textit{A. Kandel}, \textit{S. C. Lee}, Fuzzy switching and automata, Crane Russak, New York 1979; Zbl 0406.94022)].
M. Z. Ragab, E. G. Emam
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Fuzzy Sets and Systems, 1984
The author derives many properties of the fuzzy matrix operation \(B\leftarrow D=[\bigwedge^{p}_{k=1}(b_{ik}\leftarrow d_{kj})]\) where \(a\leftarrow b\) is 1 or a as \(a\geq b\) or not. He studies subinverses and regularity.
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The author derives many properties of the fuzzy matrix operation \(B\leftarrow D=[\bigwedge^{p}_{k=1}(b_{ik}\leftarrow d_{kj})]\) where \(a\leftarrow b\) is 1 or a as \(a\geq b\) or not. He studies subinverses and regularity.
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International Journal of Fuzzy System Applications, 2018
This article describes how information technology and internet together infused organizations with huge amount of data. Consequently, accumulating, storing, understanding and analyzing data at a large scale is equally important and complex. Out of this data not all is information data, in order to extract information, one needs to discard redundant ...
Omdutt Sharma +2 more
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This article describes how information technology and internet together infused organizations with huge amount of data. Consequently, accumulating, storing, understanding and analyzing data at a large scale is equally important and complex. Out of this data not all is information data, in order to extract information, one needs to discard redundant ...
Omdutt Sharma +2 more
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On Fuzzy Equations with 2 ×2 Matrices
2015The question of probability of a system of fuzzy equations solvability in a max –t-norm fuzzy algebra for several t-norms and 2 ×2 matrices is considered. We derive that the probability of solving such a system is very low, namely \(\frac{1}{10}\) for Godel norm, \(\frac{11}{60}\) for Łukasiewicz norm, \(\frac{5}{36}\) for product norm and zero for ...
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