Max-min Composition Research Articles

An investigation of the relationship between surface temperature and total ozone over New Delhi, India, using a frequency domain technique and binary fuzzy relation

ABSTRACT This work has explored spectral analysis to view the relationship between the time series of surface temperature and total ozone concentration (TOC) over New Delhi from 1995 to 2005. The time series has a discernible spectral density when analysed using harmonic analysis. Between the surface temperature and TOC, a common cycle of period of 10 months has been noted for the years under investigation. In addition, a binary fuzzy relation method has been used to examine the relationship between surface temperature and TOC using membership matrices produced by max-min composition. Overall, a fuzzy set theoretic approach has established a connectivity between surface temperature and TOC, and a spectral analysis approach which falls under the category of frequency domain approach has established the existence of a common cycle between these two time series.

Inverse inference based on interpretable constrained solutions of fuzzy relational equations with extended max–min composition

Inverse inference based on interpretable constrained solutions of fuzzy relational equations with extended max–min composition

Test Case Selection through Novel Methodologies for Software Application Developments

Test case selection is to minimize the time and effort spent on software testing in real-time practice. During software testing, software firms need techniques to finish the testing in a stipulated time while uncompromising on quality. The motto is to select a subset of test cases rather than take up all available test cases to uncover most bugs. Our proposed model in the research study effort is termed SCARF-RT, which stands for Similarity coefficient (SC), Creating Acronyms, Regression test (RT), and Fuzzy set (FS) with Dataset (DS). Clustering of test cases using ranking and also based on similarity coefficients is to be implemented. This research considered eleven different features for clustering the test cases. Two techniques have been used. Firstly, each cluster will, to a certain extent, encompass a collection of distinct traits. Depending on the coverage of the feature, a cluster of test cases might be chosen. The ranking approach was used to create these groupings. The second methodology finds similarity among test cases based on eleven features. Then, the maxmin composition is used to find fuzzy equivalences upon which clusters are formed. Most similar test cases are clustered. Test cases of every cluster are selected as a test suite. The outcomes of this research show that the selected test cases based on the proposed approaches are better than existing methodologies in selecting test cases with less duration and at the same time not compromising on quality. Both fuzzy rank-based clustering and similarity coefficient-based clustering test case selection approaches have been developed and implemented. With the help of these methods, testers may quickly choose test cases based on the suggested characteristics and complete regression testing more quickly.

Medical Diagnosis via Refined Neutrosophic Fuzzy Logic: Detection of Illness using Neutrosophic Sets

The objective of the paper is to implement and validate diagnosis in the medical field via refined neutrosophic fuzzy logic (RNFL). As such, we have proposed a Max-Min composition (MMC) method in RNFL. This method deals with the diagnosis under certain constraints like uncertainty and indeterminacy. Further, we have considered the diagnosis problems to validate the sensitivity analysis of the novel multi attribute decision-making technique. Finally, we gave the graphical representations and compared the obtained results with other existing measures in refined neutrosophic fuzzy sets.

APPLICATION OF INTUITIONISTIC FUZZY SETS IN DETERMINING RESEARCH TOPICS FOR MATHEMATICS EDUCATION STUDENTS THROUGH THE NORMALIZED EUCLIDEAN DISTANCE METHOD

An intuitionistic fuzzy set (IFS) can be helpful in decision-making as a concept to describe uncertainty. This study proposes the application of IFS in determining research topics for students of the mathematics education study program using the normalized Euclidean distance method. This study also shows the differences in the analysis results using the max-min composition method revised by De et al. (2001) with the normalized Hamming distance method and the normalized Euclidean distance method. The results show that the normalized Euclidean distance method can determine student research topics more accurately than other methods because they are careful in looking at distance differences. The normalized Euclidean distance method provides the best distance measure with a high confidence level in terms of accuracy.

Compositions of Picture Fuzzy Relations with Application in Decision Making

Picture fuzzy relation is an important and powerful concept which is suitable for describing correspondences between objects. It represents the strength of association of the elements of picture fuzzy sets. In this paper we have defined min-max composition for picture fuzzy relations and some properties are explored based on this definition. Also we have discussed some properties of max-min composition for picture fuzzy relations. Finally, an application is discussed as illustration to show how the picture fuzzy relation are applied in decision making.

