Adjustable Security Proportions in the Fuzzy Portfolio Selection under Guaranteed Return Rates

Based on the concept of high returns as the preference to low returns, this study discusses the adjustable security proportion for excess investment and shortage investment based on the selected guaranteed return rates in a fuzzy environment, in which the return rates for selected securities are characterized by fuzzy variables. We suppose some securities are for excess investment because their return rates are higher than the guaranteed return rates, and the other securities whose return rates are lower than the guaranteed return rates are considered for shortage investment. Then, we solve the proposed expected fuzzy returns by the concept of possibility theory, where fuzzy returns are quantified by possibilistic mean and risks are measured by possibilistic variance, and then we use linear programming model to maximize the expected value of a portfolio’s return under investment risk constraints. Finally, we illustrate two numerical examples to show that the expected return rate under a lower guaranteed return rate is better than a higher guaranteed return rates in different levels of investment risks. In shortage investments, the investment proportion for the selected securities are almost zero under higher investment risks, whereas the portfolio is constructed from those securities in excess investments.

Arithmetic Operations and Expected Values of Regular Interval Type-2 Fuzzy Variables

High computation complexity restricts the application prospects of the interval type-2 fuzzy variable (IT2-FV), despite its high degree of freedom in representing uncertainty. Thus, this paper studies the fuzzy operations for the regular symmetric triangular IT2-FVs (RSTIT2-FVs)—the simplest IT2-FVs having the greatest membership degrees of 1. Firstly, by defining the medium of an RSTIT2-FV, its membership function, credibility distribution, and inverse distribution are analytically and explicitly expressed. Secondly, an operational law for fuzzy arithmetic operations regarding mutually independent RSTIT2-FVs is proposed, which can simplify the calculations and directly output the inverse credibility of the functions. Afterwards, the operational law is applied to define the expected value operator of the IT2-FV and prove the linearity of the operator. Finally, some comparative examples are provided to verify the efficiency of the proposed operational law.

Solving fully fuzzy linear programming problems by controlling the variation range of variables

This paper deals with a fully fuzzy linear programming problem (FFLP) in which the coefficients of decision variables, the right-hand coefficients and variables are characterized by fuzzy numbers. A method of obtaining optimal fuzzy solutions is proposed by controlling the left and right sides of the fuzzy variables according to the fuzzy parameters. By using fuzzy controlled solutions, we avoid unexpected answers. Finally, two numerical examples are solved to demonstrate how the proposed model can provide a better optimal solution than that of other methods using several ranking functions.

Law of large numbers for the sequence of uncorrelated fuzzy random variables

This work proposes the concept of uncorrelation for fuzzy random variables, which is weaker than independence. For the sequence of uncorrelated fuzzy variables, weak and strong law of large numbers are studied under the uniform Hausdorff metric d H ∞ . The results generalize the law of large numbers for independent fuzzy random variables.

A Possibilistic Kalman Filter for the Reduction of the Final Measurement Uncertainty, in Presence of Unknown Systematic Errors

A Kalman filter is a concept that has been in existence for decades now and it is widely used in numerous areas. It provides a prediction of the system states as well as the uncertainty associated to it. The original Kalman filter can not propagate uncertainty in a correct way when the variables are not distributed normally or when there is a correlation in the measurements or when there is a systematic error in the measurements. For these reasons, there have been numerous variations of the original Kalman filter, most of them mathematically based (like the original one) on the theory of probability. Some of the variations indeed introduce some improvements, but without being completely successful. To deal with these problems, more recently, Kalman filters have also been defined using random-fuzzy variables (RFVs). These filters are capable of also propagating distributions that are not normal and propagating systematic contributions to uncertainty, thus providing the overall measurement uncertainty associated to the state predictions. In this paper, the authors make another step forward, by defining a possibilistic Kalman filter using random-fuzzy variables which not only considers and propagates both random and systematic contributions to uncertainty, but also reduces the overall uncertainty associated to the state predictions by compensating for the unknown residual systematic contributions.

Penerapan Algoritma Fuzzy Tahani Untuk Rekomendasi Penerima Beasiswa Peningkatan Prestasi Akademik

Relational database systems that exist until now are only able to handle data that is definite (crisp), deterministic and precise. In fact, in real conditions, vague data is often needed for the decision-making process. For decision making involving fuzzy variables based on crisp data in the database, you can use a query on the database system with the concept of fuzzification on the data. In every educational institution, especially universities, there are several types of scholarships given to students. To get a scholarship, students must meet all the requirements that have been set. This study discusses the application of the Fuzzy Tahani algorithm for the recommendation of Academic Achievement Improvement (PPA) scholarship recipients at Bumigora University, Mataram. Data for PPA scholarship recipients was used in 2014 with details of the number of registrants 64 people and recipients (quota) of 15 people. Every year the number of applicants for this scholarship is increasing, while the processing and selection process is still done semi-manually so that the expected results are less than optimal, especially in terms of transparency and distribution. There are several variables that must be calculated by PPA scholarship recipients, namely the value of the Grade Point Average (GPA), Parents' Income, Number of Dependent Parents and Number of Diplomas. From the results of trials conducted in this study, it can be seen that the system's accuracy level reaches a value of 73.3%. This value is obtained by comparing the results of the semi-manual selection of PPA scholarship recipients with the results of the PPA scholarship selection using a system that uses the Fuzzy Tahani Algorithm.

Biodiesel Supply Chain Network Design Under Hybrid Uncertainties: A Novel Multi-objective Robust Fuzzy Stochastic Approach

In the biofuel supply chain, there may be various and hybrid uncertainties that, if ignored, can lead to inefficient network design. In this study, a multi-objective robust fuzzy stochastic programming (MORFSP) model is proposed for designing biodiesel supply chain network (BSCN) under different and hybrid uncertainties. This model simultaneously minimizes total cost of the BSCN and total environmental impacts of activities of the network. Fixed costs and environmental impact of opening facilities are described as fuzzy variables. Demands, supplies, other costs and environmental impacts are considered as fuzzy scenario based variables. The proposed MORFSP model considers different risks, including possibilistic variability and scenario variability related to economic and environmental objective functions, and unsatisfied demand costs. This model is applied in a real case study to design a BSCN in Iran. Waste cooking oil (WCO), and some non-edible plants like Salvia lerifolia (SL) and Jatropha Curcas L. (JCL) are considered as sources of producing biodiesel. The proposed approach used for designing a four-echelon, multi-period, and multi-product, of BSCN. The results show the effectiveness of the proposed model for designing the BSCN under hybrid uncertainties.

The Scalar Mean Chance and Expected Value of Regular Bifuzzy Variables

As a natural extension of the fuzzy variable, a bifuzzy variable is defined as a mapping from a credibility space to the collection of fuzzy variables, which is an appropriate tool to model the two-fold fuzzy phenomena. In order to enrich its theoretical foundation, this paper explores some important measures for regular bifuzzy variables, the most commonly used type of bifuzzy variables. Firstly, we introduce the regular bifuzzy variables’ mean chance measure and some properties, including self-duality and its calculation formulas. Furthermore, we also investigate the mean chance distribution for strictly monotone functions of regular bifuzzy variables based on the proposed operational law. Finally, we present the expected value operator as well as equivalent analytical formulas of the expected value of regular bifuzzy variables and their strictly monotone functions.