Logistic Membership Function Research Articles

New membership function for poverty measure

AbstractFuzziness in a fuzzy set is determined by its membership function (m.f) which translates the reality of a problem. Accordingly, the shapes of membership functions (m.fs) are important for a particular problem such as poverty since they effect on a fuzzy inference system. Some authors have used to visualize the behaviour of poverty, different shapes like triangular, trapezoidal. In this paper, a specific (m.f), named modified logistic membership function better illustrating the complicated reality, is proposed to measure poverty. The modified logistic membership function is first formulated for several states of poverty and its flexibility in taking up vagueness in poverty is established by an analytical approach using aggregate operators in order to infer a logical conclusion measuring poverty. An application based on individual well‐being data from Tunisian households in 2010 is presented to illustrate use of proposed concepts.

Short Note on Research Findings and Results: An Innovative Fuzzy Computing for Industrial Production Planning

In the first part of this work a logistic membership function, within the non linear membership functions, has been formulated for solving IFLP (Interactive Fuzzy Linear Programming) problem as applied to industrial production system. This membership function is a modified form of the general set of S-curve membership functions. The flexibility of this membership function in applying to real world problem has been proved through an analysis [2,3].

Predictive mapping for porphyry copper mineralization: a comparison of knowledge-driven and data-driven fuzzy models in Siahrud area, Azarbaijan province, NW Iran

In this paper, we describe fuzzy models for predictive porphyry Cu potential mapping: (1) a knowledge-driven fuzzy model that uses a logistic membership function for deriving fuzzy membership values of input evidential maps and (2) a data-driven model, which uses a piece-wise linear function based on quantified spatial associations between a set of evidential evidence features and a set of known mineral deposits for deriving fuzzy membership values of input evidential maps. The mineral favorability maps for porphyry Cu exploration were produced in a geographic information systems environment and took into account three sources of data and information: (1) satellite images; (2) a geochemical survey; (3) geo-structural mapping. These data and information were integrated through a conceptual model developed for porphyry Cu mines and occurrences in the studied region. Both favorability maps highlighted the known porphyry Cu occurrences and validated the approach, but the data-driven method shows better results than the knowledge-driven method.

Hybrid genetic algorithms and line search method for industrial production planning with non-linear fitness function

Many engineering, science, information technology and management optimization problems can be considered as non-linear programming real-world problems where all or some of the parameters and variables involved are uncertain in nature. These can only be quantified using intelligent computational techniques such as evolutionary computation and fuzzy logic. The main objective of this research paper is to solve non-linear fuzzy optimization problem where the technological coefficient in the constraints involved are fuzzy numbers, which was represented by logistic membership functions using the hybrid evolutionary optimization approach. To explore the applicability of the present study, a numerical example is considered to determine the production planning for the decision variables and profit of the company.

Fuzzy Optimization with Robust Logistic Membership Function: A Case Study In For Home Textile Industry

Many engineering optimization problems can be considered as linear programming problems where the all or sum of the parameters involved are linguistic in nature. These can only be quantified using fuzzy sets. The aim of this paper is to solve fuzzy linear programming problem where the parameters involved are fuzzy numbers with logistic membership functions. To explore the applicability of the present study a numerical example is considered determine monthly production planning and profit of home-textile group. To solve this problem LINGO Software is used.

A fully fuzzified, intelligent theory-of-constraints product-mix decision

The present research work outlines a fuzzified approach using fuzzy linear programming (FLP) using a suitably designed smooth logistic membership function (MF) for finding fuzziness patterns at disparate levels of satisfaction for theory of constraints-based (TOC) product-mix decision problems. The objective of the present work is to find fuzziness patterns of product-mix decisions with disparate levels of satisfaction of the decision-maker (DM). Another objective is to provide a robust, quantified monitor of the level of satisfaction among DMs and to calibrate these levels of satisfaction against DM expectations. Product-mix decision should take into account considerations such as the DM's level of satisfaction (sometimes called ‘emotions’) in order to make the decision a robust one. Sensitivity of the decision has been focused on a bottleneck-free, optimal product-mix solution of a TOC problem. The inefficiency of traditional linear programming (LP) in handling multiple-bottleneck problems using TOC is discussed using an illustrative example. Relationships among the degree of fuzziness, level of satisfaction and the throughput of modified TOC guide decision-makers (DM) under tripartite fuzzy environment in obtaining their product-mix choice trading-off with a pre-determined allowable fuzziness.

