Title: Nonlinear fuzzy programming - a case study

Authors: Arpita Kabiraj; Swapan Raha; Prasun Kumar Nayak

Addresses: Department of Mathematics, Siksha-Bhavana (Institute of Sciences), Visva-Bharati, Santiniketan, 731235, India ' Department of Mathematics, Siksha-Bhavana (Institute of Sciences), Visva-Bharati, Santiniketan, 731235, India ' Department of Mathematics, Midnapore College (Autonomous), Midnapore, 721101, India

Abstract: In this article, we would like to attempt finding a convergent near optimal solution of a fuzzy nonlinear programming problem (FNLPP) in which the objective as well as the constraints defining the relationship between variables are so imprecisely stated that it is practically impossible to represent by any existing crisp model. The primary aim of this research is to provide more flexibility to the decision-maker. Accordingly, to solve such a FNLPP, we use approximate reasoning which involves three stages: fuzzification, aggregation and defuzzification. The process is repeated till a convergent near optimal solution is attained. An algorithm is designed for the implementation of the proposal. Artificial examples have been considered to illustrate our approach and existing results are used for comparison. Finally, a case study is undertaken to demonstrate the effectiveness of our proposal.

Keywords: fuzzy nonlinear programming problem; FNLPP; fuzzification; aggregation; defuzzification.

DOI: 10.1504/IJMOR.2025.149924

International Journal of Mathematics in Operational Research, 2025 Vol.32 No.3, pp.331 - 347

Received: 27 Nov 2023
Accepted: 24 Dec 2023
Published online: 18 Nov 2025 *

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