In this paper, an inventory model has been developed with trade credit financing and back orders under human learning. In this model, it is considered that the seller provides a credit period to his buyer to settle the account and the buyer accepts the credit period policy with certain terms and conditions. The impact of learning and credit financing on the size of the lot and the corresponding cost has been presented. For the development of the model, demand and lead times have been taken as the fuzzy triangular numbers are fuzzified, and then learning has been done in the fuzzy numbers. First of all, the consideration of constant fuzziness is relaxed, and then the concept of learning in fuzzy under credit financing is joined with the representation, assuming that the degree of fuzziness reduces over the planning horizon. Finally, the expected total fuzzy cost function is minimized with respect to order quantity and number of shipments under credit financing and learning effect. Lastly, sensitive analysis has been presented as a consequence of some numerical examples.
As an analogue here we extend and give new horizon to semimodule theory by introducing fuzzy exact and proper exact sequences of fuzzy semi modules for generalizing well known theorems and results of semimodule theory to their fuzzy environment. We also elucidate completely the characterization of fuzzy projective semi modules via Hom functor and show that semimodule µP is fuzzy projective if and only if Hom(µP ,–) preservers the exactness of the sequence µM′ α¯−→νM β¯ −→ηM′′ with β¯ being K-regular. Some results of commutative diagram of R-semimodules having exact rows specifically the “5-lemma” to name one, were easily transferable with the novel proofs in their fuzzy context. Also, towards the end apart from the other equivalent conditions on homomorphism of fuzzy semimodules it is necessary to see that in semimodule theory every fuzzy free is fuzzy projective however the converse is true only with a specific condition.
The purpose of this paper is to introduce a new category of fuzzy automata based on complete residuated lattice. We introduce and study the categorical concepts such as product, equalizer and their duals in this category. Finally, we establish a construction of a minimal fuzzy automaton for a given fuzzy language in a categorical framework. The construction of such fuzzy automaton is based on derivative of a given fuzzy language.
The present paper is devoted to the study of k, t, d −proximity on rough sets from the relation point of view. The operator O0(φ,Α) and O(φ,Α) is defined using the upper approximation and closure operators derived from the relation. The properties of induced operator and their connections are henceforth obtained. Moreover, our approach represents a new generalization of the operator using upper approximation only.
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