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In this paper, we review the idea of fuzzy measures and look at some properties of these measures. We describe a procedure for aggregating multiple fuzzy measures. We discuss the use of fuzzy measures for modeling information about uncertain variables. We carefully look at the properties of possibility measures. We look at the issue of conjuncting possibility measures. [ABSTRACT FROM AUTHOR]

The purpose of this study is to consider and modeling E-Commerce variables based on FAHP, FTOPSIS and Possibility Theory to create a new approach in decision-making techniques. Thus, modeling Market Orientations and Innovation Orientation indicators as the E-Satisfaction factors and Fulfillment & Reliability, Responsiveness and Security indicators as the E-Trust factors is done for selected banks. Data collected from customers and experts via distributing questionnaires and the data were analyzed by FAHP, FTOPSIS and Possibility Theory techniques. The results show that E-Satisfaction, Innovation Orientation and Security are the important indicators in E-Loyalty and Mellat Bank takes the highest rank in covering these indicators.

Abstract This paper presents the CoG-FPOM, an adaptation of the Fuzzy Pay-Off Method (FPOM). The FPOM is a scenario-based real option valuation method that uses fuzzy numbers as possibility distributions. The paper shows that there are situations in which the original FPOM calculates the real option value to be negative, what is theoretically incorrect. The cause is related to the method used for obtaining a single representative value out of a fuzzy number. Instead of the possibilistic expected value operation used in the original FPOM, the CoG-FPOM uses the center of gravity (CoG) to accomplish the task – a proof of its general validity is presented. An application to calculate the abandonment real option for petroleum producing fields shows that the proposal can be easily used for project valuation under uncertainty. [ABSTRACT FROM AUTHOR]

A step-by-step fuzzy diagnostic method based on frequency-domain symptom extraction and trivalent logic fuzzy diagnosis theory (TLFD), which is established by combining the trivalent logic inference theory with the possibility and fuzzy theories, is proposed herein. The features for diagnosing a number of abnormal states are extracted sequentially from the measured signals using statistical tests in the frequency domain. The symptom parameters (SPs) that can sensitively reflect symptoms of abnormal states are then selected to provide effective information for the discrimination of each state. The membership function of each state is then generated based on the possibility theory using the probability functions of the SPs. The step-by-step fuzzy diagnoses are performed based on the TLFD. This method can be used extensively to diagnose anomalies in various equipment. In this study, the diagnosis of structure faults of a rotating machine is cited as an example to demonstrate the effectiveness and universality of this method. [ABSTRACT FROM AUTHOR]

In the context of climate change, the uncertainty associated with Global Climate Models (GCM) and scenarios needs to be assessed for effective management practices and decision-making. The present study focuses on modelling the GCM and scenario uncertainty using Reliability Ensemble Averaging (REA) and possibility theory in projecting streamflows over Wainganga river basin. A macro scale, semi-distributed, grid-based hydrological model is used to project the streamflows from 2020 to 2094. The observed meteorological data are collected from the India Meteorological Department (IMD) and the streamflow data is obtained from Central Water Commission (CWC) Hyderabad. In REA, meteorological data are weighted based on the performance and convergence criteria (GCM uncertainty). Whereas in possibility theory, based on the projection of different GCMs and scenarios during recent past (2006-2015) possibility values are assigned. Based on the possibility values most probable experiment and weighted mean possible CDF for the future periods are obtained. The result shows that there is no significant difference in the outcomes is observed between REA and possibility theory. The uncertainty associated with GCM is more significant than the scenario uncertainty. An increasing trend in the low and medium flows is predicted in annual and monsoon period. However, flows during the non-monsoon season are projected to increase significantly. Moreover, it is observed that streamflow generation not only depends on the change in precipitation but also depends on the previous state of physical characteristics of the region. [ABSTRACT FROM AUTHOR]

