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Fuzzy linear regression models are used to obtain an appropriate linear relation between a dependent variable and several independent variables in a fuzzy environment. Several methods for evaluating fuzzy coefficients in linear regression models have been proposed. The first attempts at estimating the parameters of a fuzzy regression model used mathematical programming methods. In this thesis, we generalize the metric defined by Diamond and use it as a criterion to estimate these parameters. Our method, is not only computationally easy to handle, but, when compared with earlier methods, has a smaller the sum of errors of estimation.

This paper considers the generation of some interpretable fuzzy rules for assigning an amino acid sequence into the appropriate protein superfamily. Since the main objective of this classifier is the interpretability of rules, we have used the distribution of amino acids in the sequences of proteins as features. These features are the occurrence probabilities of six exchange groups in the sequences. To generate the fuzzy rules, we have used some modified versions of a common approach. The generated rules are simple and understandable, especially for biologists. To evaluate our fuzzy classifiers, we have used four protein superfamilies from UniProt database. Experimental results show the comprehensibility of generated fuzzy rules with comparable classification accuracy.

Using the notion of “belongingness ($epsilon$)” and “quasi-coincidence (q)” of fuzzy points with fuzzy sets, we introduce the concept of an ($ alpha, beta$)- fuzzyHv-ideal of an Hv-ring, where , are any two of {$epsilon$, q,$epsilon$ $vee$ q, $epsilon$ $wedge$ q} with $ alpha$ $neq$ $epsilon$ $wedge$ q. Since the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy Hv-ideals is an important and useful generalization of ordinary fuzzy Hv-ideals, we discuss some fundamental aspects of ($epsilon$, $epsilon$ $vee$ q)-fuzzy Hv-ideals. A fuzzy subset A of an Hv-ring R is an ($epsilon$, $epsilon$ $vee$ q)-fuzzy Hv-ideal if and only if an At, level cut of A, is an Hv-ideal of R, for all t$epsilon$(0, 0.5]. This shows that an($epsilon$, $epsilon$ $vee$ q)-fuzzy Hv-ideal is a generalization of the existing concept of fuzzy Hv-ideal. Finally, we extend the concept of a fuzzy subgroup with thresholds to the concept of a fuzzy H_{v}-ideal with thresholds.

In this paper, we give some new definitions of M-fuzzy metric spaces and we prove a common fixed point theorem for six mappings under the condition of weakly compatible mappings in complete M-fuzzy metric spaces.

Using the notion of anti fuzzy points and its besideness to and nonquasi-coincidence with a fuzzy set, new concepts in anti fuzzy subalgebras in BCK/BCI-algebras are introduced and their properties and relationships are investigated.

In this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring R. These fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. Using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set theoretic proof of the fact that the lattice $vartheta$(R) of all fuzzy ideals of a ring R is modular.

In this paper, using pre-semi-open L-sets and their inequality, a new notion of PS-compactness is introduced in L-topological spaces, where L is a complete De Morgan algebra. This notion does not depend on the structure of the basis lattice L and L does not need any distributivity.

The concepts of fuzzy semi-ideals of R with respect to H≤R and generalized fuzzy quotient rings are introduced. Some properties of fuzzy semiideals are discussed. Finally, several isomorphism theorems for generalized fuzzy quotient rings are established.

The main purpose of this paper is to find t-best approximations in fuzzy normed spaces. We introduce the notions of t-proximinal sets and F-approximations and prove some interesting theorems. In particular, we investigate the set of all t-best approximations to an element from a set.

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