Min-max Operations Research Articles

Efficient fuzzy multi-criteria decision-making for optimal college location selection: A comparative study of min–max fuzzy TOPSIS approach

Ranking fuzzy values is often essential in fuzzy multi-criteria decision-making (FMCDM) systems since it is established on the comparison of hazy data pairs, even though the comparison needs temporal complexity. Then to provide a fuzzy MCDM approach under min–max operations for avoiding the fuzzy comparison. By using fuzzy TOPSIS’s min and max operations, the suggested method produces two positive and negative ideal solutions of each alternative. Here, before discussing the effectiveness of the matrices between the alternatives, first to analyze the weighted strength and weakness indices from both positive and negative indices. The results of the method have been described using a straightforward case study of a proper location for creating a college. The best location can be identified using this method based on various criteria. The outcomes are also compared with the suggested method for its effectiveness. Additionally, this problem analyzes the fuzzy TOPSIS approach in an interval-valued number for greater efficiency.

Generalized Distribution Feeder Switching with Fuzzy Indexing for Energy Saving

The objective of this study is to analyze feeder loss minimization and load balance under given constrains. Effective methods are required for feeder switching/reconfiguration. Feeder switching is a mixed-integer large-scale combinatorial problem for optimization, not easily solvable with classical optimization techniques, especially involving a great number of switches. This paper proposes a fuzzy indexing algorithm for feeder switching, with membership functions defined for switches such as thermometers or indices. The optimal switches can be determined through fuzzy index operations. With membership functions defined, the developed method used numerical operations for indices instead of the “set” operation or the min-max operations of traditional fuzzy algorithms. The optimization problem becomes a simple numeric calculation instead of a large-scale sorting problem and is much faster than most algorithms. It greatly reduces the computation time and enhances efficiency, which is suitable for either planning or operation purposes. Many algorithms were tested with three typical examples chosen for illustration, including the “optimal” results with an exhausted search. It shows that the proposed algorithm is very effective and can balance the load to reduce the loss and costs in obtaining the solution.

A New Similarity Measure of Fuzzy Signatures with a Case Study Based on the Statistical Evaluation of Questionnaires Comparing the Influential Factors of Hungarian and Lithuanian Employee Engagement

Similarity between two fuzzy values, sets, etc., may be defined in various ways. The authors here attempt introducing a general similarity measure based on the direct extension of the Boolean minimal form of equivalence operation. It is further extended to hierarchically structured multicomponent fuzzy signatures. Two versions of this measure, one based on the classic min–max operations and one based on the strictly monotonic algebraic norms, are proposed for practical application. A real example from management science is chosen, namely the comparison of employee attitudes in two different populations. This example has application possibilities in the evaluation and analysis of employee behaviour in companies as, due to the complex aspects in analysing multifaceted behavioural paradigms in organizational management, it is difficult for companies to make reliable decisions in creating processes for better social interactions between employees. In the paper, the authors go through the steps of building a model for exploring a set of different features, where a statistical pre-processing step enables the identification of the interdependency and thus the setup of the fuzzy signature structure suitable to describe the partially redundant answers given to a standard questionnaire and the comparison of them with help of the (pair of the) new similarity measures. As a side result in management science, by using an internationally applied standard questionnaire for exploring the factors of employee engagement and using a sample of data obtained from Hungarian and Lithuanian firms, it was found that responses in Hungary and Lithuania were partially different, and the employee attitude was thus in general different although in some questions an unambiguous similarity could be also discovered.

Total Prediction Decision Support System Bakery and Cake Production Using Mamdani Fuzzy Method

The decision support system for predicting the amount of bakery and cake production using the fuzzy mamdani method is one of the processes for determining the prediction of the amount of bakery and cake production for the next month so that the desired production amount is according to needs. Neko-Neko Bakery & Cake so far in predicting the amount of production where the demand for bakery and cake is sometimes not fulfilled considering that the available bakery and cake production is not sufficient because the bakery and cake supplies in the production section do not meet and vice versa, namely the amount of production sometimes experiences excess in production. production so that it is not in accordance with demand, then there is often an error in predicting the amount of production in producing bakery and cake because the number of bakery and cake productions produced is not really needed while bakery and cake which are often needed are not produced since so far the Neko-Neko Bakery and Cake in Prediction data collection on the number of bakery and cake productions only relies on the Microsoft Office Excel application system where the data that is processed or processed is sometimes double in value. The method used in the decision support system to predict the amount of bakery and cake production is fuzzy mamdani. Mamdani fuzzy method is one method that has a simple structure and easy to understand. Mamdani fuzzy logic uses MIN-MAX or max-product operations with a predetermined set of rules, namely the previous IF…AND…THEN. Based on the application of this mamdani fuzzy method in predicting the amount of bakery and cake production, it can be stated that it is very feasible to apply to Neko-Neko Bakery & Cake. This decision support system was built using the PHP programming language and MySQL database.

