Nearest fuzzy number of type L-R to an arbitrary fuzzy number with applications to fuzzy linear system

Nearest fuzzy number of type L-R to an arbitrary fuzzy number with applications to fuzzy linear system

Blog Article

The sheath fuzzy operations on fuzzy numbers of type L-R are much easier than general fuzzy numbers.It would be interesting to approximate a fuzzy number by a fuzzy number of type L-R.In this paper, we state and prove two significant application inequalities in the monotonic functions set.These inequalities show that under a condition, the nearest fuzzy number of type L-R to an arbitrary fuzzy number exists and is unique.After that, the nearest fuzzy number of type L-R can be obtained by solving a linear system.

Note that the trapezoidal fuzzy numbers are a particular case of the fuzzy numbers of type L-R.The proposed method can represent the nearest trapezoidal fuzzy number to a given fuzzy number.Finally, to approximate fuzzy solutions of a fuzzy linear system, we apply our idea to construct a framework to find solutions of Fridge Light Cover crisp linear systems instead of the fuzzy linear system.The crisp linear systems give the nearest fuzzy numbers of type L-R to fuzzy solutions of a fuzzy linear system.The proposed method is illustrated with some examples.