A Confidence Set Analysis for Observed Samples: A Fuzzy Set Approach

Association analysis of amino acids in molecular sequences can reveal crucial information and knowledge for understanding structure, function and interaction of proteins. The traditional methods of association rule mining like apriori, F-P Growth etc. fail to generate appropriate patterns due to inherent uncertainty present in data. The uncertainty in sequence data caused by variation in the length of sequences and lack of parameterization lead to under prediction and over prediction of the results. In this paper an attempt has been made to develop a soft set based approach for mining fuzzy association patterns in peptide sequences of dengue virus. The fuzzy set approach is employed to incorporate the degree of relationships among amino acids due to variation in length of the sequences. The soft set approach is employed to incorporate the relationship of parameters with amino acid association patterns. The 12,581 sequences of dengue virus are downloaded from NCBI and screened for redundancy to obtain non redundant 6995 sequences. The amino acid associations are explored and analyzed using soft fuzzy approach. Also the results obtained by soft fuzzy approach are compared with the results obtained individually by ordinary, fuzzy and soft set approaches. The soft fuzzy approach is able to overcome the issue of under prediction and over prediction of the results obtained by other approaches. Also the interesting association rules have been generated to predict the structure and physico chemical properties of the peptide sequences.

Data reconciliation consists in modifying noisy or unreliable data in order to make them consistent with a mathematical model (herein a material flow network). The conventional approach relies on least-squares minimization. Here, we use a fuzzy set-based approach, replacing Gaussian likelihood functions by fuzzy intervals, and a leximin criterion. We show that the setting of fuzzy sets provides a generalized approach to the choice of estimated values, that is more flexible and less dependent on oftentimes debatable probabilistic justifications. It potentially encompasses interval-based formulations and the least squares method, by choosing appropriate membership functions and aggregation operations. This paper also lays bare the fact that data reconciliation under the fuzzy set approach is viewed as an information fusion problem, as opposed to the statistical tradition which solves an estimation problem.

In Calcutta metro, railways, roads and waterways are available to provide mass transport services. An attempt has been made to use non-conventional abstract mathematical theory to solve the multimodal mass transport system. Fuzzy functions have been used as an analytical tool, to express the satisfaction level of attributes as viewed by different interest groups. The central concept of fuzzy set theory is the membership function which represents numerically the degree to which an element belongs to a set. This function takes values from zero to one. For synthesizing information, rating matrices have been constructed with different alternative modes as columns against various attributes/factors as rows. Each rating matrix represents the evaluation made by a respective interest group. Having identified the corridor and selective modal characteristics, the preferred mode may be chosen by this method. Additionally, when the need for introducing some new mode or increasing the services of some old mode are felt, this procedure may be used as a simplified tool.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Uncertainty modelling in measurement represents a crucial task since the final result of a measurement process cannot be expressed by a single value, but by a distribution of values over an interval within which the measurements lie with a given confidence level. A classical Type-1 fuzzy set could be the natural choice for uncertainty model, since a Membership Function (MF) intrinsically embeds the concepts of confidence interval and confidence level. Moreover, from computational aspects, working on fuzzy sets is much more easily than a Montecarlo simulation, that is actually the recommended approach. However, both the approaches need reliable and specific assumptions on the probability distribution of the input variables. So, in many practical cases, a Type-2 fuzzy set is needed in order to overcome this problem. In this paper, we will provide a full description of how a Type-2 MF can be built in order to model the uncertainty of a variable and how to evaluate uncertainty propagation through a generic function. A practical example of this representation will be also provided and compared with a Montecarlo simulation.

Tolerance-based intuitionistic fuzzy-rough set approach for attribute reduction

The text explains that the fuzzy approaches have the objective to bring the decision process in planning closer to the decision maker, by allowing him to understand better the diversity of aspects that must be considered in planning decisions and helping the decision process while keeping as much information as possible, represented in the definition of fuzzy sets. The paper shows that the qualitative aspects of uncertainty, risk and decision making may be adequately modeled with a fuzzy set approach. It could help the decision maker guiding him towards a decision that takes in account uncertainty in the future, the multiple criteria evaluation of plans, as well as hedging policies.