Based on possibility theory, this paper deals with the portfolio adjusting problem for an existing portfolio under the assumption that the returns of risky assets are fuzzy numbers and there exists transaction costs in portfolio adjusting process. We propose a possibilistic mean-semi-absolute deviation portfolio model with V-shaped transaction costs, which are associated with a shift from the current portfolio to an adjusted one. In the proposed model, we take the possibilistic mean of the return as the investment return and possibilistic semi-absolute deviation of the return as the investment risk. To solve the proposed portfolio problem, a hybrid technique named as FA-SA algorithm combining firefly algorithm (FA) and simulated annealing algorithm (SA) is developed by taking the advantage of both FA and SA. In this algorithm, FA operates in the direction of enhancing the exploitation ability while SA improves the exploration using the lévy flight. Finally, a numerical example is given to demonstrate the effectiveness of the proposed model and the hybrid algorithm. [ABSTRACT FROM AUTHOR]

Possibility theory and possibilistic logic are well-known uncertainty frameworks particularly suited for representing and reasoning with uncertain, partial and qualitative information. Belief update plays a crucial role when updating beliefs and uncertain pieces of information in the light of new evidence. This paper deals with conditioning uncertain information in a qualitative interval-valued possibilistic setting. The first important contribution concerns a set of three natural postulates for conditioning interval-based possibility distributions. We show that any interval-based conditioning satisfying these three postulates is necessarily based on the set of compatible standard possibility distributions. The second contribution consists in a proposal of efficient procedures to compute the lower and upper endpoints of the conditional interval-based possibility distribution while the third important contribution provides a syntactic counterpart of conditioning interval-based possibility distributions in case where these latter are compactly encoded in the form of possibilistic knowledge bases. [ABSTRACT FROM AUTHOR]

The possibility theory, which is an extension of fuzzy sets and fuzzy logic, has shown considerable potential for solving active learning (AL) problems, particularly for multiclass scenarios' classification. Hence, two recently proposed fuzzy multiclass AL algorithms (classification ambiguity (CA) and fuzzy C‐order ambiguity (FCOA)) are investigated to properly generalise them for classifying hyperspectral images, and two improved versions of the CA and FCOA are proposed. In addition to comparing the performances of the original and improved algorithms, several other state‐of‐the‐art AL methods are evaluated, such as breaking ties, margin sampling, and multi‐class level uncertainty, with or without diversity criteria such as angle‐based diversity (ABD), clustering‐based diversity (CBD), and enhanced clustering‐based diversity (ECBD). Tests on two benchmark hyperspectral images confirm that the proposed improved algorithms are superior to and more effective than the original ones. [ABSTRACT FROM AUTHOR]

Conventional distribution network departs to the smart grid. The parking lot will have an important role in the smart grid as a distributed generation. Due to the output power of parking lots is uncertain, More accurate modeling of parking lot output power is necessary for the future of distribution network studies such as Distribution Network Expansion Planning (DNEP). In this paper, a systematic method based on the Z ‐number concept is utilized to represent the uncertainty of Vehicle to Grid's (V2G's) presence. In order to investigate the impact of V2Gs uncertainty on the DNEP, we proposed a Probabilistic–Possibilistic DNEP in the presence of V2Gs referred to as P‐PDNEPV2G. If the V2Gs historical data is incomplete, the proposed structure can significantly consider the effects of V2G on the DNEP. In P‐PDNEPV2G, parking lots output power is described as a probabilistic–possibilistic variable by Z ‐number method. The optimization of P‐PDNEPV2G is executed by the Non‐Dominated Sorting Genetic Algorithm (NSGA‐II). A 24‐bus test system and the real 20 kV distribution network of Ghale‐Ganj city of Kerman province in Iran are used to demonstrate the effectiveness of the proposed methodology. Eventually, several analyses are conducted to investigate the impact of probabilistic–possibilistic V2G model on the DNEP problem. [ABSTRACT FROM AUTHOR]

This paper introduces a method of data clustering that is based on linguistically specified rules, similar to those applied by a human visually fulfilling a task. The method endeavors to follow these remarkable capabilities of intelligent beings. Even for most complicated data patterns a human is capable of accomplishing the clustering process using relatively simple rules. His/her way of clustering is a sequential search for new structures in the data and new prototypes with the use of the following linguistic rule: search for prototypes in regions of extremely high data densities and immensely far from the previously found ones. Then, after this search has been completed, the respective data have to be assigned to any of the clusters whose nuclei (prototypes) have been found. A human again uses a simple linguistic rule: data from regions with similar densities, which are located exceedingly close to each other, should belong to the same cluster. The goal of this work is to prove experimentally that such simple linguistic rules can result in a clustering method that is competitive with the most effective methods known from the literature on the subject. A linguistic formulation of a validity index for determination of the number of clusters is also presented. Finally, an extensive experimental analysis of benchmark datasets is performed to demonstrate the validity of the clustering approach introduced. Its competitiveness with the state-of-the-art solutions is also shown. [ABSTRACT FROM AUTHOR]

