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Regularization Of Inverse Problems

The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

Ingredients of Locational Analysis (J. Krarup & P. Pruzan). The p-Median Problem and Generalizations (P. Mirchandani). The Uncapacitated Facility Location Problem (G. Cornuejols, et al.). Multiperiod Capacitated Location Models (S. Jacobsen). Decomposition Methods for Facility Location Problems (T. Magnanti & R. Wong). Covering Problems (A. Kolen & A. Tamir). p-Center Problems (G. Handler). Duality: Covering and Constraining p-Center Problems on Trees (B. Tansel, et al.). Locations with Spatial Interactions: The Quadratic Assignment Problem (R. Burkard). Locations with Spatial Interactions: Competitive Locations and Games (S. Hakimi). Equilibrium Analysis for Voting and Competitive Location Problems (P. Hansen, et al.). Location of Mobile Units in a Stochastic Environment (O. Berman, et al.). Index.

https://link.springer.com/content/pdf/10.1057%2Fjors.1991.208.pdf

Discrete location theory

Models in Ecology

Sustainable supplier selection: A multi-criteria intuitionistic fuzzy TOPSIS method

Doubt intuitionistic fuzzy hyper filters in hyper BE-algebras

One important problem in graph theory is graph coloring or graph labeling. Labeling problem is a well-studied problem due to its wide applications, especially in frequency assignment in (mobile) communication system, coding theory, ray crystallography, radar, circuit design, etc. For two non-negative integers, labeling of a graph is a function from the node set to the set of non-negative integers such that if and if, where it represents the distance between the nodes. Intersection graph is a very important subclass of graph. Unit disc graph, chordal graph, interval graph, circular-arc graph, permutation graph, trapezoid graph, etc. are the important subclasses of intersection graphs. In this chapter, the authors discuss labeling for intersection graphs, specially for interval graphs, circular-arc graphs, permutation graphs, trapezoid graphs, etc., and have presented a lot of results for this problem.

L(h,k)-Labeling of Intersection Graphs

In this paper, we have studied some properties of imprecise numbers, namely, interval numbers and triangular fuzzy numbers. Also we studied the imprecise matrices of different kinds. Using the operations defined on them, we have proposed the orthogonality of such matrices and some theorem for those type of orthogonal matrices.

Orthogonality of Imprecise Matrices

In this chapter, the authors establish decomposition theorems of Generalized Interval-Valued Intuitionistic Fuzzy Sets (GIVIFS) by use of cut sets of generalized interval-valued intuitionistic fuzzy sets. First, new definitions of eight kinds of cut sets generalized interval-valued intuitionistic fuzzy sets are introduced. Second, based on these new cut sets, the decomposition generalized interval-valued intuitionistic fuzzy sets are established. The authors show that each kind of cut sets corresponds to two kinds of decomposition theorems. These results provide a fundamental theory for the research of generalized interval-valued intuitionistic fuzzy sets.

Decomposition Theorem of Generalized Interval-Valued Intuitionistic Fuzzy Sets

In this chapter, a very important class of graphs called intersection graph is introduced. Based on the geometrical representation, many different types of intersection graphs can be defined with interesting properties. Some of them—interval graphs, circular-arc graphs, permutation graphs, trapezoid graphs, chordal graphs, line graphs, disk graphs, string graphs—are presented here. A brief introduction of each of these intersection graphs along with some basic properties and algorithmic status are investigated.

Madhumangal Pal

Papers

Doubt intuitionistic fuzzy hyper filters in hyper BE-algebras

L(h,k)-Labeling of Intersection Graphs

Orthogonality of Imprecise Matrices

Decomposition Theorem of Generalized Interval-Valued Intuitionistic Fuzzy Sets

An Introduction to Intersection Graphs