Title: Notes on triangular intuitionistic fuzzy numbers

Authors: Mijanur Rahaman Seikh; Prasun Kumar Nayak; Madhumangal Pal

Addresses: Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721 102, India ' Bankura Christian College, Bankura-722 101, India ' Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721 102, India

Abstract: The notion of triangular fuzzy number is put forward on the basis of intuitionistic fuzzy sense. The basic algebra and some non-linear operations of triangular intuitionistic fuzzy numbers (TIFNs) are devised. The average ranking index is introduced to find out order relations between two TIFNs. A method is described to approximate a TIFN to a nearly approximated interval number. Applying this result and using interval arithmetic, a bound unconstrained optimisation problem is solved whose coefficients are fixed TIFNs. Numerical examples are also given for illustration.

Keywords: triangular intuitionistic fuzzy numbers; TIFN; average ranking index; interval approximation; triangular fuzzy numbers; unconstrained optimisation.

DOI: 10.1504/IJMOR.2013.054730

International Journal of Mathematics in Operational Research, 2013 Vol.5 No.4, pp.446 - 465

Received: 17 Feb 2012
Accepted: 07 Jun 2012
Published online: 31 Mar 2014 *

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