Abstract

We introduce the notions of (L,M)-double fuzzy grill bases where L and M are strictly two-sided, commutative quantales. We investigate the relationships between (L,M)- double fuzzy grill and (L,M)-double fuzzy grill bases. Furthermore, we investigate the image of (L,M)-double fuzzy grills.

Highlights

  • As a generalization of fuzzy sets, the notion of intuitionistic fuzzy sets was introduced by Atanassov [3,4]

  • Working under the name “intuitionistic” did not continue because doubts were thrown about the suitability of this term, especially when working in the case of complete lattice L

  • These doubts were quickly ended in 2005 by Garcia and Rodabaugh [10]. They proved that this term is unsuitable in mathematics and applications

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Summary

Introduction

As a generalization of fuzzy sets, the notion of intuitionistic fuzzy sets was introduced by Atanassov [3,4]. We always assume that (L, ≤, ⊙, ⊕,′ ) (respectively, (M, ≤ , ⊙, ⊕,′ )) is a stsc-quantale with an order-reversing involution ′ and the binary operation ⊕ is defined by:. [2] The pair (G, G∗) of maps G, G∗ : LX → M is called an (L, M )-double fuzzy grill on X if it satisfies the following conditions:. The pair (B, B∗) of maps B, B∗ : LX → M is called an (L, M )-double fuzzy grill base on X if it satisfies the following conditions:. Let (B1, B1∗) and (B2, B2∗) be two (L, M )-double fuzzy grill bases on X and Y respectively, and f : X → Y be a map.

Then we obtain
We obtain
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