Generalised Single Valued Neutrosophic Number And Its Application To Neutrosophic Linear Programming

In this paper, the concept of single valued neutrosophic number (SV N-number) is presented in a generalized way. Using this notion, a crisp linear programming problem (LP-problem) is extended to a neutrosophic linear programming problem (NLP-problem).

A neutrosophic set has the potentiality of being a general framework of intuitionistic fuzzy set, classical set, and fuzzy set. The idea of neutrosophic set provides a new tool to deal with uncertainty analysis in data sets. Single valued trapezoidal neutrosophic numbers is a special case of neutrosophic set that handles ill-defined and very difficult data. This work intends to introduce the weighted average ranking to transportation problem in neutrosophic environment.

In this study we define the generalizing single valued triangular neutrosophic number. In addition, single valued neutrosophic numbers are transformed into single valued triangular neutrosophic numbers according to the values of truth, indeterminacy and falsity. Furthermore, we extended the Hamming distance given for triangular intuitionistic fuzzy numbers to single valued triangular neutrosophic numbers. We have defined new score functions based on the Hamming distance.

Neutrosophic set is considered as a generalized of crisp set, fuzzy set, and intuitionistic fuzzy set for representing the uncertainty, inconsistency, and incomplete knowledge about the real world problems. In this paper, a neutrosophic linear programming (NLP) problem with single-valued trapezoidal neutrosophic numbers is formulated and solved. A new method based on the so-called score function to find the neutrosophic optimal solution of fully neutrosophic linear programming (FNLP) problem is proposed.

In information technology, the concepts of cost, time, delivery, space, quality, durability, and price have gained greater importance in solving managerial decision-making problems in supply chain models, transportation problems, and inventory control problems. Moreover, competition is becoming tougher in imprecise environments. Neutrosophic sets and logic are gaining significant attention in solving real-life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy. Neutrosophic Sets in Decision Analysis and Operations Research is a critical, scholarly publication that examines various aspects of organizational research through mathematical equations and algorithms and presents neutrosophic theories and their applications in various optimization fields. Featuring a wide range of topics such as information retrieval, decision making, and matrices, this book is ideal for engineers, technicians, designers, mathematicians, practitioners of mathematics in economy and technology, scientists, academicians, professionals, managers, researchers, and students.

Smarandache presented neutrosophic theory as a tool for handling undetermined information, and together with Wang et al. introduced single valued neutrosophic sets that is a special neutrosophic set and can be used expediently to deal with real-world problems, especially in decision support.

In this research article, we envisage the neutrosophic number from various distinct rational perspectives & viewpoints to give it a look of a conundrum. We focused & analysed various types of linear and non-linear generalized trapezoidal neutrosophic numbers which serves an indispensable role for uncertainty concept related problem.

Papers on neutrosophic programming, neutrosophic hypersoft set, neutrosophic topological spaces, NeutroAlgebra, NeutroGeometry, AntiGeometry, NeutroNearRings, neutrosophic differential equations, etc.

This work was carried out in collaboration between all authors. Author OE designed the study, performed the statistical analysis, wrote the protocol and wrote the first draft of the manuscript. Authors MS and AK managed the analyses of the study. Author AK managed the literature searches. All authors read and approved the final manuscript.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Some articles in this issue: n-Refined Neutrosophic Modules, A Neutrosophic Approach to Digital Images, A Novel Method for Neutrosophic Assignment Problem by using Interval-Valued Trapezoidal Neutrosophic Number.