Title: On differentiable harmonic univex fuzzy mappings and its applications to fuzzy mathematical programming problem
Authors: Minakshi Parida; Sunita Chand
Addresses: Department of Mathematics, Siksha 'O' Anusandhan (Deemed to be University), Khandagiri Square, Bhubaneswar – 751030, Odisha, India ' Department of Mathematics, Siksha 'O' Anusandhan (Deemed to be University), Khandagiri Square, Bhubaneswar – 751030, Odisha, India
Abstract: In this paper, harmonic preunivex (H-preunivex) and harmonic preunicave (H-preunicave) fuzzy mappings have been introduced and several interesting results have been obtained related to generalised convexity. By using the concept of differentiability with H-preunivex and H-preunicave fuzzy mappings, harmonic univex (H-univex) and harmonic unicave (Hunicave) fuzzy mappings have been obtained respectively. Furthermore, H-univex and pseudo H-univex fuzzy mappings have been applied to study the sufficient optimality conditions and the duality results for Harmonic univex fuzzy programming problem (HUFP). Moreover, KKT conditions for the HUFP have been studied by using the H-univex fuzzy mappings. Suitable examples have been given to illustrate the results.
Keywords: fuzzy optimisation; H-preunivex; H-preunicave; H-univex; H-unicave; fuzzy mappings; sufficient optimality conditions; duality results.
International Journal of Mathematics in Operational Research, 2019 Vol.15 No.4, pp.464 - 497
Received: 02 Nov 2017
Accepted: 29 May 2018
Published online: 20 Sep 2019 *