• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.545-557
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• 2015

A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we define two new operation on vague graphs namely normal product and tensor product and study about the degree of a vertex in vague graphs which are obtained from two given vague graphs G₁ and G₂ using the operations cartesian product, composition, tensor product and normal product. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large vague graph as a combination of small, vague graphs and to derive its properties from those of the smaller ones.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.625-634
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• 2024

The thrust of this paper is to extend the notion of Plithogenic vertex domination to the basic operations in Plithogenic product fuzzy graphs (PPFGs). When the graph is a complete PPFG, Plithogenic vertex domination numbers (PVDNs) of its Plithogenic complement and perfect Plithogenic complement are the same, since the connectivities are the same in both the graphs. Since extra edges are added to the graph in the case of perfect Plithogenic complement, the PVDN of perfect Plithogenic complement is always less than or equal to that of Plithogenic complement, when the graph under consideration is an incomplete PPFG. The maximum and minimum values of the PVDN of the intersection or the union of PPFGs depend upon the attribute values given to P-vertices, the number of attribute values and the connectivities in the corresponding PPFGs. The novelty in this study is the investigation of the variations and the relations between PVDNs in the operations of Plithogenic complement, perfect Plithogenic complement, union and intersection of PPFGs.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1995.10b
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• pp.378-383
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• 1995

Kandil[5] introduced and studied the notion of fuzzy bitopological spaces as a natural generalization of fuzzy topological In [10], Sampath Kumar introduced and studied the concepts of ( i, j)-fuzzy semiopen sets, fuzzy pairwise semicontinuous mappings in the fuzzy bitopological spaces. Also, he defined the concepts of ( i, j)-fuzzy -open sets, ( i, j)-fuzzy preopen sets, fuzzy pairwise -continuous mappings and fuzzy pairwise precontinuous mappings in the fuzzy bitopological spaces and studied some of their basic properties. In this paper, we generalize the concepts of fuzzy -open sets, fuzzy -continous mappings ？ 새 Mashhour, Ghanim and Fata Alla[6] into fuzzy bitopological spaces, We first define the concepts of ( i, j)-fuzzy -open sets and then consider the generalizations of fuzzy pairwise -continuous mappings is obtained Besides many basic results, results related to products and graph of mapping are obtained in the fuzzy bitopological spaces.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.666-668
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• 1998

In this paper, we consider a bi-objective vehicle routing problem to minimize total distance traveled and maximize minimum integrated satisfaction level of selecting desirable routes in an fuzzy graph. The fuzzy graph reflects a real delivery situation in which there are a depot, some demand points, paths linking them, and distance and integrated satisfaction level are associated with each route. For solving the vi-objective problem we introduce a concept of routing vector and define non-dominated solution for comparing vectors. An efficient algorithm involving a selection method of non-dominated solutions based on DEA is proposed for the vehicle routing problem with rigid distance and integrated satisfaction level.

• Journal of Biomedical Engineering Research
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• v.13 no.2
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• pp.115-124
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• 1992

An algorithm has been proposed for the automatic detection of optimal epiand endocardial left ventricular borders from 2-D short axis echocardiogram which is degraded by noise and echo drop out. For the implementation of the algorithm, we modified Ballard's Generalized Hough Transform which can be applicable only for deterministic object border, and newly proposed Fuzzy Hough Transform method. The algorithm presented here allows detection of object whose exact shapes are unknown. The algorithm only requires an approximate model of target object based on anatomical data. To detect the approximate epicardial contour of left ventricle, Fuzzy Hough Transform was applied to the echocardiogram. The optimal epicardial contour was founded by using graph searching method which contains cost function analysis process. Using this optimal epicardial contour and average thickness imformation of left ventricular wall, the approximate endocardial line was founded, and graph searching method was also used to detect optimal endocardial contour.

• East Asian mathematical journal
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• v.36 no.5
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• pp.561-570
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• 2020

We compute the extended four operations of the 2-dimensional quadratic fuzzy numbers. Then we calculate the intersection between a plane perpendicular to the x-axis, which passes through each vertex, and the resulting 2-dimensional quadratic fuzzy number. We confirm that the equations of the two intersections acquired in this way and the graphs are actually identical, respectively.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.765-782
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• 1998

The purpose of this paper is to give convergence theorems both for closed convex set valued and relative fuzzy valued martingales, and sub- and super- martingales. These kinds of martingales, sub- and super-martingales are the extension of classical real valued martingales, sub- and super-martingales. Here we compare two kinds of convergences, in the Hausdorff metric and in the Kuratowski-Mosco sense. We also introduce a new convergence for the fuzzy valued case in the graph sense and obtain convergence theorems.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1114-1117
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• 1993

The paper presents an effective method for finding the propagation structure of the real origin of a system malfunction. It uses a combined system model consisting of Structural Model (SM) in the form of Fuzzy Directed Graph and Behavior Model (BM) as a set of Fuzzy Relational Equations $A\;{\circ}\;R\;=\;B$. Here a specially proposed fuzzy inference technique is checked and investigated. Finally a test example for fault diagnosis of an industrial system is given and analyzed.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.6
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• pp.2785-2792
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• 2011

Such problems as delay, congestion, and crosstalk in the proxy system degrade not only QoS (Quality of Service) but responsiveness and reliability of the streaming media service. To solve this problem this paper proposed a FRTP (Fuzzy Relevance-based Transcoding Proxy) mechanism. The proposed FRTP mechanism analyzes fuzzy similarity for partitioned segment versions of media objects to create a FRTG (Fuzzy Relevance-based Transcoding Graph). Created FRTG determines the transcoding for partitioned media object segment versions. Determined transcoding improves DSR (Delay Saving Ratios), CHPR (Cache Hit Precision Ratio), and CHRR (Cache Hit Recall Ratio). The proposed mechanism is simulated to evaluate such performance parameters as DSR, CHPR, and CHRR. Simulation results shows that the proposed mechanism outperforms in DSR, CHPR and CHRR compared with the other existing mechanisms.

• Journal of the Korean Institute of Intelligent Systems
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• v.23 no.2
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• pp.133-138
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• 2013

This paper addresses a state consensus controller design technique of Takagi-Sugeno fuzzy model-based multi-agent systems in a continuous-time domain. We express the interconnection topology among the agents through graph theory. The design condition is represented in terms of linear matrix inequalities. Numerical example is provided to demonstrate the effectiveness of the proposed method.