Title: A new approach to find optimal solution of fuzzy assignment problem using penalty method for hendecagonal fuzzy number

Authors: M. Revathi; M. Valliathal

Addresses: Tamilnadu School of Architecture, Coimbatore – 641659, Tamilnadu, India ' Chikkaiah Naicker College, Erode – 638004, Tamilnadu, India

Abstract: Fuzzy assignment problem (FAP) is a well-known topic and it is used to solve many real-life problems. In many situations, the parameters are used to characterise the uncertainty either triangular or trapezoidal fuzzy number. But the representation of fuzzy number is not always a triangular or trapezoidal fuzzy number. In this paper, a new generalisation of fuzzy number called hendecagonal fuzzy number (HDFN) is introduced with its arithmetic operations. This research aims to introduce a new penalty approach in order to solve fuzzy assignment problem such that the solution is optimum. The cost of assignment is represented by trapezoidal fuzzy number (TrapFN) and HDFN. The proposed method overcomes the limitations of existing method and HDFN is more optimal than TrapFN.

Keywords: hendecagonal fuzzy number; HDFN; alpha cut; fuzzy arithmetic; fuzzy assignment problem; FAP; penalty approach; ranking method; fuzzy optimal solution; trapezoidal fuzzy number; TrapFN; fuzzy cost; graphical representation.

DOI: 10.1504/IJFCM.2020.106101

International Journal of Fuzzy Computation and Modelling, 2020 Vol.3 No.1, pp.61 - 74

Received: 04 Jul 2018
Accepted: 23 Jun 2019
Published online: 30 Mar 2020 *