In this paper, we present a new approach based on possibility theory to deal with the power flow problems in electrical networks. The approach takes into account the available information of a power system that is characterized generally by big data, often uncertain, redundant or insufficient for a correct description of the network status. In particular, we present a method to deal with nested information that can be generated by inaccurate measurements of electrical parameters. In order to solve the power flow problem we define a way to model nested information in power system and formalize an AC fuzzy power flow problem. The power flow results are obtained by an innovative approach based on the solution of a simultaneous nonlinear equations fuzzy system. The effectiveness of the proposed method is proven by applying the proposed approach to two modified IEEE benchmark test systems. Simulation results show accuracy, robustness and good computational cost of the implemented method in the search of the solution. [ABSTRACT FROM AUTHOR]

Using the central value operator and the semi-dispersion measure of fuzzy number, this paper proposes the definitions of the lower and upper semi-variances. A general multiperiod fuzzy portfolio optimization model with return demand on the portfolio at each period is proposed with the objectives of maximizing both terminal wealth and the cumulative diversification degree of portfolios over the whole investment horizon, and minimizing terminal risk. A fuzzy multiobjective nonlinear programming technique is applied to convert the proposed model into a single-objective model. A genetic algorithm (GA) is given to solve it. Besides, a numerical example is given to illustrate the application of the proposed model and the effectiveness of the designed algorithm. [ABSTRACT FROM AUTHOR]

When dealing with measurement uncertainty, a metrologist is required to take into consideration many different points. The most important ones are: the uncertainty contributions affecting the measurement process; the random or systematic nature of these contributions; the available metrological information about these contributions; and last, but not less important, the particular measurement process itself. This paper shows, with two simple examples, the importance of correctly considering all the aforementioned points in evaluating uncertainty. The guide to the expression of uncertainty in measurement (GUM) approach, a Monte Carlo approach, sometimes different from the one recommended by the GUM Supplement 1, and the random-fuzzy variable (RFV) approach are compared, proving that the RFV approach leads to the simplest and most straightforward way to consider all these points. [ABSTRACT FROM AUTHOR]

While a vast amount of literature shows that psychological factors are major pricing determinants, portfolio optimization models ignore the emotional aspects of financial markets. Accordingly, this paper presents a two-stage portfolio rebalancing method to integrate mean-variance theory with market psychology. At the first stage, the psychological state of market participants is translated into a set of criteria to evaluate stocks, and then, in a fuzzy environment, the process of ratiocination used by technical analysts is simulated to assess the status of these criteria and determine under- and overvaluation possibilities of stocks. At the second stage, a fuzzy programming approach utilizes the calculated possibilities to revise an existing portfolio considering investor profile, transaction costs, and risk-free rate of return. An empirical study using the obtained data from Tehran Stock Exchange is employed to validate the designed method and compare it against several other investment strategies, including Buy-and-Hold strategy and a conventional portfolio rebalancing model. The results show that the proposed fuzzy method responds appropriately to the psychological component of the market. In addition, for all investor profiles, the recommended strategy completely outperforms the market and the remaining strategies. [ABSTRACT FROM AUTHOR]

Microgrids represent a smart solution to increase power system reliability through the development of self-supplied islands that integrate distributed power generation and other smart technologies. In this paper, we formulate and solve an optimal generation rescheduling and load shedding problem in microgrids to determine a stable equilibrium state following outages. To address this problem, focused on MV distribution systems, we use a new methodology based on the use of fuzzy numbers is proposed. The approach allows representing the sources of uncertainty in the data or approximations made during the computation and considering many possible scenarios in case of outages. In order to demonstrate the performance and the effectiveness of the proposed method, several simulations have been carried out on a 69-bus radial distribution system, and results have been compared with those obtained by using a stochastic optimization approach. The encouraging results are presented and discussed. [ABSTRACT FROM PUBLISHER]