Showing papers by "Madhumangal Pal published in 2013"
TL;DR: Fuzzy competition graph as a generalization of competition graph is introduced here and two generalizations of fuzzy competition graphs as fuzzy k-competition graphs and p-comp competition fuzzy graphs are also defined.
163 citations
01 Jan 2013
TL;DR: It is shown that the tensor product of two interval-valued fuzzy graphs is a product interval- valued fuzzy graph and given three independent theorems based on ring sum, join and isomorphism of product interval’s fuzzy graphs, balanced and strictly balanced fuzzy graphs are defined.
Abstract: In this paper, we discuss notion of ring sum of product interval-valued fuzzy graphs. We define tensor product of two interval-valued fuzzy graphs and shown that the tensor product of two product interval-valued fuzzy graphs is a product interval-valued fuzzy graph. Likewise, given three independent theorems based on ring sum, join and isomorphism of product interval-valued fuzzy graphs. Finally, we define balanced and strictly balanced interval-valued fuzzy graphs and investigated several properties.
53 citations
TL;DR: This paper discusses a manufacturing inventory model with shortages where carrying cost, shortage cost, setup cost and demand quantity are considered as fuzzy numbers and the transformed problem has been solved by intuitionistic fuzzy programming technique.
51 citations
01 Jan 2013
TL;DR: Isomorphism properties of µ-complement, self µ- complement and self weak µ- complement of highly irregular interval-valued fuzzy graph are established and interval- valued fuzzy digraphs are defined.
Abstract: Theoretical concepts of graphs are highly utilized by computer science applications. Especially in research areas of computer science such as data mining, image segmentation, clustering, image capturing and networking. The interval-valued fuzzy graphs are more flexible and compatible than fuzzy graphs due to the fact that they allowed the degree of membership of a vertex to an edge to be represented by interval values in (0.1) rather than the crisp values between 0 and 1. In this paper, we discussed some properties of isomorphism, weak isomorphism and co-weak isomorphism between highly irregular interval-valued fuzzy graphs and its complement. Isomorphism properties of µ-complement, self µ-complement and self weak µ- complement of highly irregular interval-valued fuzzy graph are established. Finally, we defined interval- valued fuzzy digraphs.
46 citations
TL;DR: The basic algebra and some non-linear operations of triangular intuitionistic fuzzy numbers (TIFNs) are devised and the average ranking index is introduced to find out order relations between two TIFNs.
Abstract: The notion of triangular fuzzy number is put forward on the basis of intuitionistic fuzzy sense. The basic algebra and some non-linear operations of triangular intuitionistic fuzzy numbers (TIFNs) are devised. The average ranking index is introduced to find out order relations between two TIFNs. A method is described to approximate a TIFN to a nearly approximated interval number. Applying this result and using interval arithmetic a bound unconstrained optimisation problem is solved whose coefficients are fixed TIFNs. Numerical examples are also given for illustration.
26 citations
Proceedings Article•
14 Nov 2013TL;DR: A very close association of fuzzy planar graph is fuzzy dual graph, which is defined and studied and several properties of this graph are established.
Abstract: Fuzzy graph is now a very important research area due to its wide application. Fuzzy multigraph and fuzzy planar graphs are two subclasses of fuzzy graph theory. In this paper, we define both of these graphs and studied a lot of properties. A very close association of fuzzy planar graph is fuzzy dual graph. This is also defined and studied several properties. The relation between fuzzy planar graph and fuzzy dual graph is also established.
21 citations
TL;DR: In this paper, the similarity relations of intuitionistic fuzzy matrices are studied, together with invert- ibility conditions and eigenvalues of the intuitionistic matrices, and some properties and results for IFMs investigated, including idempotent, regularity, permutation matrix and spectral radius.
20 citations
29 Mar 2013
TL;DR: A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained.
Abstract: Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.
16 citations
01 Jan 2013
TL;DR: This paper defines multiplication between intuitionistic fuzzy matrices (IFMs) and it derives the conditions for a block IFM to be regular and a method to find the generalized inverse of it with the help of the generalized inverses of the blocks of the original matrix is described.
Abstract: In this paper we define multiplication between intuitionistic fuzzy matrices (IFMs) and we derive the conditions for a block IFM to be regular. Also a method to find the generalized inverse of it with the help of the generalized inverses of the blocks of the original matrix is described. Again, it is shown that a block intuitionistic fuzzy matrix can be decomposed into an upper triangular idempotent intuitionistic fuzzy matrix and a lower triangular idempotent intuitionistic fuzzy matrix when the decomposition is symmetric.
