Max-min Composition Research Articles

On the max-contraction powers of a fuzzy matrix

In the literature, the powers of a fuzzy matrix with max-arithmetic mean/convex combination of max-min and max-arithmetic mean/convex combination of max-product and max-min compositions have been studied. It turns out that the limiting behavior of the powers of a fuzzy matrix depends on the composition involved. In this paper, we consider the max-contraction powers of a fuzzy matrix which is an extension of the max-arithmetic mean/convex combination of max-min and max-arithmetic mean/convex combination of max-product and max-arithmetic mean operation. We show that the powers of such a fuzzy matrix are always convergent and the limit matrix has the feature that all elements of each column are identical.

Column stacking approach to resolution of systems of fuzzy relational inequalities

This paper investigates several kinds of fuzzy relational inequalities (FRIs) and systems of fuzzy relational inequalities (SFRIs) with the max–min composition, and proposes a column stacking approach. Firstly, the equivalent column stacking forms of the considered FRIs and SFRIs are obtained based on the Boolean Kronecker product of matrices, which converts the resolution of the considered FRIs and SFRIs to the resolution of an FRI with the same form. Secondly, using the semi-tensor product (STP) of matrices, the resolution of FRIs is converted to finding all the parameter set solutions, based on which, the solution set of the considered FRIs and SFRIs is characterized. Finally, a general algorithm is established for the resolution of the considered FRIs and SFRIs.

Zadeh max–min composition fuzzy rule for dominated pixel values in iris localization

Iris detection fails at the iris localization stage pulling out of the sub-image from the original image; the objective of this paper is to realize the narrative approach for iris localization and to solve the localization problem in an image using a dominant localization max–min algorithm which increases accuracy and reduces the search time. In the proposed system Zadeh dominated fuzzy rule composition algorithm was used to create the dominant values by comparing the values with the neighbours in the meticulous route. This algorithm helps to localize the iris image with a precision of 98.6% and a search time of 8.4 ms.

A Score Function-Based Method of Forecasting Using Intuitionistic Fuzzy Time Series

Intuitionistic fuzzy set plays a vital role in data analysis and decision-making problems. In this paper, we propose an enhanced and versatile method of forecasting using the concept of intuitionistic fuzzy time series (FTS) based on their score function. The developed method has been presented in the form of simple computational steps of forecasting instead of complicated max–min compositions operator of intuitionistic fuzzy sets to compute the relational matrix [Formula: see text]. Also, the proposed method is based on the maximum score and minimum accuracy function of intuitionistic fuzzy numbers (IFNs) to fuzzify the historical time series data. Further intuitionistic fuzzy logical relationship groups are defined and also provide a forecasted value and lies in an interval and is more appropriate rather than a crisp value. Furthermore, the proposed method has been implemented on the historical student enrollments data of University of Alabama and obtains the forecasted values which have been compared with the existing methods to show its superiority. The suitability of the proposed model has also been examined to forecast the movement of share market price of State Bank of India (SBI) at Bombay Stock Exchange (BSE). The results of the comparison of MSE and MAPE indicate that the proposed method produces more accurate forecasting results.

Fuzzy proximal relator spaces

This paper introduces fuzzy Lodato–Smirnov proximal relator spaces. We define fuzzy proximity relation to evaluate the proximity of the sets. Also, it is shown that the max–min composition of fuzzy proximity relations is associative and the Smirnov proximity measure on the Lodato proximity space is a fuzzy spatial Lodato proximity relation. Fuzzy proximity relation approach can be applied to some problems. Therefore, it is used to solve a few issues such as precise sorting of near sets, solution of classification problems and given examples for the problems.

