iosr-Jm   National Conference On Discrete Mathematics & Computing (NCDMC-2017)

Abstract: In this paper, we study the topological structure of multi-fuzzy rough sets based on fuzzy logical operators. We discuss the relationship between generalized multi-fuzzy rough sets and multi-fuzzy topological spaces. This paper examines the peculiarities of approximation operators when the associated binary relation 𝑅 is reflexive and transitive. We obtain the conditions under which the collection of ℐ-lower approximation sets becomes a multi-fuzzy topology. It is seen that the reflexivity and transitivity of relation 𝑅 and the properties of the implicator ℐ play a role in describing the topological structure of (ℐ−𝒯) multi-fuzzy rough sets.

[1]. Atanassov, K. T. (1986). Intuitionistic Fuzzy Set. Fuzzy Sets and Systems.
[2]. Baczynski, M., & Jayaram, B. (2008). Fuzzy_Implications.pdf. Springer.
[3]. Chang, C. L. (1968). Fuzzy topological spaces. Journal of Mathematical Analysis and Applications, 110(1), 141–178.
[4]. Çoker, D. (1997). An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets and Systems, 88(1), 81–89.
[5]. Goguen, J. . (1967). L-fuzzy sets. Journal of Mathematical Analysis and Applications, 18(1), 145–174.

Abstract: Multiple set theory is a new mathematical approach to handle vagueness together with multiplicity. Multiple set is expert in formalising numerous properties of objects multifariously. This paper proposes a generalization for t-norms and t-conorms on multiple sets. Recently, a study on the concept of uninorm aggregation operators on bounded lattice has been done.................
Keywords – Aggregation operator, multiple set, t-norm, t-conorm, uninorm.

[1]. Zadeh, Lotfi A. "Fuzzy sets." Information and control 8(3), 1965, 338-353.
[2]. Gau, Wen-Lung, and Daniel J. Buehrer. "Vague sets." IEEE transactions on systems, man, and cybernetics 23(2),1993, 610-614.
[3]. Atanassov, Krassimir T. "Intuitionistic fuzzy sets." Fuzzy sets and Systems 20(1),1986, 87-96.
[4]. Sebastian, Sabu, and T. V. Ramakrishnan. "Multi-fuzzy sets." International Mathematical Forum. 5(50), 2010.
[5]. Yager, Ronald R. "On the theory of bags." International Journal of General System 13(1), 1986, 23-37.

Abstract: Let tt : (V, E, W ) be a finite, connected, weighted graph without loops and multiple edges. In a weighted graph each arc is assigned a weight by the weight function W............
Keywords: Geodesic, graph convexity, intervals in graphs.

[1]. J. A. Bondy, G. Fan, Cycles in weighted graphs, Combinatorica 11, pp. 191- 205, (1991).
[2]. J. A. Bondy, G. Fan, Optimal paths and cycles in weighted graphs , Ann. Discrete Mathematics 41, pp. 53-69 (1989).
[3]. F. Buckley and F. Harary, Distance in Graphs. Addision-Wesley, Redwood City, CA (1990).
[4]. J. Caceres, M. L. Puertas, Searching for geodetic boundary vertex sets, Elec- tronic Notes in Discrete Mathematics (ELSEVIER), 19, pp. 25-31, 2005.
[5]. G. A. Dirac, Some theorems on abstract graphs, Proc. London Math. Soc. (3) 2, pp. 69 - 81 (1952)

Abstract: In this paper, we define conjugate multisets and establish some of its properties. Corresponding to every multiset, a unique upper triangu- lar nonsingular matrix is formed by making use of this conjugate multiset. A novel approach in encryption and decryption is made using multisets and conjugate multisets.
Keywords: Multiset, Integer partition, Conjugate partition, Conjugate multiset, Encryption, Decryption

[1]. K. P. Girish and Sunil Jacob John. (2009). Relations and functions in multiset context. Information sciences. 179. 758–768.
[2]. Chris Brink. (1988). Multisets and the Algebra of Relevance logic. Non- Classical Logic. 5. 75–95.
[3]. C. S. Calude , G. Paun , G. Rozenberg and A. Salomaa. (2001).
[4]. Mathematics of Multisets. Springer Verlag. 347–358
[5]. N.J.Wildberger. (2003). A new look at multisets. School of Mathematics UNSW Sydney 2053.

Abstract: In this paper some simple categorical aspects of c-spaces are at- tempted. Separators and co-separators are characterized.

[1] Bo¨rger, R. Connectivity Spaces and Component Categoreis, Categorical Topology, Proc. Con- ference Toledo, Ohio, 71 − 89, 1983.
[2] Dugowson, S. On Connectivity Spaces, arXiv: 1001.2378v1 [math.GN], 2010.
[3] Heijmans, H. J. A. M. Connected Morphological Operators for Binary Images, Computer Vision and Image Understanding Vol.73, No.1, 99 − 120, 1999.
[4] Kong, T. Y., Roscoe, A. W. and Rosenfeld, A. Concept of Digital Topology, Topology Appl., 219-262, 1992.
[5] Muscat, J. and Buhagiar, D. Connective Spaces, Mem. Fac. Sci. Shimane Univ. Series B: Mathematical Science, 39,, 1 − 13, 2006

Abstract:Multiple set theory is a new mathematical approach to handle vagueness together with multiplicity. Multiple set is expert in formalising numerous properties of objects multifariously. This paper proposes a generalization for t-norms and t-conorms on multiple sets. Recently, a study on the concept of uninorm aggregation operators on bounded lattice has been done............
Keywords: Aggregation operator, multiple set, t-norm, t-conorm, uninorm.

[1]. Zadeh, Lotfi A. "Fuzzy sets." Information and control 8(3), 1965, 338-353.
[2]. Gau, Wen-Lung, and Daniel J. Buehrer. "Vague sets." IEEE transactions on systems, man, and cybernetics
23(2),1993, 610-614.
[3]. Atanassov, Krassimir T. "Intuitionistic fuzzy sets." Fuzzy sets and Systems 20(1),1986, 87-96.
[4]. Sebastian, Sabu, and T. V. Ramakrishnan. "Multi-fuzzy sets." International Mathematical Forum. 5(50), 2010.
[5]. Yager, Ronald R. "On the theory of bags." International Journal of General System 13(1), 1986, 23-37.