Fuzzy Set

Material handling equipment selection problem (MHESP) is an important decision making area for the companies, since it has a direct effect on manufacturing and service productivity. In this study, an integrated fuzzy multi-criteria decision making methodology for MHESP is proposed. The proposed approach is utilized from fuzzy sets, Analytic Network Process (ANP) and Preference Ranking Organization METHod for Enrichment Evaluations (PROMETHEE) approaches. Evaluation criteria for the MHESP is weighted by fuzzy-ANP (F-ANP) approach, then, alternative material handling equipments are evaluated by fuzzy-PROMETHEE (F-PROMETHEE) approach. The methodology is applied for a manufacturing company to prove its effectiveness. Finally, some sensitivity analyses are conducted to show the results’ sensitiveness to the changes of the weights of the evaluation criteria.

This paper provides the reader with a presentation of preference modelling fundamental notions as well as some recent results in this field. Preference modelling is an inevitable step in a variety of fields: economy, sociology, psychology, mathematical programming, even medicine, archaeology, and obviously decision analysis. Our notation and some basic definitions, such as those of binary relation, properties and

This paper presents a review of the current liter- ature on rough set and near set-based approaches to solving various problems in medical imaging such as medical image segmentation, object extraction and image classification. Rough set frameworks hybridized with other computational intelligence technologies that include neural networks, particle swarm op- timization, support vector machines and fuzzy sets are also presented.

Data, as being the vital input of system modelling, contain dissimilar level of imprecision that necessitates different modelling approaches for proper analysis of the systems. Numbers, words and perceptions are the forms of data that has varying levels of imprecision. Existing approaches in the literature indicate that, computation of different data forms are closely linked with the level of imprecision, which the data already have. Traditional mathematical modelling techniques have been used to compute the numbers that have the least imprecision. Type-1 fuzzy sets have been used for words and type-2 fuzzy sets have been employed for perceptions where the level of imprecision is relatively high. However, in many cases it has not been easy to decide whether a solution requires a traditional approach, i.e., type-1 fuzzy approach or type-2 fuzzy approach. It has been a difficult matter to decide what types of problems really require modelling and solution either with type-1 or type-2 fuzzy approach. It is certain that, without properly distinguishing differences between the two approaches, application of type-1 and type-2 fuzzy sets and systems would probably fail to develop robust and reliable solutions for the problems of industry. In this respect, a review of the industrial applications of type-2 fuzzy sets, which are relatively novel to model imprecision has been considered in this work. The fundamental focus of the work has been based on the basic reasons of the need for type-2 fuzzy sets for the existing studies. With this purpose in mind, type-2 fuzzy sets articles have been selected from the literature using the online databases of ISI-Web of Science, ScienceDirect, SpringerLink, Informaworld, Engineering Village, Emerald and IEEE Xplore. Both the terms “type-2 fuzzy” and “application” have been searched as the main keywords in the topics of the studies to retrieve the relevant works. The analysis on the industrial applications of type-2 fuzzy sets/systems (FSs) in different topics allowed us to summarize the existing research areas and therefore it is expected be useful to prioritize future research topics. This review shows that there are still many opportunities for application of type-2 FSs for several different problem domains. Shortcomings of type-1 FSs can also be considered as an opportunity for the application of type-2 FSs in order to provide a better solution approach for industrial problems.

The aim of the work was to map and analyse benthic habitats in the Polish zone of the Baltic Sea using the Geographical Information Systems (GIS). The habitats definitions were analogous to those proposed in the HELCOM classification, which is based on two concepts—the euphotic zone has no clearly defined boundaries and the bottom sediments are defined on the basis of their fractions. The mapping was done using the theory of fuzzy sets.The fuzzy set map for each HELCOM category was created as a result of an intersection operation on two fuzzy set maps—the first showed bottom position relative to euphotic depth, and the second described the presence of a given sediment type on the bottom. The maps obtained were used to create a thematic map of habitats, which was generated at a pre-set significance level from the statistical analysis of a set of random realizations of habitat maps generated by stochastic simulation. The GIS-based analyses of the thematic map allowed a map of habitat groups to be developed and also allowed to find whether and to what extent the definitions proposed by HELCOM were applicable to the mapping of benthic habitats in the study area.

Specific applications of fuzzy logic in project management are relatively few in comparison to other application areas. The criteria of project cost, project time, and project quality may be considered as project management internal measures of efficiency. The objective of this research is to present an approach that employs fuzzy decision making (FDM) to combine these three measures into one measure namely the project management internal efficiency (PMIE) which should represent an overall estimate of how well the project was managed and executed. The proposed approach for the evaluation of PMIE is illustrated on a case study. A fuzzy decision making system is designed and implemented using the MATLAB software for the evaluation of the PMIE. The methodology and procedure proposed in this research may be easily implemented by project management organizations. The evaluation of PMIE can serve for project managers and for project organizations as an indicator for the level of achievement of the project management internal objectives. PMIE may help in the evaluation of the performance of project teams.

