Fuzziness and Fuzzy Equality

An entropy based solid transportation problem for general fuzzy costs and time with fuzzy equality

Mathematical and Computer Modelling ◽

10.1016/j.mcm.2009.04.010 ◽

2009 ◽

Vol 50 (1-2) ◽

pp. 166-178 ◽

Cited By ~ 47

Author(s):

A. Ojha ◽

B. Das ◽

S. Mondal ◽

M. Maiti

Keyword(s):

Transportation Problem ◽

Solid Transportation Problem ◽

Fuzzy Equality

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NORMALIZATION IN TYPE-2 FUZZY RELATIONAL DATA MODEL BASED ON FUZZY FUNCTIONAL DEPENDENCY USING FUZZY FUNCTIONS

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488512500067 ◽

2012 ◽

Vol 20 (01) ◽

pp. 99-138 ◽

Cited By ~ 2

Author(s):

P. C. SAXENA ◽

D. K. TAYAL

Keyword(s):

Relational Databases ◽

Normal Forms ◽

Functional Dependency ◽

Data Dependencies ◽

Redundant Storage ◽

Membership Value ◽

Definition Of ◽

Relationship Of ◽

Fuzzy Equality

In fuzzy relational databases, the data dependencies, especially the fuzzy functional dependency(ffd) plays an important role in maintaining the consistency of the database and in avoiding the redundant storage of the data. In the past, it has been shown that the type-2 fuzzy relational databases captures impreciseness and incompleteness in data in a better way. The aim of this paper is to provide the concepts for database normalization in a type-2 fuzzy relational database, so that the normalized schemas can be obtained. Here, we deal with the fuzzy functional dependency(ffd) based normalization of type-2 fuzzy relational databases. We use the concepts of fuzzy functions to derive the fuzzy equality and using this fuzzy equality, we define a new definition of fuzzy functional dependency. First we discuss various approaches proposed by the researchers in this context and show why our fuzzy functional dependency is better, as compared to the earlier ffds proposed by the researchers. We call our ffd as non-0 LHS ffd. We identify an anomaly called "spurious ffd" and show that some of the significant contributions proposed by the earlier researchers are suffering from this anomaly, but the non-0 LHS ffd does not suffer from it. Then, we prove that the set of inference rules for the non-0 LHS ffd are sound and complete. We use the definition of non-0 LHS ffd in obtaining the first three normal forms upto BCNF for type-1 and type-2 fuzzy relational schemas. The result of the decomposition and the procedure to obtain the membership value of the decomposed relations is proposed. The associated concepts like the fuzzy key, fuzzy superkey, fuzzy foreign key are defined in terms of non-0 LHS ffd. On the basis of these concepts, we define full ffd, partial ffd etc. In the last, we show that in our case, the relationship of total-ordering between the three normal forms in classical relational databases is also observed.

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FUZZY LOGIC WITH EQUALITY

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001488000212 ◽

1988 ◽

Vol 02 (02) ◽

pp. 351-365 ◽

Cited By ~ 7

Author(s):

CHURN JUNG LIAU ◽

BERTRAND I-PENG LIN

Keyword(s):

Fuzzy Logic ◽

Word Problems ◽

Term Rewriting ◽

Computational Logic ◽

Term Rewriting System ◽

Fuzzy Algebra ◽

Algorithmic Solution ◽

Computational Paradigm ◽

Fuzzy Equality ◽

Order Predicate Calculus

The concept of fuzzy equality and its related contents to the first order predicate calculus are discussed. It is proved that, in the viewpoint of computational logic, resolution and paramodulation mechanisms are complete and sound for fuzzy logic with equality. Term rewriting system, that is the set of left to right directional equations, provides an essential computational paradigm for word problems in universal algebra. We embody the fuzzy equality to the theory of this computation system and give an algorithmic solution to the word problems in fuzzy algebra.

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On fuzzy equality and approximation in fuzzy logic

Soft Computing ◽

10.1007/s00500-003-0324-9 ◽

2003 ◽

Vol 8 (10) ◽

pp. 668-675 ◽

Cited By ~ 3

Author(s):

V. Nov�k

Keyword(s):

Fuzzy Logic ◽

Fuzzy Equality

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Solving a Fully Fuzzy Linear Programming Problem through Compromise Programming

Journal of Applied Mathematics ◽

10.1155/2013/726296 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Haifang Cheng ◽

Weilai Huang ◽

Jianhu Cai

Keyword(s):

Linear Programming ◽

Programming Problem ◽

Linear Programming Problem ◽

Fuzzy Numbers ◽

Equality Constraints ◽

Compromise Programming ◽

Fuzzy Linear Programming ◽

Programming Approach ◽

Optimal Value ◽

Fuzzy Equality

In the current literatures, there are several models of fully fuzzy linear programming (FFLP) problems where all the parameters and variables were fuzzy numbers but the constraints were crisp equality or inequality. In this paper, an FFLP problem with fuzzy equality constraints is discussed, and a method for solving this FFLP problem is also proposed. We first transform the fuzzy equality constraints into the crisp inequality ones using the measure of the similarity, which is interpreted as the feasibility degree of constrains, and then transform the fuzzy objective into two crisp objectives by considering expected value and uncertainty of fuzzy objective. Since the feasibility degree of constrains is in conflict with the optimal value of objective function, we finally construct an auxiliary three-objective linear programming problem, which is solved through a compromise programming approach, to solve the initial FFLP problem. To illustrate the proposed method, two numerical examples are solved.

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