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In this paper, we study the problem of closing or opening a ternary relation with respect to various relational properties, with a focus on the many transitivity properties that have been proposed for ternary relations over the pa...
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In this paper, we study the problem of closing or opening a ternary relation with respect to various relational properties, with a focus on the many transitivity properties that have been proposed for ternary relations over the past years. In particular, we consider the transitivity properties corresponding to the six relational compositions of ternary relations recently introduced by Bakri et al., making a careful distinction between the four associative ones and the two non-associative ones.
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In this paper, we generalize the notion of traces of a binary relation to the setting of ternary relations. With a given ternary relation, we associate three binary relations: its left, middle and right trace. As in the binary cas...
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In this paper, we generalize the notion of traces of a binary relation to the setting of ternary relations. With a given ternary relation, we associate three binary relations: its left, middle and right trace. As in the binary case, these traces facilitate the study and characterization of properties of a ternary relation. Interestingly, the traces themselves turn out to be the greatest solutions of relational inequalities associated with newly introduced compositions of a ternary relation with a binary relation (and vice versa).
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Soft set theory initiated by Molodtsov in 1999 has been emerging as a generic mathematical tool for dealing with uncertainty. A noticeable progress is found concerning the practical use of soft set in decision-making problems. The...
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Soft set theory initiated by Molodtsov in 1999 has been emerging as a generic mathematical tool for dealing with uncertainty. A noticeable progress is found concerning the practical use of soft set in decision-making problems. The purpose of this manuscript is to explore the novel of multi-valued picture fuzzy set (MPFS) and multi-valued picture fuzzy soft set (MPFSS) which are the generalizations of the notions of picture fuzzy soft set (PFSS) and multi-fuzzy soft set (MFSS). This notion can be used to express fuzzy information in more general and effective way. In particular, some basic operations such as union, intersection, complement and product of the proposed MPFSS are developed, and their properties are investigated. Furthermore, some aggregation operators corresponding to the proposed MPFSSs are called multi-picture fuzzy soft weighted averaging, multi-picture fuzzy soft ordered weighted averaging and multi-picture soft hybrid weighted averaging operators for a collections of MPFSSs are also developed. Moreover, based on these operators, we presented a new method to deal with the multi-attribute group decision-making problems under the multi-valued picture fuzzy soft environment. Finally, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods. The graphical interpretation of the explored approaches is also utilized with future directions.
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In this paper, we introduce six basic types of composition of ternary relations, four of which are associative. These compositions are based on two types of composition of a ternary relation with a binary relation recently introdu...
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In this paper, we introduce six basic types of composition of ternary relations, four of which are associative. These compositions are based on two types of composition of a ternary relation with a binary relation recently introduced by Zedam et al. We study the properties of these compositions, in particular the link with the usual composition of binary relations through the use of the operations of projection and cylindrical extension.
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The ideas of q-rung ortho pair fuzzy set (q-ROPFS) and interval-valued q-rung ortho pair fuzzy set (IVq-ROPFS) are two major recent developments in the field of fuzzy set theory. A q-ROPFS and IVq-ROPFS improved the limited struct...
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The ideas of q-rung ortho pair fuzzy set (q-ROPFS) and interval-valued q-rung ortho pair fuzzy set (IVq-ROPFS) are two major recent developments in the field of fuzzy set theory. A q-ROPFS and IVq-ROPFS improved the limited structures of Pythagorean fuzzy set, intuitionistic fuzzy set as well as fuzzy set by improving the conditions that makes these concepts restricted. The goal of this research is to introduce a new notion of interval-valued q-rung ortho pair fuzzy graph (IVQ-ROPFG) and to study the related graphical terms such as subgraph, complement, degree of vertices and path etc. Each of the graphical concept is demonstrated with an example. Another valuable contribution of this manuscript is the modeling of some traffic networks, telephone networks and social networks using the concepts of IVQ-ROPFGs. First, the famous problem of finding a shortest path in a traffic network is studied using two different approaches. A study of social network describing the strength of co-authorship between different researchers from several countries is also established using the concept of IVq-ROPFGs. Finally, a telephone networking problem is demonstrated showing the calling ratios of incoming and outgoing calls among a group of people. Two engineering decision-making problems are also studied using some aggregation operators and the concepts of IVq-ROPFGs. Through comparative study, the advantages of working in the environment of IVq-ROPFG are specified.
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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 transi...
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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 perpendicular to-semi-trellis to the entire perpendicular to-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. (c) 2023 Elsevier B.V. All rights reserved.
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In this paper, we study and characterize some properties of a given binary operation on a lattice. More specifically, we show necessary and sufficient conditions under which a binary operation on a lattice coincides with its meet ...
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In this paper, we study and characterize some properties of a given binary operation on a lattice. More specifically, we show necessary and sufficient conditions under which a binary operation on a lattice coincides with its meet (resp. its join) operation. Importantly, we construct two new posets based on a given binary operation on a lattice and investigate some cases that these two posets have a lattice structure. Moreover, we provide some representations of a given lattice based on these new constructed lattices.
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In a recent paper, we have introduced the notion of clone relation of a given binary relation. Intuitively, two elements are said to be clones if they are related in the same way w.r.t. every other element. In this paper, we gener...
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In a recent paper, we have introduced the notion of clone relation of a given binary relation. Intuitively, two elements are said to be clones if they are related in the same way w.r.t. every other element. In this paper, we generalize this notion from pairs of elements to sets of elements of any cardinality, resulting in the introduction of clonal sets. We investigate the most important properties of clonal sets, paying particular attention to the introduction of the clonal closure operator, to the analysis of the (lattice) structure of the set of clonal sets and to a distance metric expressing how close two elements are to being clones.
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Recently, Jun et al. have introduced the concept of cubic set as a generalization of the concept of fuzzy set and that of the interval valued fuzzy set. This concept has been widely applied in many circumstances like pattern recog...
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Recently, Jun et al. have introduced the concept of cubic set as a generalization of the concept of fuzzy set and that of the interval valued fuzzy set. This concept has been widely applied in many circumstances like pattern recognition, decision making etc. So far, no attention has been paid towards graph of cubic set therefore leads us in this manuscript to study the concepts of interval valued bipolar fuzzy graph (IVBFG) and cubic bipolar fuzzy graph (CBFG). Some graph theoretic terms for CBFGs are defined along with the several operations. Illustrative examples are provided to explain the defined terms and several results are discussed. As application, a cubic bipolar fuzzy influence graph in a social group is elaborated.
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Recently, De Baets et al. have characterized the fuzzy tolerance relations that a given strict order relation is compatible with. In general, the compatibility of a strict order relation with a binary fuzzy relation guarantees als...
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Recently, De Baets et al. have characterized the fuzzy tolerance relations that a given strict order relation is compatible with. In general, the compatibility of a strict order relation with a binary fuzzy relation guarantees also the compatibility of its associated betweenness relation with that binary fuzzy relation. In this paper, we study the compatibility of an arbitrary ternary relation with a binary fuzzy relation. We prove that this compatibility can be expressed in terms of inclusions of the binary fuzzy relation in the traces of the given ternary relation.
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