Sensing degree of fuzziness in MCDM model using modified flexible S -curve MF

It is hard to sense the degree of vagueness while using a Multiple Criteria Decision-Making (MCDM) model in industrial engineering problems. Selection of best candidate-alternative is an important issue when the attributes of the candidate-alternatives are conflicting in nature and they have incommensurable units. An MCDM model makes it possible to select the candidate-alternative that suits best for the investor. An example illustrating an MCDM model applied in plant-site selection problem has been considered in this article to demonstrate the veracity of the proposed methodology. The degree of vagueness hidden in the proposed approach has been investigated using a flexible modified logistic membership function (MF). The approach presented here provides feedback to the decision maker, implementer and analyst and gives a clear indication about the appropriate application and usefulness of the MCDM model. The key objective of this article is to guide decision makers in finding out the best candidate-alternative with higher degree of satisfaction and lesser degree of vagueness.

Detection of level of satisfaction and fuzziness patterns for MCDM model with modified flexible S-curve MF

The present research work deals with a logistic membership function (MF), within non-linear MFs, in finding out fuzziness patterns in disparate level of satisfaction for Multiple Criteria Decision-Making (MCDM) problem. This MF is a modified form of general set of S-curve MF. Flexibility of this MF in applying to real world problem has also been validated through a detailed analysis. An example illustrating an MCDM model applied in an industrial engineering problem has been considered to demonstrate the veracity of the proposed technique. The approach presented here provides feedback to the decision maker, implementer and analyst and gives a clear indication about the appropriate application and usefulness of the MCDM model. The key objective of this paper is to guide decision makers in finding out the best candidate-alternative with higher degree of satisfaction with lesser degree of vagueness under tripartite fuzzy environment.

Decision making in toc-product-mix selection via fuzzy cost function optimization

This paper presents an innovated fuzzy decision-making under Theory-of-Constraints for the product-mix problem using a smooth logistic membership function for finding out fuzziness patterns in disparate level of satisfaction. Agility of this membership function when applied to real-world product-mix problems has been validated. This contribution is believed to provide a robust, quantified monitoring of the level of satisfaction among decision-makers and to calibrate these levels of satisfaction against decision-makers’ expectations, thus providing a computational intelligence procedure. Inefficiency of traditional linear programming in handling multiple-bottleneck problem through the traditional Theory-of-Constraints concept is discussed via an illustrative example.

A Hybrid Fuzzy Weights-of-Evidence Model for Mineral Potential Mapping

This paper describes a hybrid fuzzy weights-of-evidence (WofE) model for mineral potential mapping that generates fuzzy predictor patterns based on (a) knowledge-based fuzzy membership values and (b) data-based conditional probabilities. The fuzzy membership values are calculated using a knowledge-driven logistic membership function, which provides a framework for treating systemic uncertainty and also facilitates the use of multiclass predictor maps in the modeling procedure. The fuzzy predictor patterns are combined using Bayes’ rule in a log-linear form (under an assumption of conditional independence) to update the prior probability of target deposit-type occurrence in every unique combination of predictor patterns. The hybrid fuzzy WofE model is applied to a regional-scale mapping of base-metal deposit potential in the south-central part of the Aravalli metallogenic province (western India). The output map of fuzzy posterior probabilities of base-metal deposit occurrence is classified subsequently to delineate zones with high-favorability, moderate favorability, and low-favorability for occurrence of base-metal deposits. An analysis of the favorability map indicates (a) significant improvement of probability of base-metal deposit occurrence in the high-favorability and moderate-favorability zones and (b) significant deterioration of probability of base-metal deposit occurrence in the low-favorability zones. The results demonstrate usefulness of the hybrid fuzzy WofE model in representation and in integration of evidential features to map relative potential for mineral deposit occurrence.

