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 ∧ 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.

Optimizing system reliability through selective maintenance allocation: A novel multi‐objective programming approach using neutrosophic fuzzy concept

“…Four valued neutrosophic set (FVNS) 43 By dividing indeterminacy in various ways, a FVNS can be described in a variety of ways. A FVNS is a neutrosophic set wherein indeterminacy is divided into two parts and mathematically defined as: R𝐹𝑁 = {(𝑥, 𝑇 R𝐹𝑁 (𝑥), 𝑈 R𝐹𝑁 (𝑥), 𝐼 R𝐹𝑁 (𝑥), 𝐹 R𝐹𝑁 (𝑥) ∶ 𝑥 ∈ 𝑋)}.…”

A Novel Similarity Measure of Single-Valued Neutrosophic Sets Based on Modified Manhattan Distance and Its Applications

“…of SVN sets based on cosine and cotangent functions, respectively, and applied them to deal with medical diagnosis. For more references to SVN sets, one can refer to the work of [34][35][36][37][38].…”

An Interval-Valued Intuitionistic Hesitant Fuzzy Methodology and Application

“…And its validity and superiority are explained by an illustrative example, and a comparison with existing algorithms is tabulated. Recently Freen et al [ 11 , 15 ] have presented comparative study and application of neutrosophic sets for multiobjective nonlinear programming problems. The present paper may provide a computational insight into several real-life optimization problems that are encountered in engineering and management sectors, since in many existing optimization techniques, the fuzzy sets or their other versions were used to address the uncertainty and hesitation of a real life problems.…”