In recent years, there has been a growing interest in multi-bit error correction codes (ECCs) to protect SRAM memories. This has been caused by the increased number of multiple errors that memories suffer as technology scales. To be suitable to protect an SRAM memory, an ECC has to be decodable in parallel and with low latency. Among the codes proposed for memory protection are orthogonal latin square (OLS) codes that provide low latency decoding and a modular construction. For some applications, like multimedia or signal processing, the effect of errors on the memory bits can be very different depending on their position on the word. Therefore, in these cases, it is more effective to provide different degrees of error correction for the different bits. This is done with unequal error protection (UEP) codes. In this paper, UEP codes are derived from double error correction (DEC) OLS codes. The derived codes are implemented for an FPGA platform to evaluate the decoder complexity and latency. The results show that the new codes can be implemented with lower decoding delay than traditional SEC-DED codes and with a cost similar to that of both DEC OLS and SEC-DED codes.

This paper introduces strict fuzzy orderings in the framework of similarity-based fuzzy orderings, i.e. where a context of similarity/indistinguishability is given by means of a fuzzy equivalence relation. We consider how to construct strict fuzzy orderings from partial fuzzy orderings and vice versa. The appropriateness of the concepts introduced in this paper is underlined by theoretical results and examples. We observe that the strongest results are achieved if the underlying triangular norm induces an involutive residual negation.

For a fixed integral commutative cl-monoid M=(L, ≤, *), introducing the notions of M-partitions and M-equivalence relations as the extensions of T-partitions and T-equivalence relations to the integral commutative cl-monoid M=(L, ≤, *), respectively, it is shown that the previous approaches on T-partitions and T-equivalence relations can be unified, and most of the results in these works can be easily stated based on the integral commutative cl-monoid M=(L, ≤, *). Modifying the notion of T-redundancy of finite family of fuzzy sets of a nonempty ordinary set X, it is extended to arbitrary family of L-fuzzy sets on the basis of the integral commutative cl-monoid M, and is shown that the proposed definition has more desirable properties than the previous one. Furthermore, handling the works of Höhle, Klawonn, Gebhardt and Kruse on fuzzy partitions and fuzzy equivalence relations, some of their results are improved, and several new results in this direction are pointed out.

Two fundamental questions on the extensions of many-valued equivalence relations, whose solutions have a crucial concern for the applications of many-valued equivalence relations, are explicitly stated to characterize the extensions of many-valued equivalence relations. Thereafter introducing the satisfactory solutions of these questions, the desirable characterizations of the extensions of many-valued equivalence relations are pointed out.

In this paper, deriving the type-m fuzzy sets, intuitionistic fuzzy sets, Φ-fuzzy sets, rough sets, fuzzy rough sets and rough fuzzy sets as particular genuine sets, and establishing their connections with genuine sets, it is demonstrated that the theory of genuine sets provides a powerful tool to model various different kinds of uncertainty in a mathematical way. Furthermore, it is also shown that the genuine set theoretic descriptions of type-m fuzzy sets, intuitionistic fuzzy sets and fuzzy rough sets point out new features of these set notations, originated from the peculiar characteristics of genuine sets.