Automatically determine the membership function based on the maximum entropy principle

Human coronaviruses (HCoVs) are associated with a range of respiratory complications. In the last two decades, three major outbreaks have been reported due to HCoVs including the current pandemic. In December 2019, a newly emerged virus, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was first reported in Wuhan city, China. This paper presents a detailed review of the literature and discusses the uncertain spread of coronavirus disease 2019 (COVID-19) using fuzzy set as classical set theory logic to measure uncertainty and vagueness of COVID-19 in China. Our findings show that both infection and death rate touched the peak (normal fuzzy sets) and have shown a decline. The graphs are not convex, which shows that there remains much uncertainty in the spread of COVID-19. Effective vaccines are clearly needed to control and prevent the COVID-19 pandemic.

Flax fibre is an environmentally friendly, pure vegetable material with high durability. During the long flax fibres production, the short fibres, which have limited using, are formed. One of the ways of short flax fibre using is the cellulose with various purposes production because the short fibre is a valuable raw material. The problem of vegetable raw materials rational using is relevant. The previous results showed the possibility of obtaining cellulose from flax materials. Flax raw materials, in comparison with wood, has a higher content of cellulose and lower content of lignin and in its properties is approaching to the cotton. The soda boiling of flax cellulose from short flax fibre with preliminary aqueous hydrolysis is carried out in the research. The alkali consumption for boiling is 20% of the mass of dry raw materials with anthraquinonoid catalyst. An attempt to solve such a problem was carried out with the participation of the authors. The quality of the boiling process was controlled by the indexes: cellulose output ( Y 1 , %), lignin content ( Y 2 , %), α-cellulose content ( Y 3 , %), celluloses viscosity ( Y 4 , mPas/s). The second order regression models that describe the dependence of the process quality indexes was built. The aim of the research is solution the multi-criteria optimization problem of the flax celluloses soda boiling with the previous aqueous hydrolysis process. Optimality criteria are given in the linguistic expressions form: cellulose output – “as high as possible”; α-cellulose content – “above 90%”; the content of lignin – “less than 2.5%”; the viscosity – “about 20 mPas/s”. Therefore, for optimization problem solution the linguistically defined optimality criteria must be formalized. For the formalization of the optimality criteria, we use the methods of the fuzzy set theory. The optimality criteria are considered as fuzzy sets and the membership functions are built for these sets. We suggest using S -shaped membership functions for the indexes Y 1 and Y 2 , Z -shaped functions for index Y 3 and U-shaped function for index Y 4 . In order to facilitate the optimization problem solution, we consider expedient to use sigmoidal type of membership functions for indexes form Y 1 to Y 3 , and bell-shared type for index Y 4 . The upper and lower limits of the membership functions’ universe are the worst values of quality indexes obtained in the experiment and the best theoretically possible values of these indexes. Because the both sigmoidal and bell-shared membership functions generate not strictly normal, but subnormal fuzzy sets, we suggest the maximum deviation of 0.01. Based on the above considerations, we established the numerical values for the membership functions’ parameters. The Bellman-Zade optimality principle is used to find the optimal solution. According to this principle, the solution is considered the optimal one, for which the lowest of the membership functions has the maximum value. The optimum values of technological parameters for obtaining linseed cellulose are established, namely: the duration of aqueous pre-hydrolysis is 2 hours 12 minutes, the temperature of preliminary hydrolysis is 154 O C, the duration of sodium hydroxide is 3 hours, and the boiling temperature is 166 O C with the hydro-module is 6:1. As can be seen from the results, the content of lignin and the content of α-cellulose limit for the found optimum value. Our optimal results are in good agreement with solutions obtained by other methods. Thus, the proposed approach allows obtaining the high quality cellulose. Linseed cellulose can be used after bleaching for the cellulose nitrates or carboxymethyl-cellulose production.