Algebraic formulae for solving systems of max-min inverse fuzzy relational equations

This article is intended to solve the systems of inverse fuzzy relational equations with max–min composition, which is beneficial for solving the well-known problems of fuzzy abductive/backward reasoning. Almost all the existing methods are based on numerical algorithms, and either cannot find the globally optimal solutions or consume significant computational cost to acquire the most accurate result. Due to these drawbacks, the existing methods seem not to render the retroduction applying inverse fuzzy relation popular in many real-time expert systems such as intelligent diagnosis. It is well known that the system of inverse fuzzy relational equations is not always consistent. In this case, according to the preselected weights, we employ weighted L1 norm distances to define a variety of best approximate solutions. Then we show that there exist very straightforward algebraic formulae for finding the best approximate solutions. The proposed approach not only finds the globally optimal solutions, but also has the advantage of being computationally very simple and efficient, and hence it has a lot of potentials to perform real-time abductive reasoning in many expert systems.

Optimum pricing of smart home appliances based on carbon emission and system cost

Concurrent optimization of two different objective functions is a prominent subject in power systems. A model based on a multi-objective mixed-integer program is presented for smart home scheduling with economic and environmental considerations. One of the objective functions minimizes the operational cost of the building, whereas, the other one minimizes the carbon release. To solve the suggested multi-objective problem, the ɛ-constraint technique and the weighted addition method are utilized. Therefore, to choose the desirable win–win approach from the achieved effective outcomes, a min–max composition of fuzzy is used in order to obtain desirable evaluation results. The CPLEX solver of the GAMS is used to solve the suggested problem. In addition, to assess the effectiveness of the suggested model, ɛ-constraint technique and the weighted addition method case studies have been used. In a comparison of the achieved results, it is seen that by incorporating the ɛ-constraint technique, the overall operational cost of the smart home is 28.57% lower when economically optimizing the model. Also, by environmentally optimizing the model, 7.63% less carbon was emitted. Moreover, using the weighted addition method demonstrates a decrease of 28.76% and 11.37% from economic and environmental viewpoints, respectively. The simulation results show that to minimize carbon release, the building’s electrical power control system prefers utilizing CHP over the boiler.

View materialization using fuzzy MAX–MIN composition with association rule mining (VMFCA)

View materialization using fuzzy MAX–MIN composition with association rule mining (VMFCA)

Application of Smooth Fuzzy Model in Image Denoising and Edge Detection

In this paper, the bounded variation property of fuzzy models with smooth compositions have been studied, and they have been compared with the standard fuzzy composition (e.g., min–max). Moreover, the contribution of the bounded variation of the smooth fuzzy model for the noise removal and edge preservation of the digital images has been investigated. Different simulations on the test images have been employed to verify the results. The performance index related to the detected edges of the smooth fuzzy models in the presence of both Gaussian and Impulse (also known as salt-and-pepper noise) noises of different densities has been found to be higher than the standard well-known fuzzy models (e.g., min–max composition), which demonstrates the efficiency of smooth compositions in comparison to the standard composition.

Upper Bounded Minimal Solution of the Max-Min Fuzzy Relation Inequality System

Resolution of the minimal solutions plays an important role in the research on fuzzy relation equations or inequality systems. Most of the existing works focused on the general minimal solutions or some specific minimal solutions that optimize particular objective functions. In a recently published work [43], the restricted minimal solution of fuzzy relation inequalities with addition-min composition was studied by M. Li et al. Motivated by the idea presented in [43], we investigate the so-called upper bounded minimal solution of fuzzy relation inequalities with max-min composition in this work. The upper bounded minimal solution is defined as the minimal solution that is no more than a given vector. Here, the given vector can be viewed as the upper bound. The major content in this work consists of two components: the existence and the resolution of the upper bounded minimal solution. First, we provide some necessary and sufficient conditions to determine whether the upper bounded minimal solution exists with respect to a given vector. Second, when it exists, we further develop two algorithms to search for the upper bounded minimal solution in a step-by-step approach. The validity of our proposed Algorithms I and II is formally proved in theory. The computational complexities of Algorithms I and II are <i>O</i>(<i>mn</i>) and <i>O</i>(<i>mn</i>²), respectively. Moreover, our proposed algorithms are illustrated by some numerical examples.

