In this paper, we first consider a multi-objective Portfolio Selection model and then we add another entropy objective function and next we generalized the model. We solve the problems using Neutrosophic optimization technique. The models are illustrated with numerical examples.

This book explores the risk-return paradox in portfolio selection by incorporating multi-objective criteria. Empirical research is presented on the development of alternate portfolio models and their relative performance in the risk/return framework to provide solutions to multi-objective optimization. Next to outlining techniques for undertaking individual investor’s profiling and portfolio programming, it also offers a new and practical approach for multi-objective portfolio optimization. This book will be of interest to Foreign Institutional Investors (FIIs), Mutual Funds, investors, and researchers and students in the field.

“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.

“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. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation and with their spectrum of neutralities in between them (i.e. notions or ideas supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic).

Neutrosophic (NS) set hypothesis gives another way to deal with the vulnerabilities of the shortest path problems (SPP). Several researchers have worked on fuzzy shortest path problem (FSPP) in a fuzzy graph with vulnerability data and completely different applications in real world eventualities. However, the uncertainty related to the inconsistent information and indeterminate information isn't properly expressed by fuzzy set. The neutrosophic set deals these forms of uncertainty. This paper presents a model for shortest path problem with various arrangements of integer-valued trapezoidal neutrosophic (INVTpNS) and integer-valued triangular neutrosophic (INVTrNS). We characterized this issue as Neutrosophic Shortest way problem (NSSPP). The established linear programming (LP) model solves the classical SPP that consists of crisp parameters. To the simplest of our data, there's no multi objective applied mathematics approach in literature for finding the Neutrosophic shortest path problem (NSSPP).

The purpose of this paper was to model, with the help of neutrosophic fuzzy numbers, the optimal financial asset portfolios, offering additional information to those investing in the capital market. The optimal neutrosophic portfolios are those categories of portfolios consisting of two or more financial assets, modeled using neutrosophic triangular numbers, that allow for the determination of financial performance indicators, respectively the neutrosophic average, the neutrosophic risk, for each financial asset, and the neutrosophic covariance as well as the determination of the portfolio return, respectively of the portfolio risk.

“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.