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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

In a graph G, a spanning tree T is said to be a tree t-spanner of the graph G if the distance between any two vertices in T is at most t times their distance in G. The tree t-spanner has many applications in networks and distributed environments. In this paper, we present an algorithm to find a tree 4-spanner on trapezoid graphs in O(n) time, where n is the number of vertices.

A linear time algorithm to construct a tree 4-spanner on trapezoid graphs

In this study, Dombi operations are introduced on two m-polar fuzzy sets (mFSs). Here, Dombi operation on m-polar fuzzy numbers (mFNs), some new averaging and geometric averaging operators, namely mF Dombi weighted averaging (mFDWA) operator, mF Dombi ordered weighted averaging (mFDOWA) operator, mF Dombi hybrid weighted averaging (mFDHWA) operator, mF Dombi weighted geometric (mFDWG) operator, mF Dombi ordered weighted geometric (mFDOWG) operator, and mF Dombi hybrid weighted geometric (mFDHWGA) operator, have been proposed. Further, some properties like idempotency, boundedness, monotonicity, and commutativity are established. Next, a multi-attribute decision-making (MADM) method in mFNs environment based on mFDWA and mFDWG operators is constructed. Finally, an application of the present MADM method for selecting the best location for the construction of thermal power stations is presented. The present approach with the existing procedure is also compared and a sensitivity analysis of the proposed plan is given.

Some m-polar fuzzy operators and their application in multiple-attribute decision-making process

The aim of fuzzy intersection graph is twofold: to work with objects with continuum grades of membership and to acknowledge their inter-relationships. Its working elements are fuzzy logic and reasoning with the objective of providing accessible representation of objects and relationships having a blurry backdrop. This article embarked a comprehensive study of fuzzy intersection graph using fuzzy geometry by defining fuzzy graph and fuzzy intersection region with the help of fuzzy points and fuzzy line segments. The main motive behind revamping fuzzy graphs using fuzzy geometry is to represent the linguistic variables and their inter-dependencies as an exact reflection of human thinking. We have interpreted a detailed study on parallel fuzzy lines and intersecting fuzzy lines and deduced a mathematical relation between the measure of parallelness and degree of intersection of fuzzy lines. Fuzzy intersection region, depending on the types of intersecting fuzzy sets, plays an important role. We have defined few of the most important and useful classes of fuzzy intersection graph from fuzzy geometric view point that will be helpful in expressing human thoughts and communication of information as has been demonstrated through an application on supplier–purchaser relationship in any business. The present study on fuzzy interval graph in detail, ensued in obtainment of results that nullified previously obtained results arising the question—are fuzzy interval graphs always strong intersection graphs?

Fuzzy intersection graph: a geometrical approach

Molodtsov initiated soft set theory which has provided a general mathematical framework for handling uncertainties that occur in various real life problems. The aim of this paper is to provide fuzzy soft algebraic tools in considering many problems that contain uncertainties. In this article, the notion of $(\in_\alpha,\in_\alpha\vee q_\beta)$-fuzzy soft $BCI$-subalgebra of $BCI$-algebra is introduced. Some operational properties on $(\in_\alpha,\in_\alpha\vee q_\beta)$-fuzzy soft $BCI$-subalgebras are discussed as well as lattice structures of this kind of fuzzy soft set on $BCI$-subalgebras are derived.

On $(\in_\alpha,\in_\alpha\vee q_\beta)$-fuzzy Soft $BCI$-algebras

In this paper, the concept of semiring of generalized interval-valued intuitionistic fuzzy matrices are introduced and have shown that the set of GIVIFMs forms a distributive lattice. Also, prove that the GIVIFMs form an generalized interval valued intuitionistic fuzzy algebra and vector space over (0,1). Some properties of GIVIFMs are studied using the definition of comparability of GIVIFMs. Subject classification: 06D72 • 15B15

/pdf/semiring-of-generalized-interval-valued-intuitionistic-fuzzy-468qx7gptx.pdf

Madhumangal Pal

Papers

A linear time algorithm to construct a tree 4-spanner on trapezoid graphs

Some m-polar fuzzy operators and their application in multiple-attribute decision-making process

Fuzzy intersection graph: a geometrical approach

On $(\in_\alpha,\in_\alpha\vee q_\beta)$-fuzzy Soft $BCI$-algebras

Semiring of Generalized Interval-valued Intuitionistic Fuzzy Matrices