13 citations
01 Jan 2013
TL;DR: The notion of an interval-valued fuzzy closed ideal of a B-algebra is introduced, and some related properties are investigated.
Abstract: In this paper, we apply the concept of interval-valued fuzzy set to ideals and closed ideals in B-algebras. The notion of an interval-valued fuzzy closed ideal of a B-algebra is introduced, and some related properties are investigated. Also, the product of interval-valued fuzzy B-algebra is investigated.
13 citations
TL;DR: A new intuitionistic fuzzy optimisation (IFO) approach to solve matrix games under uncertainty to incorporate ambiguity of human judgements and converts the said problem into two conventional linear programming problems.
Abstract: This paper presents a new intuitionistic fuzzy optimisation (IFO) approach to solve matrix games under uncertainty. This approach is an application of the intuitionistic fuzzy set. First we have considered matrix game with intuitionistic fuzzy (IF) goals for each of a strategy in a payoff matrix in order to incorporate ambiguity of human judgements. The degree of membership is defined as the degree of satisfaction and the degree of nonmembership function have been taken for the degree of rejection. Then it converts the said problem into two conventional linear programming problems. Numerical example is provided to illustrate our approach.
01 Jan 2013
TL;DR: It is shown that the power of intuitionistic fuzzy matrices with maxar arithmetic mean-minarithmetic mean operation are always convergent.
Abstract: Intuitionistic fuzzy relations on finite universes can be represent by intuitionistic fuzzy matrices and the limiting behavior of the power matrices depends on the algebraic operation employed on the matrices. In this paper, the power of intuitionistic fuzzy matrices with maxarithmetic mean-minarithmetic mean operation have been studied. Here it is shown that the power of intuitionistic fuzzy matrices with the said operations are always convergent.
Proceedings Article•
14 Nov 2013TL;DR: A generalization of fuzzy competition graph known as fuzzy k-competition graph is also defined, which is related to fuzzy digraphs and some relations between fuzzy competition graphs and fuzzy neighbourhood graphs have been established.
Abstract: Fuzzy competition graph as the generalization of competition graph is introduced here. A generalization of fuzzy competition graph known as fuzzy k-competition graph is also defined. These graphs are related to fuzzy digraphs. Fuzzy neighbourhood graphs, which are related to fuzzy graphs are defined here. Some relations between fuzzy competition graphs and fuzzy neighbourhood graphs have been established. Also several results to find strong edges of the stated graphs are obtained.
TL;DR: A fuzzy simulation based hybrid genetic algorithm is designed to solve the proposed models using Prufer like code representation of labeled trees using the m λ measure, a generalization of credibility measure.
Abstract: In this paper, we have studied the constrained version of the fuzzy minimum spanning tree problem. Costs of all the edges are considered as fuzzy numbers. Using the m λ measure, a generalization of credibility measure, the problem is formulated as chance-constrained programming problem and dependent-chance programming problem according to different decision criteria. Then the crisp equivalents are derived when the fuzzy costs are characterized by trapezoidal fuzzy numbers. Furthermore, a fuzzy simulation based hybrid genetic algorithm is designed to solve the proposed models using Prufer like code representation of labeled trees.
01 Jan 2013
TL;DR: This work investigates the problem for interval graph and presents an efficient algorithm for finding the (0,1) L -labelling of the said graph.
Abstract: (0,1) L -labelling of a graph ) , ( = E V G is a function f from the vertex set ) (G V to the set of non-negative integers such that adjacent vertices get number zero apart, and vertices at distance two get distinct numbers. The goal of (0,1) L -labelling problem is to produce a legal labelling that minimize the largest label used. Since (0,1) L -labelling problem is NP-complete for general graph, we investigate the problem for interval graph and present an efficient algorithm for finding the (0,1) L -labelling of the said graph.
TL;DR: An efficient algorithm to find a minimum 2-tuple dominating set on permutation graphs with n vertices which runs in O(n2) time is presented.