Fuzzy linear programming with vague objective coefficients in an uncertain environment

In this paper, a new fuzzy linear programming (FLP)-based methodology using a specific membership function named modified logistic membership function is proposed. The modified logistic membership function is first formulated and its flexibility established by an analytical approach. This membership function is tested for its useful performance through an illustrative example by employing FLP. The developed methodology of FLP has provided confidence in applying to real-life industrial production planning problem. This approach of solving industrial production planning problem can provide feedback to the decision maker, implementer and analyst. In such cases, this approach can be called interactive FLP. There is a possibility to design the self-organizing of the fuzzy system for the product mix selection problem in order to find a satisfactory solution. The decision maker, analyst and implementer can incorporate their knowledge and experience to obtain the best outcome.

Application of Fuzzy Linear Programming in Production Planning

In this paper, a new fuzzy linear programming based methodology using a specific membership function, named as modified logistic membership function is proposed. The modified logistic membership function is first formulated and its flexibility in taking up vagueness in parameters is established by an analytical approach. This membership function is tested for its useful performance through an illustrative example by employing fuzzy linear programming. The developed methodology of FLP has provided a confidence in applying to real life industrial production planning problem. This approach of solving industrial production planning problem can have feed back within the decision maker, the implementer and the analyst. In such case this approach can be called as IFLP (Interactive Fuzzy Linear Programming). There is a possibility to design the self organizing of fuzzy system for the mix products selection problem in order to find the satisfactory solution. The decision maker, the analyst and the implementer can incorporate their knowledge and experience to obtain the best outcome.

Knowledge-Driven and Data-Driven Fuzzy Models for Predictive Mineral Potential Mapping

In this paper, we describe new fuzzy models for predictive mineral potential mapping: (1) a knowledge-driven fuzzy model that uses a logistic membership function for deriving fuzzy membership values of input evidential maps and (2) a data-driven model, which uses a piecewise linear function based on quantified spatial associations between a set of evidential evidence features and a set of known mineral deposits for deriving fuzzy membership values of input evidential maps. We also describe a graphical defuzzification procedure for the interpretation of output fuzzy favorability maps. The models are demonstrated for mapping base metal deposit potential in an area in the south-central part of the Aravalli metallogenic province in the state of Rajasthan, western India. The data-driven and knowledge-driven models described in this paper predict potentially mineralized zones, which occupy less than 10% of the study area and contain at least 83% of the “model” and “validation” base metal deposits. A cross-validation of the favorability map derived from using one of the models with the favorability map derived from using the other model indicates a remarkable similarity in their results. Both models therefore are useful for predicting favorable zones to guide further exploration work.

Fuzzzy Portfolio Selection

This paper deals with portfolio selection in terms of fuzzy concept. The objective of this fuzzy portfolio selection is to decide the portfolio selection based on vague aspiration level which decision makers have. The vague aspiration level is expressed by a fuzzy number and maximized by Bellman-Zadeh's maximization principle.In the model logistic membership functions are employed to overcome the several theoretical defects which trapezoidal membership functions result in.

Bi-objective analysis of waste load allocation using fuzzy linear programming

Because of its complexity from both a legal and economic standpoint, the problem of optimal waste load allocation is multiobjective by nature and should be treated accordingly. To perform this task, an optimization technique known as fuzzy linear programming is utilized in solving a multiple-discharge, two-objective waste load allocation problem. The two objectives considered are: (1) the maximization of waste discharge and (2) the minimization of the largest difference in equity measure between the various dischargers. Results from this study reveal that fuzzy linear programming is a valuable tool for solving the multiple-objective water quality management problems. Moreover, it is shown that the selection of a linear or logistic membership function in providing preference criteria between the two objects, has no effect on the ‘best compromising solution’.