In a world of chaotic alignments, traditional logic with its strict boundaries of truth and falsity has not imbued itself with the capability of reflecting the reality. Despite various attempts to reorient logic, there has remained an essential need for an alternative system that could infuse into itself a representation of the real world. Out of this need arose the system of Neutrosophy (the philosophy of neutralities, introduced by FLORENTIN SMARANDACHE), and its connected logic Neutrosophic Logic, which is a further generalization of the theory of Fuzzy Logic. In this book we study the concepts of Fuzzy Cognitive Maps (FCMs) and their Neutrosophic analogue, the Neutrosophic Cognitive Maps (NCMs). Fuzzy Cognitive Maps are fuzzy structures that strongly resemble neural networks, and they have powerful and far-reaching consequences as a mathematical tool for modeling complex systems. Neutrosophic Cognitive Maps are generalizations of FCMs, and their unique feature is the ability to handle indeterminacy in relations between two concepts thereby bringing greater sensitivity into the results. Some of the varied applications of FCMs and NCMs which has been explained by us, in this book, include: modeling of supervisory systems; design of hybrid models for complex systems; mobile robots and in intimate technology such as office plants; analysis of business performance assessment; formalism debate and legal rules; creating metabolic and regulatory network models; traffic and transportation problems; medical diagnostics; simulation of strategic planning process in intelligent systems; specific language impairment; web-mining inference application; child labor problem; industrial relations: between employer and employee, maximizing production and profit; decision support in intelligent intrusion detection system; hyper-knowledge representation in strategy formation; female infanticide; depression in terminally ill patients and finally, in the theory of community mobilization and women empowerment relative to the AIDS epidemic.

This paper suggests a new decision-making model based on Neutrosophic Cognitive Maps (NCMs) for making comprehensive decisions from a multi-objective approach (diagnosis, decisions, and prediction) during the execution of many projects simultaneously.

There are various factors which lead to the criminal behaviour in humans. Prominent researchers monitoring the situation of crime in Nigeria cite poverty, unemployment, family-breakdown, bribing & corruption, lack of co-operation from public and negative perception of police to be the major causes behind criminal behaviour.

In this book authors for the first time introduce new mathematical models analogous to Fuzzy Cognitive Maps (FCMs) and Neutrosophic Cognitive Maps (NCMs) models. Several types of MOD Cognitive Maps models are constructed in this book. They are MOD Cognitive Maps model, MOD dual number Cognitive Maps model, MOD neutrosophic Cognitive Maps model, MOD finite complex number Cognitive Maps model, MOD special dual like number Cognitive Maps model, and MOD special quasi dual number Cognitive Maps model.

In spite of researchers’ concerns to find causalities, reviewing the literature of psychological studies one may argue that the classical statistical methods applied in order to find causalities are unable to find uncertainty and indeterminacies of the relationships between concepts.

The wisdom of crowds (WOC) is a theory where it is believed that a multitude of people, unknown to each other and not experts in some subject, can reach more accurate conclusions on this subject than each of them would achieve individually; it could even have more accuracy than the result that a group of experts would obtain. This theory can be used to obtain information from the individual knowledge of an inexperienced crowd, including knowledge on complex phenomena. In this paper, the complex phenomenon is represented with the help of Neutrosophic Cognitive Maps (NCM), which allow us to capture the cause-effect relations among the concepts according to each of the individuals’ judgments. In this case, a dynamic processing of the results is carried out. The NCMs are aggregated following the WOC principles using an aggregation algorithm, which is based on the Fuzzy Negative-Positive-Neutral (NPN) logic. The advantage of using NCM is that indeterminacy is included in the modeling, thus individuals can express their opinions more reliably.