Abstract
The purpose of this paper is to put forward the notion of intuitionistic fuzzy soft matrix theory and some basic results. In this paper, we define intuitionistic fuzzy soft matrices and have introduced some new operators with weights, some properties and their proofs and examples which make theoretical studies in intuitionistic fuzzy soft matrix theory more functional. Moreover, we have given one example on weighted arithmetic mean for decision making problem.
Highlights
Most of our traditional tools for formal modeling, reasoning, and computing are crisp, deterministic, and precise in character
In real life, there are many complicated problems in engineering, economics, environment, social sciences medical sciences etc. that involve data which are not all always crisp, precise and deterministic in character because of various uncertainties typical problems. Such uncertainties are being dealing with the help of the theories, like theory of probability, theory of fuzzy sets, theory of intuitionistic fuzzy sets, theory of interval mathematics and theory of rough sets etc
Deli and Cagmam[9] introduced intuitionistic fuzzy parameterized soft sets. They have applied to the problems that contain uncertainties based on intuitionistic fuzzy parameterized soft sets
Summary
Most of our traditional tools for formal modeling, reasoning, and computing are crisp, deterministic, and precise in character. Consider the example 1, here we can not express with only two real numbers 0 and 1, we can characterized it by a membership function instead of crisp number 0 and 1, which associate with each element a real number in the interval [0,1]. (ffAA,E) = { ffAA(ee1) = { ( uu1,.7) ,(uu2,.5) ,(uu3,.4) ,(uu4,.2) }, ffAA(ee2) = { (uu1,.5) , (uu2,.1) , (uu3,.5)} } is the fuzzy soft set representing the “colour of the shirts” which Mr X is going to buy. We can say that a fuzzy soft set (ffAA ,E) is uniquely characterized by the matrix [μiiii ]mmmmmm and both concepts are interchangeable.
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