RT journal article
T1 Developing solution algorithm for LR-type fully interval-valued intuitionistic fuzzy linear programming problems using lexicographic-rankingmethod
A1 Malik, Manisha
A1 Gupta, S. K.
A1 Arana Jiménez, Manuel
A2 Estadística e Investigación Operativa
K1 Fuzzy mathematical programming
K1 Interval-valued intuitionistic fuzzy number
K1 LR-type fuzzy number
K1 Lexicographic ranking criterion
K1 Score function
K1 Accuracy function
AB The current article is devoted tomathematically handling the inherent uncertainties of variouspractical problems by introducing the concept of LR-type interval-valued intuitionistic fuzzynumbers (LR-type IVIFN). The theoretic development of this concept has also been enhancedby providing various diagrammatic representations of LR-type IVIFNs and establishingthe arithmetic operations among these fuzzy numbers. The notion of α, β-cuts and intervalarithmetic have been employed to derive the expressions for the arithmetic operations on LRtypeIVIFNs. In addition to this, the total order properties of lexicographic-ranking criteriaalong with considering seven distinct parameters have been used to define the ordering onLR-type IVIFNs. Further, a linear programming problem (LPP) with both equality andinequality type constraints, all parameters in the form of LR-type IVIFNs, and unrestricteddecision variables has been modeled. In order to obtain a unique optimal solution for theproposed LPP, the lexicographic ranking-based solution methodology has been developed inwhich by introducing some binary variables, the original LPP is converted to an equivalentmixed 0-1 lexicographic non-linear programming problem having seven components in theobjective function. Various theorems have also been proved to show the equivalence of theoriginal problem and its different proposed constructions. The model formulation, algorithm,and discussed results have not only developed a new idea but also generalized various wellknownrelated works existing in the literature. Moreover, a numerical illustration has beenprovided to clarify the step-wise procedure of the proposed solution approach. Additionally, to establish the practical significance of the study, a real-world production planning problem isframed, solved, and analyzed under the LR-type interval-valued intuitionistic fuzzy scenario.In last, a comparative study has also been carried out to prove the relevancy of the developedalgorithm.
PB Springer
SN 1807-0302
YR 2023
FD 2023-07-18
LK http://hdl.handle.net/10498/32257
UL http://hdl.handle.net/10498/32257
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026