Multi-objective non-linear four-valued refined neutrosophic optimization

Abstract

The neutrosophic sets are the prevailing frameworks that not only generalize the concept of fuzzy sets, but also analyse the connectivity of neutralities with different ideational spectra. In this article, we define a special type of neutrosophic set, named four-valued refined neutrosophic set (FVRNO), based on which various set-theoretic operators and properties of four-valued refined neutrosophic sets are studied. Often in many optimization problems of the real world, only the partial information about the values of parameters is available. In such situations, where impreciseness is involved in the information, classical techniques do not exhibit an appropriate optimal solution. A new concept to handle imprecise information is introduced and computational algorithm is formulated in four-valued refined neutrosophic environment. The new concept of optimization problem is an extension of intuitionistic fuzzy optimization as well as single-valued neutrosophic optimization. In this extended concept, indeterminacy is further refined as uncertain (U) and contradiction $(C= T\wedge F)$. Some examples to illustrate FVRNO are given and a comparative study of optimal solution between intuitionistic fuzzy optimization, single-valued neutrosophic optimization, multi-objective optimization using genetic algorithm, multi-objective goal attainment and four-valued refined neutrosophic optimization techniques were carried out and that concludes better optimal approximation is attained with new proposed optimization technique.