Max Min Composition Based Multilevel PID Selector with Reduced Rules and Complexity in FIS for Servo Applications

Max Min Composition Based Multilevel PID Selector with Reduced Rules and Complexity in FIS for Servo Applications

Comparison between images via bilinear fuzzy relation equations

We present a comparison between two images A and B based on the greatest solution of a system of bilinear fuzzy relation equations A○x = B○x, where “○” is the max–min composition, being A and B known as fuzzy relations and x is unknown. Here A and B are images considered as fuzzy relations being their pixels normalized in [0, 1] with respect to the grey scale used. Due to symmetry of every equation involved, A (resp., B) could be the original image and B (resp., A) is an image modified of A (resp., B), for instance, either noised or watermarked. The comparison is made by using an index which is more robust than other two indices used in previous works: the first one is based on the greatest eigen fuzzy set (with respect to max–min composition) and smallest eigen fuzzy set (with respect to min–max composition) and the second one is based on the Lukasiewicz triangular norm. The comparison is made between the original image and the same image with noise introduced at several values σ of the standard deviation.

Optimization Model of Fuzzy Rule Based Expert System Using Max-Min Composition and Schema Mapping Translation

Abstract— Fuzzy Decision Making involves a process of selecting one or more alternatives or solutions from a finite set of alternatives which suits a set of constraints. In the rule-based expert system, the terms following in the decision making is using knowledge based and the IF Statements of the rule are called the premises, while the THEN part of the rule is called conclusion. Membership function and knowledge based determines the performance of fuzzy rule based expert system. Membership function determines the performance of fuzzy logic as it relates to represent fuzzy set in a computer. Knowledge Based in the other side relates to capturing human cognitive and judgemental processes, such as thinking and reasoning. In this paper, we have proposed a method by using Max-Min Composition combined with Genetic Algorithm for determining membership function of Fuzzy Logic and Schema Mapping Translation for the rules assignment.Keywords— Fuzzy Decision Making, Rule-Based Expert System, Membership Function, Knowledge Based, Max-Min Composition, Schema Mapping Translation

STUDY OF CLIENT VARIABLES INFLUENCE ON THE PERFORMANCE OF RETAIL COMMERCIAL ENTERPRISES

There are four groups of indicators influenced on the performance of retail commercial enterprise. They are characteristics of the store (retail space), store location, transport and pedestrian accessibility of the store and the attitude of buyers to the shop (customer metrics). The present paper is dealt with the influence of the fourth group- «customer metrics ". The authors of this article consider such factors of this group as: the work of salespeople and other staff; the internal atmosphere of commercial enterprise; the security area of the enterprise location; brand awareness; additional services. The article describes the application of the proposed approach to the assessment and change forecast of turnover depending on the studied factors using the method of fuzzy logic by the example of the results of such shops as "Ocean" and "Pervomayskiy", retail outlets "Gastronom" format "supermarket", Izhevsk. The authors define term-sets and membership functions for each client criterion. The rule base is also developed. The presence of aggregate functions is implemented by Mamdani logical inference, which uses the min-max composition of fuzzy sets. The adequacy of the proposed mathematical model is performed on the example of results forecasting of investigated stores activities "retail network " Gastronom " format "supermarket" (Izhevsk, Russia) using the software Matlab, and then comparing the calculated value of the average purchase with actual. Monitored client performance on the basis of a network "Gastronom" has also allowed the authors to develop recommendations for shops as described in this article.

A fuzzy medical diagnosis based on quantiles of diagnostic measures

For medical diagnosis based on fuzzy relations of diseases and symptoms, max-min composition method and distance-based method are frequently used. However, they often lead to diagnostic confusion and puzzle due to their different results. In this paper, we suggest a new method for medical diagnosis using the quantiles of the measures used in both methods to avoid such problems. As an illustration of usefulness, the proposed method is applied to medical diagnosis of headache. The results of the simulation show that the two methods with the normal measures have significant difference in headache diagnosis, while the difference decreases when the quantiles of the normal measures are used as a diagnostic measure.

