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Information value has been proposed and used as a probabilistic sensitivity measure, the idea being that uncertain parameters having higher information value are precisely those to which an optimal decision is more sensitive. In this paper, we study the notion of information density as a graphical complement to information value analysis, one that augments an information value calculation with associated directions of information gain. We formally examine mathematical details absent from its earlier presentation that guarantee information density exists and is well posed and describe its relationship to alternate measures of information value. We present its application in the context of a realistic case study and discuss the associated insights.

Tracing the development of economics since the 19th century up to the present day makes it evident that at its core there is a sequence of rather precise and mathematically sophisticated axiomatic theories. At the same time, there is always a noticeable and persistent gap between economic reality and the economic predictions derived from these theories. The main reason why economic theories have not been successful so far in modeling economic reality is the fact that these theories are formulated in terms of hard sciences characterized by their nature of preciseness. In economics, as in any complex multi-agent humanistic system, motivations, intuition, human knowledge, and human behavior, such as perception, emotions, and norms, play dominant roles. Consequently, real economic and socioeconomic world problems are too complex to be translated into classical mathematical and bivalent logic languages, solved and interpreted in the language of the real world. The traditional modeling methodology (economics deals with models of economic reality) is perhaps not relevant or at least not powerful enough to satisfy the requirements of human reasoning and decision making activities. A new much more effective modeling language is needed to capture economic reality. According to Prof. L. Zadeh, in general, fuzzy-logic-based modeling languages have a higher power of cointension than their bivalent logic-based counterparts and present the potential for playing an essential role in modeling economic, social, and political systems. The sheer complexity of causation in the economic arena mandates a fuzzy approach. We argue that many economic dynamical systems naturally become fuzzy due to the uncertain initial conditions and parameters. In this study we consider an economic system as a human centric and imperfect information-based realistic multi-agent system with fuzzy-logic-based representation of the economic agents' behavior and with imprecise constraints. We use fuzzy "if-then" language and fuzzy differential equations for modeling the economic agents. This paper looks beyond the standard assumptions of economics that all people are similarly rational and self-interested. To be able to incorporate motivation input variables of economic agents into their models, we created behavioral model of agents by using the fuzzy and Bayes-Shortliffe approaches. Nowadays, adding norms and motivations to utility function has become an issue for economists and business people. They also recognized that something is missing in standard utility function and even in standard economic theory. Everything is not as simple as just profit or utility maximization under budget constraint. They recognized that during all these years they have been ignoring the most important thing: the norms and motivations that actually directed the human nature of the decision makers. It is obvious that these norms and motivations cannot be captured by statistical analysis, there are deeper and more subtle uncertain relationships between well-being and its determinants. We suggest the fuzzy graph-based approach to utility function construction. The proposed approach is consistent with the behavioral and uncertainty paradigms of the decision makers. Here we put the emphasis on mathematical background rather than real case analysis. The suggested fuzzy approaches to economic problem-solving are applied to fuzzy decision making in an oligopolistic economy.

This paper derives a general prescriptive model for group decision analysis based on a set of logical and operational assumptions analogous to those for individual decision analysis. The approach accounts for each group member's potentially different frames of their common decision, including different events and different consequences of concern. Assuming that each group member accepts the decision analysis assumptions to evaluate his or her analysis of what the group should do and that the group accepts an analogous set of decision analysis assumptions for the group's decision, it is proven that the group expected utility for an alternative should be a weighted sum of the individual member's expected utilities for the alternatives. After each group member does his or her decision analysis of the group's alternatives, the essence of the group decision analysis is to specify the weights based on the interpersonal comparison of utilities and on the relative importance or power of each individual in the group.

In managing finances, each aims to be able to generate income for himself. Investment is one of the individual decisions to increase the assets owned by allocating a certain amount of funds, time, and assets that are considered to generate returns. Millennial investors are the government's main target through financial literacy education that the Financial Services Authority has promoted in encouraging an increase in stock investment by the public. However, many factors influence investors to invest, including the environment and the investor's personal experience. The purpose of this study is to analyze the factors that influence the investment decisions of millennial private investors, including financial literacy, perceptions of risk and return, financial technology, family background, and income. The data taken for this study is primary data obtained through online questionnaires to people who are currently investing in the age range of 20-40. The number of samples of this study was 224 respondents through data collection using google form for two months. The research data were analyzed using SPSS 26 software. By using descriptive statistical data, validity and reliability tests, classical assumption tests such as autocorrelation, multicollinearity, heteroscedasticity. The results showed that financial literacy, perceptions of risk and return, financial technology, family background, and income influence millennial investor investment decisions. The implication of this result shows that parents should start to provide basic investment knowledge to teenagers as soon as possible, and the firm can invest more in financial technologies to serve young customers.