A Novel Adaptive Fuzzy Deep Learning Approach for Histopathologic Cancer Detection.

We proposed a novel model that integrates the fuzzy theory and group equivariant convolutional neural network for histopathologic cancer detection. The proposed fuzzy group equivariant convolutional neural network consists of the convolutional network, a novel fuzzy global pooling layer, and a fully connected network. In the fuzzy global pooling layer, the generated feature maps are transferred into the fuzzy domain by two different fuzzification methods. One of the fuzzy feature maps exploits the uncertainty information of histopathologic images, and the other keeps the original information. Furthermore, the fuzzy feature maps are processed by using Min-max operations. The experiments verified that the proposed method could always find the maximum fuzzy entropy and exploit and present the uncertainty of histopathologic images well. The experiments using the benchmark dataset demonstrate that the proposed model becomes more accurate and outperforms the existing models including the benchmark models. Compared to the benchmark model with 89.8% of accuracy, 96.3% of AUC, and 0.260 of negative log-likelihood loss, the proposed model obtained 91.7% of accuracy, 97.2% of AUC, and 0.214 of negative log-likelihood loss.

Computational insights on intensification of hydrodenitrogenation in a trickle bed reactor using periodic flow modulation

Trickle bed reactors (TBRs) are widely used in petroleum industries, which are subjected to stringent environmental laws. Hydrodenitrogenation (HDN), a crucial process for nitrogen removal employed in crude oil processing, is typically carried out in steady state TBRs. Acquainted with this operation, researchers are focused on exploring the efficacy of flow modulation in TBRs for improved reaction conversion. A CFD model of a hydrotreating reactor is used in this work to examine potential benefits of periodic operation for a HDN reaction. Results of continuous flow were compared with time averaged conversions for slow and fast modes of on-off and min–max operations having different split ratios. All flow modulated cases proved to be beneficial than steady state operation with respect to enhanced time averaged conversion. However, this enhancement deteriorated with increase in cycle time for slow mode of operation. Additionally, this was associated with substantial undulations in overall pressure drop, which is detrimental to process safety. Nonetheless, fast mode of on–off and min–max operations at low split ratio resulted in maximum improvement of about 47% and 35%, respectively, which revealed the efficacy of fast mode flow modulation in achieving maximum conversion with lower pressure drop undulations.

Novel techniques for memristive multifunction logic design

We present novel techniques for realising reliable low overhead logic functions and more complex systems based on the switching characteristics of memristors. Firstly, we show that memristive circuits have inherent properties for realising multiple valued MIN-MAX operations over the post algebra. We then present an efficient hybrid 1T-4M logic architecture for dual XOR/AND and XNOR/OR functionality, which can be seamlessly integrated with the existing CMOS technology. Although memristors are usually considered to operate at lower frequencies, however, recent advances in technology show their potentiality at high frequencies. To this end, we also explore the effects of high frequencies on their performance and thereby propose reliable high frequency design techniques based on our 1T-4M architectures. Experimental results, based on the design of full adders and multipliers over GF, show that the proposed designs require significantly lower power and overhead while maintaining reliable performance at low as well as at high frequencies compared to the existing techniques.

Vector retrieval, fuzzy retrieval and the universal fuzzy IR surface for IR evaluation

It is shown that vector information retrieval (IR) and general fuzzy IR uses two types of fuzzy set operations: the original “Zadeh min–max operations” and the so-called “probabilistic sum and algebraic product operations”. The universal IR surface, valid for classical 0–1 IR (i.e. where ordinary sets are used) and used in IR evaluation, is extended to and reproved for vector IR, using the probabilistic sum and algebraic product model. We also show (by counterexample) that, using the “Zadeh min–max” fuzzy model, yields a breakdown of this IR surface.