Graphic Representation of a Dimensional Expansion of Triangular Fuzzy Number

We calculate Zadeh’s max-min composition operators for two 3-dimensional triangular fuzzy numbers. We prove that if the 3-dimensional result is limited to 2 dimensions, it is the same as the 2-dimensional result, which is shown as a graph. Since a 3-dimensional graph cannot be drawn, the value of the membership function is expressed with color density. We cut a 3-dimensional triangular fuzzy number by a perpendicular plane passing a vertex, and consider the cut plane as a domain. The value of the membership function for each point on the cut plane is also expressed with color density. The graph expressing the value of the membership function, defined in the plane as a 3-dimensional graph using the z -axis value instead of expressing with color density, is consistent with the results in the 2-dimensional case.

Resolution of Fuzzy Relational Inequalities with Boolean Semi-Tensor Product Composition

Resolution of fuzzy relational inequalities (FRIs) plays a significant role in decision-making, image compression and fuzzy control. This paper studies the resolution of a kind of FRIs with Boolean semi-tensor product composition. First, by resorting to the column stacking technique, the equivalent form of FRIs with Boolean semi-tensor product composition is obtained, which is a system of FRIs (SFRIs) with max–min composition. Second, based on the semi-tensor product method, all the solutions to FRIs with Boolean semi-tensor product composition are obtained by finding all possible parameter set solutions. Finally, a general procedure is developed for the resolution of FRIs with Boolean semi-tensor product composition. Two illustrative examples are worked out to show the effectiveness of the obtained new results.

ENHANCING ADEQUACY OF GRADING STUDY PROJECTS ON THE BASE OF PARAMETRIC RELAXATION OF PAIRWISE COMPARISONS

A problem of automated assessing of students’ study projects is regarded. A heuristic algorithm based on fuzzy estimating of projects and on pairwise comparisons among them is proposed. For improving adequacy and naturalness of grades, an approach based on introducing a parameter named relaxation parameter was suggested in the paper. This enables to reduce the spread between maximum and minimum values of projects in comparison with the one in the standard scale suggested by T. Saati. Reasonable values of this parameter were selected experimentally. For estimating the best alternative, a center of mass of a fuzzy max-min composition should be calculated. An estimation algorithm for a case of non-transitive preferences based on getting strongly connected components and on pairwise comparisons between them is also suggested. In this case, relaxation parameters should be chosen separately for each subtask. So the combined technique of evaluating alternatives proposed in the paper depends of the following parameters: relaxation parameters for pairwise comparisons matrices within each strongly connected components; relaxation parameter for pairwise comparisons matrices among strongly connected components; membership function for describing the best alternative.

Fuzzy Model for Risk Assessment of Machinery Failures

The main goal of this research was the development of an algorithm for the implementation of negative risk parameters in a synthesis model for a risk level assessment for a specific machine used in the mining industry. Fuzzy sets and fuzzy logic theory, in combination with statistical methods, were applied to analyze the time picture state of the observed machine. Fuzzy logic is presented through fuzzy proposition and a fuzzy composition module. Using these tools, the symmetric position of the fuzzy sets with regard to class was used, and the symmetric fuzzy inference approach was used in an outcome calculation. The main benefit of the proposed model is being able to use numerical and linguistic data in a risk assessment model. The proposed risk assessment model, using fuzzy logic conclusions and min–max composition, was used on a mobile crushing machine. The results indicated that the risk level of the mobile crushing machine was in the “high” category, which means that it is necessary to introduce maintenance policies based on this high risk. The proposed risk assessment model is useful for any engineering system.