On the resolution of bipolar max-min equations

This paper investigates bipolar max-min equations which can be viewed as a generalization of fuzzy relational equations with max-min composition. The relation between the consistency of bipolar max-min equations and the classical boolean satisfiability problem is revealed. Consequently, it is shown that the problem of determining whether a system of bipolar max-min equations is consistent or not is NP-complete. Moreover, a consistent system of bipolar max-min equations, as well as its solution set, can be fully characterized by a system of integer linear inequalities.

Some results associated with the max–min and min–max compositions of bifuzzy matrices

Abstract In this paper, we define some kinds of bifuzzy matrices, the max–min (○) and the min–max (*) compositions of bifuzzy matrices are defined. Also, we get several important results by these compositions. However, we construct an idempotent bifuzzy matrix from any given one through the min–max composition.

Mobius transform for Cadiag-2

This study presents how the Mobius transform can be used for Max-Min compositions of rules of the CADIAG-2. The algorithm for Mobius transform to find new weights of rules for CADIAG-2 is proposed. This method is tested for different examples and some remarks are indicated.

Analyzing Human Communities using Fuzzy Graphs

<span>Fuzzy Graphs are used for analyzing and modeling levels of information<br /><span>in real-time systems (simple or complex networks). A community<br /><span>(network) is formed when human eProfiles (nodes) have links (edges)<br /><span>and interactions with each other. Considering multiple medium of<br /><span>communications like email, chatting and short message service (SMS)<br /><span>in the network, it will make the graph more complex (dense graph or<br /><span>forest). To address this issue in this paper analyzes those human<br /><span>communities with the help of fuzzy graphs and highlights the status of<br /><span>individuals in a human community. Max-Min Composition (fuzzy<br /><span>relation) was applied along with statistical analysis on fuzzy graphs of<br /><span>human community. Interaction Index (II) is used to estimate the intensity<br /><span>of communication and Role Index (RI) determine the participation status<br /><span>of individual in a human community. All this analysis will be used in<br /><span>our research and development of Community Algorithm, which will be<br /><span>used as a tool that will help in identifying, analyzing, manipulating,<br /><span>monitoring, and transforming human communities based on human<br /><span>eProfiles.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /><br class="Apple-interchange-newline" /></span>

Method development of organization and planning monitoring for regional gas supply

In connection with the obsolescence of the gas supply equipment and increasing the volume of leaks in the gas pipelines, the problem of monitoring for regional gas supply at the moment is becoming more urgent. An analysis of previous studies in the article were identified outstanding issues in the problems of monitoring for regional gas supply system, formulated the aim of article and the basic objectives of the study.Important steps that precede the process of synthesis of the monitoring system for regional gas supply are the organization and planning monitoring. Each of these steps can be decomposed, and the results obtained at the upper levels, will be the source data for the lower levels.The research allowed developing a method of organization and planning monitoring, highlighting the basic steps in solving problems of organization and planning monitoring for regional gas supply. Based on earlier models of organization and planning at every stage of this method it is proposed to use a scheme of compromise or procedure max-min composition. This allows developers to make decisions under multicriteriality and fuzzy of initial data.

A fuzzy logic model for differential diagnosis of lower urinary tract dysfunctions

ABSTRACTLower urinary tract dysfunctions (LUTD) restrict quality of life, resulting in decreased work productivity and emotional well‐being. However, most people are not diagnosed because they do not seek medical treatment. In addition, some facilities do not adequately train health professionals in the evaluation, diagnosis and treatment of these conditions. The study's objective was to develop a decision support system modelled on fuzzy logic that defines LUTD using the terminology of the International Continence Society. This methodological study aimed to develop a model that uses the maximum–minimum composition (max–min) of fuzzy relations that can perform differential diagnoses of LUTD. The model was tested in 100 cases (50 men and 50 women), and the data were obtained from medical records containing the clinical data and results of urodynamic studies. All medical records were reviewed by a specialist in urology. The model was capable of determining a diagnosis in full (62%) or partial (36%) agreement with the medical report. Agreement between the model and the medical report was excellent (kappa = 0·98, p ≪ 0·001, CI = 0·88–1) or substantial (kappa = 0·53, p ≪ 0·001, CI = 0·45–0·60), considering overestimative accordance (where accordance is assumed when at least one diagnosis is equal) and underestimative accordance (where accordance is assumed when all diagnoses are equal), respectively. The proposed model based on the max–min composition of fuzzy relationships is very simple and performed well. However, more tests are recommended before the model is used as a decision support system.

