Multi-objective non-linear four-valued refined neutrosophic optimization
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(2020) 39:35
Multi-objective non-linear four-valued refined neutrosophic optimization Gul Freen1 · Sajida Kousar1 · Sumbal Khalil1 · Muhammad Imran2 Received: 8 April 2019 / Revised: 22 October 2019 / Accepted: 11 November 2019 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019
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 ∧ 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.
Communicated by Marcos Eduardo Valle.
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Sajida Kousar [email protected] Gul Freen [email protected] Sumbal Khalil [email protected] Muhammad Imran [email protected]
1
Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan
2
NUST Business School (NBS), National University of Sciences and Technology, Islambad, Pakistan
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Keywords Neutrosophic set · Single-valued neutrosophic set · Four-valued refined neutrosophic set · Neutrosophic optimization · Riser design problem · Car-side impact Mathematics Subject Classification 90C30 · 90C70
1 Introduction The theory of fuzzy set was introduced by Zadeh (1965). A fuzzy set basically consists of subjects with a series of grades. The fuzzy set is described by a function(commonly termed as membership function) from any non-empty set to the closed interval [0, 1]. The set-theocratic ideas of relation, union, inclusion, complement, intersection, convexity, etc. are extended to fuzzy sets. Moreover, several characteristics of all those notions are established in the context of the fuzzy sets. After the introduction of fuzzy set, the fuzzy logic (FL) ha
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