Properties of Composition of Fuzzy Relations and its Verifications

This paper, deals with fundamental notions in pure and applied sciences, i.e., basic operations related to fuzzy relations. The composition of fuzzy relations are defined in two ways such as max-min composition and max-product composition with suitable example. This paper also introduces the properties of composition of fuzzy relations. The newly introduced properties inculcates zero, identity, equal, not-equal, subset, associative, union, intersection and distributive fuzzy relations. Finally, the paper verifies the properties of composition of fuzzy relations using some numerical values for 2x2 order of matrix. Also gives some exercise problems related to the above concepts with accurate answer keys.

A Zadeh′s max-min composition operator for 3-dimensional triangular fuzzy number

We generalized triangular fuzzy numbers from ℝ to ℝ 2 . By defining parametric operations between two α-cuts, which are regions, we obtained parametric operations for two triangular fuzzy numbers defined on ℝ 2 . We also generalized triangular fuzzy numbers from ℝ 2 to ℝ 3 . By defining parametric operations between two α-cuts, which are subsets of ℝ 3 , we derived parametric operations for two triangular fuzzy numbers defined on ℝ 3 . For the calculation of Zadeh’s principle operators, the definition of parametric operations between two α-cuts, which are subsets of ℝ 3 , is critical.

AN Application of Neutrosophic Vague Max-Min Composition Technique

The theory of fuzzy set was introduced by Zadeh, has a wider scope in terms of applications than the classical set theory in solving various problems. Extensive applications of the fuzzy set theory have been found in various fields such as Computer Sciences, Artificial Intelligence, Medical Sciences, Economics, Statistics, Neural Networks, etc. In fuzzy set each element had a degree of membership. Smarandache defined the neutrosophic set theory, which was one of the most important new mathematical tools for handling problems involving imprecise, indeterminacy, and inconsistent data. The theory of vague sets was first proposed by Gau and Buehrer as an extension of fuzzy set theory and vague sets are regarded as a special case of context-dependent fuzzy sets. Shawkat Alkhazaleh introduced the concept of neutrosophic vague set as a combination of neutrosophic set and vague set. Neutrosophic vague theory is an effective tool to process incomplete, indeterminate and inconsistent information. This paper attempts to develop a new model known as neutrosophic vague max-min composition technique to examine the daily life problems. One of the major problems that everyone comes across is their children’s studies. Education is a very important aspect of the lives of all people all over the world. What we learn, not just in the classroom, shapes who we are. We take our education everywhere we go. Student life is not as easier as it seems. Now a days the studies of the student is deviated due to various reasons. Here we identify those problems of students and by using neutrosophic vague max-min composition technique we analyze the problem faced by the students that affect their lack of concentration in studies.

Fuzzy rule-based reliability analysis using NSGA-II

Practically, reliability-based system designs are modeled in various kinds of uncertainty such as expert’s information character, qualitative statements, vagueness, etc. Fuzzy set theory is suitable for tackling such types of uncertainty effectively. In most of the practical situations, where reliability enhancement is an essential requirement, decision-making is a complicated task due to the presence of several mutually conflicting objectives such as system’s cost, weight, and volume. To solve such problems, multi-objective evolutionary algorithms (MOEAs) are efficient techniques for finding multiple Pareto-optimal solutions in a single simulation run. This paper applies an elitist MOEA, namely, NSGA-II to fuzzy multi-objective reliability optimization problem consisting of conflicting objectives such as system reliability and its cost. Linguistic hedges (or modifiers) are used to modify the Pareto-optimal solution set obtained by NSGA-II in terms of the membership grades of the objective values. The max–min composition of the membership grades gives the maximum satisfaction level to each possible combination of the linguistic hedges. After that, fuzzy rule-based system (FRBS) is proposed for evaluating the system efficiency to each case which is used in the decision-making of reliability. A numerical example is given to illustrate the method. Finally, the proposed approach is comparatively studied with the existing approach.

Analyzes of Mouth Cancer Using Max-Min Composition in Soft Computing

Analyzes of Mouth Cancer Using Max-Min Composition in Soft Computing