There are several algorithms, in literature, for obtaining the fuzzy optimal solution of fuzzy transportation problems (FTPs). To the best of the author's knowledge, in the history of mathematics, no one has been able to solve transportation problem (TP) under four different uncertain environment using single method in the past years. So, in this chapter, the author tried to categories the TP under four different environments and formulates the problem and utilizes the crisp numbers, triangular fuzzy numbers (TFNs), and trapezoidal fuzzy numbers (TrFNs) to solve the TP. A new method, namely, PSK (P. Senthil Kumar) method for finding a fuzzy optimal solution to fuzzy transportation problem (FTP) is proposed. Practical usefulness of the PSK method over other existing methods is demonstrated with four different numerical examples. To illustrate the PSK method different types of FTP is solved by using the PSK method and the obtained results are discussed.

The modeling, numerical simulation and control of a HVAC (heating, ventilating and air-conditioning) system having two different zones with variable flow-rate were performed by considering the ambient temperature in this study. The sub-models of the system were obtained by deriving to heat transfer equations of heat loss of two zones by conduction and convection, cooling unit and fan. All models

: The application of Artificial Intelligence (AI) methods in power system protection has been addressed in this paper. Particular emphasis has been put on Artificial Neural Networks (ANN) and Fuzzy Logic (FL). Several novel concepts have been introduced including ANN application to CT and CVT transients correction, fuzzy criteria signals, fuzzy settings and multi-criteria decision making for digital relays. Attached examples illustrate application of ANN and FL techniques to resolve the selected relaying problems such as the fault classification or CT and CVT dynamic error correction. Differential protection for power transformers is selected as an important example to show efficiency of the proposed concepts of FL and ANN application. I. INTRODUCTION The microprocessor technology brings unquestionable improvements of the protection relays- criteria signals are estimated in a shorter time; input signals are filtered-out more precisely; it is easy to apply sophisticated corrections; ...

Rapid urbanization and the growing demand for faster transportation has led to heavy congestion in road traffic networks, necessitating the need for traffic-responsive intelligent signal control systems. The developed signal control system must be capable of determining the green time that minimizes the network-wide travel time delay based on limited information of the environment. This paper adopts a distributed multiagent-based approach to develop a traffic-responsive signal control system, i.e., the geometric fuzzy multiagent system (GFMAS), which is based on a geometric type-2 fuzzy inference system. GFMAS is capable of handling the various levels of uncertainty found in the inputs and rule base of the traffic signal controller. Simulation models of the agents designed in PARAMICS were tested on virtual road network replicating a section of the central business district in Singapore. A comprehensive analysis and comparison was performed against the existing traffic-control algorithms green link determining (GLIDE) and hierarchical multiagent system (HMS). The proposed GFMAS signal control outperformed both the benchmarks when tested for typical traffic-flow scenarios. Further tests show the superior performance of the proposed GFMAS in handling unplanned and planned incidents and obstructions. The promising results demonstrate the efficiency of the proposed multiagent architecture and scope for future development.

With the increasing popularity of using Web services, Quality of Service (QoS) is becoming a significant concern for both service consumers and providers. Several models for considering functional and non-functional QoS requirements for the purpose of Web service discovery and selection have been proposed. We present in this paper a new Web services selection model based on fuzzy logic. In

In this paper we investigate various properties of equivalence classes of fuzzy equivalence relations over a complete residuated lattice. We give certain characterizations of fuzzy semi-partitions and fuzzy partitions over a complete residuated lattice, as well as over a linearly ordered complete Heyting algebra. In the latter case, for a fuzzy equivalence relation over a linearly ordered complete Heyting algebra, we construct an algorithm for calculation of a minimal family of its equivalence classes which generates it. Most of the presented results are new, but some of them are generalizations of known results given in a way which simplifies and clarifies them.

In this article, the crisp, fuzzy and intuitionistic fuzzy optimization problem is formulated. The basic definitions and notations related to optimization problems are given in the preliminaries section. Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set is presented in this article. Then, with the help of the proposed algorithm the optimal solution of the crisp, fuzzy and intuitionistic fuzzy optimization problems are determined. A new theorem related to type-2 fuzzy/type-2 intuitionistic fuzzy optimization problems is proposed and proved. Some new and concrete results related to type-2 fuzzy/type-2 intuitionistic fuzzy optimization problems are presented. To illustrate the proposed method, some real-life numerical examples are presented. The proposed article provides seven fully worked examples with screenshots of output summaries from the software used in the computations for better understanding. The advantages of the proposed approach as compared to other existing work are also specified. Detail analyses of the comparative study as well the discussion are given. To show the advantages of the proposed approach, superiority analysis is discussed. Comparison analysis and the advantages of the proposed operators are also discussed. Some managerial applications and the advantages of the proposed approach are given. Finally, conclusion and future research directions are also given.