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Reliability estimation of a Network Structure using Generalized Trapezoidal Fuzzy Numbers

Kumar Amit, Dhiman Pooja

Journal of KONBiN

2021

Vol. 51, iss. 1

225--241

Classical sets are used commonly to consider reliability. Because of the uncertainty in the data (which considered in the present paper) classical sets fail to describe the reliability accurately. Uncertainty leads to fluctuation in the actual situation of the structure. Fuzzy logic method attempts to test system reliability with the benefit of membership function. Within this context, specific problems of reasoning-based approaches are studied, explored and correlated with standard reliability approaches. In this paper Generalized Trapezoidal Fuzzy numbers (GTrFN) are used to assess the structure's fuzzy reliability. The reliability of each event is assigned with different level of satisfaction and some improved operations on the generalized trapezoidal fuzzy numbers (GTrFN) are used to calculate the fuzzy boundaries for the resultant reliability of the final event along with the degree of satisfaction. Also the results are compared to demonstrate the application of the improved operations on Generalized Trapezoidal Fuzzy Numbers (GTrFN). The obtained results converge to more precise interval values as compare to the vague fuzzy number.

Orthodox and non-orthodox sets : some philosophical remarks

Pawlak Z.

Foundations of Computing and Decision Sciences

2005

Vol. 30, No. 2

133-140

We outline the relationship between classical (orthodox) sets from one side, and fuzzy and rough (non-orthodox) sets from another side. The classical concept of a set used in mathematics leads to antinomies, i.e., it is contradictory. This deficiency has, however, rather philosophical than practical meaning. Antinomies are associated with very "artificial'1 sets constructed in logic but not found in sets used in mathematics. That is why one can use mathematics safely. Fuzzy set and rough set theory are two different approaches to vagueness and are not remedy for classical set theory difficulties. Fuzzy set theory addresses graduainess of knowledge, expressed by the fuzzy membership, whereas rough set theory addresses granularity of knowledge, expressed by the indiscernibility relation. From practical point of view both theories are not competing but are rather complementary.