Linear Programming Method for Solving Semi-Latticized Fuzzy Relation Geometric Programming with Max-Min Composition

Motivated by application in BitTorrent-like Peer-to-Peer resource sharing system, we introduce the maximization and minimization semi-latticized fuzzy relation geometric programming problems with max-min composition in this paper. The objective function in the proposed problem in nonlinear and the feasible domain is non-convex. The maximization problem is converted into a fuzzy relation monomial geometric programming and then solved. However, this approach is not effective for the minimization one. The linear programming method is applied to deal with the minimization problem. A step-to-step algorithm is develop to carried out the linear programming method and tow illustrative examples are provided at last.

Posynomial geometric programming problem subject to max–min fuzzy relation equations

We discuss a class of posynomial geometric programming problem(PGPF), aimed at minimizing a posynomial subject to fuzzy relational equations with max–min composition. By introducing auxiliary variables, we convert the PGPF into an equivalent programming problem whose objective function is a non-decreasing function with an auxiliary variable. We show that an optimal solution consists of a maximum feasible solution and one of the minimal feasible solutions by an equivalent programming problem. In addition, we introduce some rules for simplifying the problem. Then by using a branch and bound method and fuzzy relational equations (FRE) path, we present an algorithm to obtain an optimal solution to the PGPF. Finally, numerical examples are provided to illustrate the steps of the procedure.

A Fuzzy Expert System for Distinguishing between Bacterial and Aseptic Meningitis

Introduction Bacterial meningitis is a known infectious disease which occurs at early ages and should be promptly diagnosed and treated. Bacterial and aseptic meningitis are hard to be distinguished. Therefore, physicians should be highly informed and experienced in this area. The main aim of this study was to suggest a system for distinguishing between bacterial and aseptic meningitis, using fuzzy logic. Materials and Methods In the first step, proper attributes were selected using Weka 3.6.7 software. Six attributes were selected using Attribute Evaluator, InfoGainAttributeEval, and Ranker search method items. Then, a fuzzy inference engine was designed using MATLAB software, based on Mamdani’s fuzzy logic method with max-min composition, prod-probor, and centroid defuzzification. The rule base consisted of eight rules, based on the experience of three specialists and information extracted from textbooks. Results Data were extracted from 106 records of patients with meningitis (42 cases with bacterial meningitis) in order to evaluate the proposed system. The system accuracy, specificity, and sensitivity were 89%, 92 %, and 97%, respectively. The area under the ROC curve was 0.93, and Kappa test revealed a good level of agreement (k=0.84, P<0.0005). Conclusion According to the results, the suggested fuzzy system showed a good agreement and high efficiency in terms of distinguishing between bacterial and aseptic meningitis. To avoid unnecessary antibiotic treatments, patient hospitalization, and misdiagnosis of bacterial meningitis, such systems are useful and highly recommended. However, no system has been yet introduced with 100% correct output and further research is required to improve the results.

A fuzzy probabilistic method for medical diagnosis.

The max-min composition in fuzzy set theory has attained reasonable success in medical diagnosis in the past thirty years for estimating the probability of a patient diagnosed with a certain disease. However, there has been no theoretical justification why the method would work. We create a theoretical model to calculate the probabilities of hypothetical patients having designated diseases, and use simulated dataset to explain why the max-min composition has been successful. In addition, based on the theoretical model, we propose a fuzzy probabilistic method to estimate the probability of a patient having a certain disease. The proposed method may produce a more accurate estimate than the max-min composition.