Abstract: For a fixed positive integer k, a k-tuple dominating set of a graph G=(V,E) is a subset D⊆V such that every vertex in V is dominated by at least k vertex in D. The k-tuple domination number γ
×k
(G) is the minimum size of a k-tuple dominating set of G. The special case when k=1 is the usual domination. The case when k=2 was called double domination or 2-tuple domination. A 2-tuple dominating set D
2 is said to be minimal if there does not exist any D′⊂D
2 such that D′ is a 2-tuple dominating set of G. A 2-tuple dominating set D
2, denoted by γ
×2(G), is said to be minimum, if it is minimal as well as it gives 2-tuple domination number. In this paper, we present an efficient algorithm to find a minimum 2-tuple dominating set on permutation graphs with n vertices which runs in O(n
2) time.
07 Jan 2013
TL;DR: In this article, the problem of determining the economic order quantity (EOQ) in the interval sense is dealt with, and a common algorithm for the optimum production quantity (economic lot-size) per cycle of a single product (so as to minimize the total average cost) is developed.
Abstract: This paper deals with the problem of determining the economic order quantity (EOQ)in the interval sense. A purchasing inventory model with shortages and lead time, whose carryingcost, shortage cost, setup cost, demand quantity and lead time are considered as interval numbers,instead of real numbers. First, a brief survey of the existing works on comparing and ranking anytwo interval numbers on the real line is presented. A common algorithm for the optimum productionquantity (Economic lot-size) per cycle of a single product (so as to minimize the total average cost) isdeveloped which works well on interval number optimization under consideration. A numerical exampleis presented for better understanding the solution procedure. Finally a sensitive analysis of the optimalsolution with respect to the parameters of the model is examined.
01 Jan 2013
TL;DR: Fuzzy soft exterior and fuzzy soft boundary of a fuzzy soft set are introduced and some properties related to these structures are established.
Abstract: This paper deals with some structural properties of fuzzy soft topological spaces. Fuzzy soft closure and fuzzy soft interior of a fuzzy soft set are studied and investigated. Fuzzy soft exterior and fuzzy soft boundary of a fuzzy soft set are introduced and some properties related to these structures are established.
TL;DR: In this article, the bimatrix game with symmetric trapezoidal pay-off is considered and a trapezoid number ranking method for such games is defined and then a Nash equilibrium solution for pure strategies and mixed strategies is established.
Abstract: In this paper the bimatrix game with symmetric trapezoidal pay -off is considered.At first trapezoidal number ranking method for such games is defined and then we define Nash equilibrium solution for pure strategies and mixed strategies.The inequality constraints involving trapezoidal co-efficients are reduced in their satisfactory crisp equivalent form and a satisfactory solution of the problem is established.Numerical example is given to illustrate the methodology.
01 Jan 2013
TL;DR: In this article, the authors have shown that a cactus graph is cordial under some restrictions, such as the number of vertices and edges of the graph having a vertex labelling such that | (0) (1) | 1 f v v v − ≤ and |(0)(1)| 1 f f e e e − ≤.
Abstract: Suppose = ( , ) G V E be a graph with vertex set V and edge set E . A vertex labelling : {0,1} f V → induces an edge labelling * : {0,1} f E → . For {0,1} i∈ , let ( ) f v i and ( ) f e i be the number of vertices v and edges e with ( ) = f v i and ( ) = f e i respectively. A graph is cordial if there exists a vertex labelling f such that | (0) (1) | 1 f f v v − ≤ and | (0) (1) | 1 f f e e − ≤ . In this paper, we label the vertices of cactus graph by cordial labelling and have shown that cactus graph is cordial under some restrictions.
TL;DR: A new approach is proposed to characterize the notion of $\alpha$-semicompactness in terms of ordinary nets and filters in fuzzy topological spaces X and these concepts are used to define and characterize $\alpha $-se micompact crisp subsets of X.
Abstract: It is widely accepted that one of the most satisfactory generalization of the concept of compactness to fuzzy topological spaces is $\alpha$-compactness, first introduced by Gantner et al. in 1978, followed by further investigations by many others. Chakraborty et al. introduced fuzzy semicompact set and investigated and characterized fuzzy semicompact spaces in terms of fuzzy nets and fuzzy prefilterbases in 2005. In this paper, we propose to introduce a new approach to characterize the notion of $\alpha$-semicompactness in terms of ordinary nets and filters. This paper deals also with the concept of $\alpha$-semilimit points of crisp subsets of a fuzzy topological space X and the concept of $\alpha$-semiclosed sets in X and these concepts are used to define and characterize $\alpha$-semicompact crisp subsets of X.