• Propose novel behavioral membership functions within the fuzzy goal programming approach. • Model decision-makers’ behavioral aspects and risk perceptions. • Develop a behavior-based fuzzy goal programming approach. • Enhance utility functions within the fuzzy goal programming methodology. • Demonstrate applicability and efficacy through a venture capital investment problem. A relevant extension of traditional goal programming (GP), fuzzy goal programming (FGP) can handle uncertainty and imprecision in multi-objective optimization problems. Based on fuzzy set theory, the notion of membership functions has been introduced to consider the fuzziness related to objectives and constraints. These membership functions are mainly intended for fuzziness in the GP rather than modeling the decision-maker's (DM's) preferences and his/her attitude toward risk in the decision-making process. In the satisfying philosophy of FGP, little attention has been given to how preferences evolve in terms of the behavior of the decision-maker (DM) and how these preferences may affect decisions in risky scenarios. To address this issue, we suggest novel behavioral-type utility functions for the FGP approach by introducing the concept of behavioral membership functions. This concept offers an innovative procedure for simulating the DM's behavioral preferences in the FGP approach. First, two main categories of objectives in relation to the DM's behavioral preferences are distinguished in this work. A risk aversion parameter is integrated into membership functions according to the nature of each objective type, obtaining the so-called behavioral membership functions. A behavioral FGP approach is subsequently formulated. Finally, an illustrative example of venture capital investments, a sensitivity analysis, and comparisons with other FGP approaches are provided to demonstrate the validity and practicality of our proposed approach.

In this paper, the production process is decomposed for typical manufacturing small and medium sized enterprises (SMEs) and the metrics of the defined sub processes, based on the requirements of ISO 9001:2008, are developed. The weight values of production process performance indicators are defined, using the experience of decision makers from the analysed manufacturing SMEs, and calculated using the fuzzy set approach. Finally, the developed solution, based on the genetic algorithm approach, is presented and tested on data from 112 Serbian manufacturing SMEs. The presented solution enables quality assessment of a production process, the ranking of indicators, optimisation and provides the basis for successful improvement of the production process quality.

The success of any enterprise, in a market‐oriented economy, depends upon it's quality. This paper describes the results of a survey of commuters on the quality of services and their relative weights, and of the attributes that determine the service level of bus transport undertakings. The model uses the theory of fuzzy sets to process the information obtained. A composite index, called level‐of‐public transport‐service (LOPTS), is defined and used to measure the service qualities. This approach is presented with guidelines for rating the quality of services, fuzzy‐set representations of the linguistic grades, definition of LOPTS and its use in a public transport quality data base. An example is presents how the approach can be employed to analyse data bases generated from a quality survey. This approach is compared with the numerical rating approach with single number representation.

An important part of predicting responses with computational models is the definition of systems parameters such as material properties. The reliability of model‐based predictions depends on the quality of these data, and the knowledge of their uncertainties. When experiments cannot be performed to determine parameter values, they must be obtained from the literature, namely handbooks, standards, specification sheets, etc. This paper addresses the use of literature‐based parameters and other information for assessing uncertainty in computational predictions. The uncertainties in the data and the solution (prediction) are described in the framework of fuzzy sets. A double‐pipe heat exchanger thermal analysis problem is used to illustrate the difficulties with computational predictions when only informations from the literature are available. It is shown that the resulting uncertainties are significant and cannot be neglected. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Application of fuzzy logic to land suitability for rubber production in peninsular Thailand

Lot output time prediction is a critical task to a wafer fab (fabrication plant). Traditional studies are focused on prediction accuracy and efficiency. Another performance measure that is as important but has been ignored in traditional studies is the achievability of an output time forecast, which is defined as the possibility that the fabrication on a wafer lot can be finished in time before the output time forecast. Theoretically, if a probability distribution can be obtained for the output time forecast, then the achievability can be evaluated with the cumulative probability of the probability distribution before the given date. However, there are many managerial actions that are more influential to the achievability. For this reason, a fuzzy set approach is proposed for evaluating the achievability of the output time forecast. The fuzzy set approach is composed of two parts: a fuzzy back propagation network (FBPN) and a set of fuzzy inference rules (FIRs). An example is used to demonstrate the applicability of the proposed methodology.