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In the present situation, the sustainable development goal on "Gender Equality" (SDG 5) is a challenging problem over the entire globe, also in India. In this paper, the fuzzy graph theory is used to analyse the overall performance of India for the SGD 5. To solve this problem, the new concept of pseudo-vertex-covering set of a fuzzy graph to make a well coverage of the entire fuzzy graph with the combined coverage of vertex-covering set and underlying edge-covering set of the fuzzy graph is defined. With this new covering concept of pseudo-vertex-covering set of fuzzy graphs, an analysis of the performance status of India for SDG 5 is made with the individual performance status of all the states/UTs of India. We show a nice covering of the whole country by some particular states/UTs which are actively helping to make the pseudo-vertex-covering of the transformed form of the graph of India as a fuzzy graph. At last, a comparison between the covering score and index score for SDG 5 is given. Here, covering score is a new term in fuzzy graph theory for coverage of a fuzzy graph by some vertices with underlying some edges. Also, an analysis is given which reflecting a clean idea of the methodology for the performance status of India and these help to find the self-governing states/UTs in India for a better performance. [ABSTRACT FROM AUTHOR]

This paper introduces a self-organizing map dedicated to clustering, analysis and visualization of categorical data. Usually, when dealing with categorical data, topological maps use an encoding stage: categorical data are changed into numerical vectors and traditional numerical algorithms (SOM) are run. In the present paper, we propose a novel probabilistic formalism of Kohonen map dedicated to categorical data where neurons are represented by probability tables. We do not need to use any coding to encode variables. We evaluate the effectiveness of our model in four examples using real data. Our experiments show that our model provides a good quality of results when dealing with categorical data. [ABSTRACT FROM AUTHOR]

A new algorithm for ranking the input features and obtaining the best feature subset is developed and illustrated in this paper. The asymptotic formula for mutual information and the expectation maximisation (EM) algorithm are used to developing the feature selection algorithm in this paper. We not only consider the dependence between the features and the class, but also measure the dependence among the features. Even for noisy data, this algorithm still works well. An empirical study is carried out in order to compare the proposed algorithm with the current existing algorithms. The proposed algorithm is illustrated by application to a variety of problems. [ABSTRACT FROM AUTHOR]

Fuzzy logic is one of the effective tools to handle uncertainty and vagueness in engineering and mathematics. One major part of fuzzy logic is ranking fuzzy numbers. In many fuzzy program systems, ranking fuzzy numbers has a remarkable role in decision making and data analysis. Despite the fact that a variety of methods exists for ranking fuzzy numbers, no one can rank fuzzy numbers perfectly in all cases and situations. In this paper, a new method for ranking fuzzy numbers based on the left and right using distance method and α-cut has been presented. To achieve this, a fuzzy distance measure between two generalized fuzzy numbers is proposed. The new measure is expanded with the help of the fuzzy ambiguity measure. The calculation of this method is derived from generalized trapezoidal fuzzy numbers and distance method concepts. Furthermore, a comparison of generalized fuzzy numbers between the proposed method and other resembled methods is provided. [ABSTRACT FROM AUTHOR]

In this paper, the structural, sensor, and actuator mathematical models of a transelevator are presented; after, the mathematical model with sensor and actuator of the transelevator is obtained by using the combination of the above mentioned mathematical models. The proposed mathematical model is validated comparing the simulation results against the experimental results. Finally, the stability analysis of the aforementioned model is studied. [ABSTRACT FROM AUTHOR]

In this paper, we define a soft intersection group (soft int-group) on a soft set. This new concept functions as a bridge among soft set theory, set theory and group theory and shows the effect of soft sets on a group structure in the sense of intersection and inclusion of sets. We then derive the basic properties of soft int-groups and give its applications to group theory. [ABSTRACT FROM AUTHOR]

In this paper, we have introduced the notion of rough M-hypersystem, rough N-hypersystem, fuzzy M-hypersystem and fuzzy N-hypersystem in a $$\Upgamma$$-semihypergroup and some related properties are investigated. Moreover, we have introduced the notion of fuzzy $$\Upgamma$$-hyperideal in $$\Upgamma$$-semihypergroup. We have also introduced rough M-hypersystem and rough N-hypersystem in a quotient $$\Upgamma$$-semihypergroup. [ABSTRACT FROM AUTHOR]

In this paper, by means of a kind of new idea, we consider the ( ∈ , ∈ ∨ q)-fuzzy hyperideals of $$\Upgamma$$-hyperrings. The notion of ( ∈ , ∈ ∨ q)-fuzzy hyperideals of $$\Upgamma$$-hyperrings is provided and some related properties are investigated. A kind of quotient $$\Upgamma$$-hyperring of a $$\Upgamma$$-hyperring by an ( ∈ , ∈ ∨ q)-fuzzy hyperideal is presented and the relationships among ( ∈ , ∈ ∨ q)-fuzzy hyperideals, quotient $$\Upgamma$$-hyperrings and homomorphisms are explored. Several homomorphism theorems in the framework of fuzzy setting are provided. [ABSTRACT FROM AUTHOR]

pplying the concept of fuzzy sets to hypernear-rings, Davvaz introduced the notion of a fuzzy hyperideal as early as 1999, and it has been studied by several authors. In this paper, we introduce the notion of fuzzy hyperideals in hypernear-rings and investigate some related properties. Also, we characterize maximal fuzzy hyperideals and show that every maximal fuzzy hyperideal of a hypernear-ring is completely normal. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of fuzzy n-folds ( P, implicative and fantastic) ideals in BCH-algebras which is a natural generalization of notion of n-folds ( P, implicative and fantastic) ideals in BCH-algebras and we stated and proved some theorems which determines the relationship between these notions. Finally we give some computational Algorithms for these notions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of some kinds of fuzzy h-ideals in $$\Upgamma$$-hemirings and obtain some of their related properties. In particular, the characterizations of prime fuzzy h-ideals in $$\Upgamma$$-hemirings are discussed. Finally, we show that the h-hemiregular and h-semisimple $$\Upgamma$$-hemirings can be described by using these kinds of fuzzy h-ideals. [ABSTRACT FROM AUTHOR]