Lemnaouar Zedam

Based on the concept of Atanassov’s intuitionistic fuzzy set on a universe X, we introduce the concepts of intuitionistic fuzzy ideals and intuitionistic fuzzy filters on an intuitionistic fuzzy lattice. More specifically, we provide characterizations of these concepts in terms of the intuitionistic fuzzy lattice meet and join operations, in terms of some associated fuzzy sets, as well as, in terms of their crisp level sets. Furthermore, we introduce the concepts of prime intuitionistic fuzzy ideals (resp. filters) as interesting kinds, and investigate their various properties and characterizations.

Recently, Milles and Hammami presented and studied the concept of a neutrosophic topology generated by a neutrosophic relation. As a continuation in the same direction, this paper studies the concepts of neutrosophic ideals and neutrosophic filters on that topology. More precisely, we offer the lattice structure of neutrosophic open sets of a neutrosophic topology generated via a neutrosophic relation and examine its different characteristics. Furthermore, we enlarge to this lattice structure the notions of ideals (respectively, filters) and characterize them with regard to the lattice operations. We end this work by studying the prime neutrosophic ideal and prime neutrosophic filter as interesting types of neutrosophic ideals and neutrosophic filters.

Recently, we have introduced and studied all possible four-point compositions (one degree of freedom) and five-point compositions (two degrees of freedom) of ternary relations in analogy with the usual composition of binary relations. In this paper, we introduce and study new types of compositions of ternary relations inspired by the compositions of binary relations introduced by Bandler and Kohout (BK-compositions, for short). Moreover, we pay particular attention to the link between BK-compositions and the traces of binary relations and use it as source of inspiration to introduce traces of ternary relations. Moreover, we show that these new notions of BK-compositions and traces are useful tools to solve some relational equations in an unknown ternary relation.

Social and economic factors, such as education, employment, social support, income, and community safety, can directly affect how well and long we live. Under the presence of the above factors, we easily look at health decisions, afford medical care and housing, manage stress, and so on. In this analysis, we derive the Choquet-integral aggregation operators based on Hamacher t-norm and t-conorm for complex Atanassov intuitionistic fuzzy (CAIF) such as CAIF Choquet-integral Hamacher averaging (CAIFCIHA), CAIF Choquet-integral Hamacher ordered averaging (CAIFCIHOA), CAIF Choquet-integral Hamacher geometric (CAIFCIHG), CAIF Choquet-integral Hamacher ordered geometric (CAIFCIHOG) operators and exposed their properties. Additionally, we discover the Technique for Order Preference by Similarity to the Ideal Solution “TOPSIS” technique under the consideration of the above-derived theory. Moreover, it is very famous and interesting to note that various unpredicted factors such as road, diesel prices, weather, and traffic conditions affect the cost of transportation. Therefore, decision-makers deal with vague and unreliable information to estimate the cost of transportation. To evaluate the above problem, we select a transportation problem with CAIF parameters, and for its evaluation, a simple and well-known computational technique is derived and illustrated. Finally, we compared our derived results with some prevailing results to show the worth and reliability of the exposed approaches.

In this paper, we introduce the notion of pseudo-triangular norm (pseudo-t-norm, for short) as a classes of weakly associative operations on trellises and as a generalization of triangular norm (t-norm, for short) on bounded trellises and we investigate their various properties and present some constructions of pseudo-t-norms on bounded trellises. Also, we study the T-distributivity on bounded trellises. Moreover, we show the relationship among pseudo-t-norms and isomorphisms on bounded trellises, which are more complicated in absence of the property of (transitivity) associativity of the trellis meet and join operations.

In this paper, we introduce the notion of a t-norm on bounded pseudo-ordered sets and in particular on bounded trellises (also known as weakly associative lattices), and provide some basic examples. The impact of abandoning transitivity is considerable: on a proper bounded trellis, the meet operation is not a t-norm, and there might actually exist no or even multiple maximal t-norms. We provide a first generic construction method that allows to extend a t-norm on an interior range of a given $\meet$-semi-trellis to the entire $\meet$-semi-trellis. Also, we discuss at length an instantiation of this method based on a particular interior range, namely a finite sub-trellis of the set of right-transitive elements of a given trellis. We pay specific attention to bounded pseudo-chains and modular trellises.