Min-max goal programming: an application to Mahanadi Reservoir Project Complex

An application of the min-max goal programming methodology to a system of multipurpose reservoirs for optimal monthly operation has been presented in this paper. The goal programming approach possesses significant advantages because of the fact that it may be based on physical operating criteria. The system goals and constraints are expressed deterministically. A constraint must be strictly satisfied, while for a goal it is desired to achieve the solution, which is as close as possible to the specified target. The min-max goal programming model is developed and applied to the Mahanadi Reservoir Project (MRP) Complex comprising of six multipurpose reservoirs in the state of Madhya Pradesh, India. The MRP Complex operations resulting from the use of the min-max goal programming model are compared to the operations resulting from three other reported optimization models with the same data set for the same operation period. The set of operations resulting from various models are comparable in their effectiveness, and in most aspects the min-max goal programming model operations are better.Key words: optimization, reservoir operation, goal programming, min-max goal programming.

An efficient computational algorithm for min-max operations

This paper describes an efficient computational algorithm for evaluating min-max operations and the derivatives of min-max functions, which are common computation problems in the training of many types of fuzzy neural networks. Analysis and simulation are used to assess the efficiency of the computational algorithm developed in this paper.

A saddle-point theorem with application to structural optimization

The relaxation for optimal complicance design is independent of whether the underlying elastic problem is formulated in terms of displacements or strains. For the purposes of numerical experimentation and computation, it may be advantageous to formulate optimal design problems in terms of displacements as is done in Ref. 1. The relaxed problem delivered by the displacement-based formulation is of min-min-max type. Because of this, efficient numerical implementation is hampered by the order of the last two min-max operations. We show here that the last two min-max operations may be exchanged, facilitating an efficient numerical algorithm. We remark that the rigorous results given here corroborate the numerical methods and experiments given in Ref. 1.

Intelligent judge neural network for speech recognition

An intelligent judge neural network (IJNN) is developed to make decisions out of contradictory arguments, which may come from different classifiers with different characteristics and/or input features. For speech recognition applications a multi-layer perceptron classifies the word as a spectro-temporal pattern, while a neural prediction model or hidden-control neural network relies on dynamic nature of the speech signal. The “judge≓ accepts input values from the lower-level neural network classifiers and provides ruling verdicts. Two intelligent judges have been investigated. The “neuro-judge≓ rules by extracting decision rules from training data, i.e. disputes between the two classifiers, while the “fuzzy-judge≓ just utilizes min-max operations. The IJNN demonstrates better recognition rates. More importantly its performance is much less sensitive to the choice of training data.

Stabilization of an inverted pendulum by a high-speed fuzzy logic controller hardware system

A high-speed fuzzy controller hardware system employing Min-Max operations is presented. It has fifteen control rule boards and one defuzzifier. Grades of membership are represented with 0 V ∼ 5 V corresponding to 0.0 ∼ 1.0. This fuzzy controller facilitates approximate reasoning at 1 000 000 FIPS (fuzzy inferences per second) and is able to be used for various purposes by programming on each control rule board. It handles fuzzy linguistic information of the form NL (negative large), NM (negative medium), NS (negative small), ZR (approximately zero), PS (positive small), PM (positive medium), PL (positive large) and NG (negation). This fuzzy controller hardware system makes an inverted pendulum stand on a vehicle by using seven control rules. Two pendulums (5 mm diameter, 15 cm length, 3.5 g weight; respectively 10 mm, 50 cm, and 50 g) can be stabilized by the same rule set. It is much easier to produce control rules than to solve the nonlinear differential equations representing the dynamics of an inverted pendulum. This fuzzy controller hardware system can be applied to attitude control of a space booster rocket and satellite, an automatic aircraft landing system, pattern recognition, stabilization of nuclear fuel rods in a reactor, an intelligent sensor, and many other applications which need swift approximate reasoning.

High-speed fuzzy controller hardware system: The mega-FIPS machine

A high-speed fuzzy controller hardware system employing min-max operations is presented. It facilitates approximate reasoning at 1,000,000 FIPS (fuzzy inferences per second) and is able to be used for various purposes in programming. This is the first step in the approach to a fuzzy computer.

On Some Properties of Min-Max Functions

Some of the properties of functions resulting from min-max operations are discussed. First, an implicit function theorem involving min-max functions is proved. Then a formula for the directional derivatives of the implicit function is given. It is shown that these results can be successfully applied to some of the problems in differential games.