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Interval Valued and Thresholds based L-fuzzy Ideals of Nearrings

Jagadeesha, B (2015) Interval Valued and Thresholds based L-fuzzy Ideals of Nearrings. Phd. Thesis thesis, Manipal Institute of Technology, Manipal.

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Abstract

The thesis entitled “Interval Valued and Thresholds based L-Fuzzy Ideals of Nearrings” relates algebraic structures namely rings and nearrings to graph theory, lattice theory, fuzzy set theory and rough set theory. In this thesis, the upper and lower bounds for the number of automorphisms on a finite lattice are obtained. Different relations between t-norms, t-conforms using automorphisms and negations are discussed. Definitions of drastic t-norm, drastic t-conorm on a lattice are applied to get different implication operators. The thesis presents a unified approach to define interval valued L-fuzzy ideals of nearrings by incorporating interval valued tnorms and t-conorms. A highlight of the thesis is that the interval valued t-norms and interval valued t-conormsunder consideration are not necessarily idempotent and the lattice need not be distributive.A characterization of interval valued L-fuzzy ideals and their prime forms are given in terms of level sets. Prime graphs of a nearing are studied and the relation between nearringhomomorphism and graph homomorphism is provided. Rough set approximations of interval valued L-fuzzy ideal using set valued homomorphisms and congruence relations are derived.

Item Type: Thesis (Phd. Thesis)
Subjects: Engineering > MIT Manipal > Mathematics
Depositing User: MIT Library
Date Deposited: 28 Jun 2016 14:49
Last Modified: 28 Jun 2016 14:49
URI: http://eprints.manipal.edu/id/eprint/146418

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