In practical multi-attribute group decision-making (MAGDM) problems, it is common to utilize heterogeneous representation forms to express distinct preference information for different experts, ...primarily due to their diverse backgrounds. To address the problem of reducing information loss from the aggregation of experts' opinions in heterogeneous MAGDM as well as improving the interpretability of the decision-making process, this paper introduces a concept lattice-based heterogeneous MAGDM approach. The heterogeneous multi-expert formal context is first proposed to capture the heterogeneous evaluation information of alternatives provided by different experts. Then, extended multi-expert concept lattices are constructed to aggregate evaluation information of alternatives by different experts. In this case, all concepts are considered to minimize information loss during the aggregation process. Second, to obtain more reasonable decision results, the distance between the concept intents and the heterogeneous positive and negative ideal solutions is considered, and the alternatives are ranked based on this measure. In addition, the MAGDM process for each alternative is visualized using the extended multi-expert concept lattices. This representation aids in identifying key concepts, their interdependencies, and the overall impact on the decision result. Finally, numerical examples and comparative analysis validate the validity and rationality of the proposed approach in heterogeneous MAGDM.
MℬJ-Filters on Lattice Implication Algebras Amarendra Babu, V; Naga Malleswari, V Siva; Begum, K Abida
Journal of physics. Conference series,
09/2022, Letnik:
2332, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Abstract
We explored the some equivalent conditions and properties of MℬJ-filters of Lattice implication algebras. As well we define MℬJ-lattice filters of Lattice implication algebras. Finally, it ...was established that MℬJ-Lattice filter is an MℬJ-filter, but not the other way around.
During the multi-attribute group decision-making (MAGDM) processing, the individuals often hold different opinions about the alternatives. It is necessary to aggregate the different individual ...opinions into a unified group opinion. In the real world, experts sometimes use linguistic expressions to evaluate attributes in uncertain environments. To address the problem of reducing the information loss of expert opinion aggregation in MAGDM, this paper proposes a MAGDM approach based on linguistic concept lattices in the context of uncertain linguistic expression. A linguistic concept lattice for multi-expert linguistic formal context is first constructed based on linguistic truth-valued lattice implication algebra, which can express both comparable and incomparable linguistic information in the decision-making process. Different expert opinions are aggregated via the extent of fuzzy linguistic concepts, which can reduce information loss in the aggregation process. Second, meet-irreducible elements in the linguistic concept lattice are introduced to reduce the computational complexity of obtaining all fuzzy linguistic concepts in the decision-making process. the distance between the intents of different fuzzy linguistic concepts is considered to enhance the rationality of linguistic decision results. In addition, the expert’s decision-making process for each alternative is visualized via linguistic concept lattices. Finally, the case study and comparative analysis illustrate the validity and rationality of the proposed approach in MAGDM with linguistic information.
•The fuzzy linguistic concepts are used to aggregate expert opinions.•The comparable and incomparable linguistic information is handled in MAGDM.•Visualize the decision-making process of experts by constructing concept lattices.•A novel linguistic concept lattice-based MAGDM approach is proposed.
Numerous linguistically valued facts from the actual world have been modeled using the fuzzy linguistic approach. Concept lattice theory has the potential to be used in information processing in ...imprecise language environments as a methodology for data analysis and knowledge representation. The concept lattice with linguistic values can manage fuzzy linguistic data which are either comparable or incomparable. However, the acquired conceptual knowledge is difficult to understand due to the substantial amount of linguistic concept knowledge in the concept lattice with imprecise linguistic information. This work proposes a linguistic-valued layered concept lattice simplification method based on three-way clustering to reduce the scale of the linguistic-valued layered concept lattice. In order to create the linguistically valued layered concept lattice, a reconstruction function is first used to produce an attribute selection model in fuzzy linguistic formal contexts. Second, the intent similarity and extent similarity are employed to achieve the concept similarity measure in linguistic-valued layered concept lattices, taking into account the relationship among various layers of fuzzy linguistic values. To get the initial concept hard clustering results, the linguistic-valued layered concepts are then clustered using k-modes clustering. In addition, we explore the classification of boundary linguistic-valued layered concepts and achieve the three-way clustering findings of linguistic-valued layered concepts to deal with the ambiguity of linguistic expressions. Finally, experimental findings on real-world datasets show how effective the proposed method is for simplifying linguistic-valued layered concept lattices.
The increasing complexity of decision-making environments has led to a rise in the involvement of decision-makers (DMs) in group decision-making problems. Clustering is widely used in large-scale ...group decision-making (LSGDM) to categorize DMs into smaller groups. Ensuring reasonable decision-making results requires providing explanations for the generated groups during the clustering process. To address the clustering problem in LSGDM within uncertain linguistic environments, this paper proposes a conceptual clustering method based on the linguistic concept lattice. The method efficiently manages comparable and incomparable linguistic information. To achieve interpretable clustering results for DMs, attribute and expert induction matrices are first introduced. Cluster stability analysis is then employed to automatically determine the optimal number of clusters. Second, linguistic truth-valued aggregation operators are proposed to aggregate the linguistic evaluation information of DMs in each cluster. In addition, a consensus reaching process is conducted within each cluster, and a feedback mechanism is established to iteratively update clusters when consensus cannot be reached. Finally, numerical examples and comparative analyses are presented that verify the effectiveness of the proposed approach in effectively addressing the LSGDM problem within uncertain linguistic environments.
•Using conceptual clustering for the LSGDM problem.•Linguistic concepts are provided as explanations for the clustering results.•The comparable and incomparable linguistic information is handled in LSGDM.•A novel linguistic concept lattice-based LSGDM approach is proposed.
A 2-dimension linguistic lattice implication algebra (2DL-LIA) can build a bridge between logical algebra and 2-dimension fuzzy linguistic information. In this paper, the notion of a Boolean element ...is proposed in a 2DL-LIA and some properties of Boolean elements are discussed. Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated. Moreover, it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.
In real decision making problems, it is always more natural for decision makers to use linguistic terms to express their preferences/opinions in a qualitative way among alternatives than to provide ...quantitative values. Additionally, many of these decision making problems are under uncertain environments with vague and imprecise information involved. Following the idea of Computing with Words (CWW) methodology, we propose in this paper a linguistic valued qualitative aggregation and reasoning framework for multi-criteria decision making problems, where a linguistic valued algebraic structure is constructed for modelling the linguistic information involved in multi-criteria decision making problems, and a linguistic valued logic based approximate reasoning method is developed to infer the final decision making result. This method takes the advantage of handling the linguistic information, no matter totally ordered or partially ordered, directly without numerical approximation, and having a non-classical logic as its formal foundation for decision making process.
The 2-dimension linguistic information includes two common linguistic labels. One dimension is used for describing the evaluation result of alternatives provided by the decision maker, and the other ...is used for describing the self-assessment of the decision maker on the reliability of the given evaluation result. In order to deal with comparability and incomparability of 2-dimension linguistic labels (2DLLs), a 2-dimension linguistic lattice implication algebra (2DL-LIA) is constructed as a linguistic evaluation set with lattice structure. In this paper, a 2DLL is firstly represented by two 2-tuples in a 2DL-LIA for more precise computing and aggregating 2-dimension linguistic information. This model allows a continuous representation of 2DLL on its domain, therefore, it can represent any continuous 2-dimension linguistic information obtained in the aggregation process. Next, two new 2-dimension linguistic aggregation operators, including 2-dimension linguistic weighted arithmetic aggregation (2DLWAA) operator and 2-dimension linguistic ordered weighted arithmetic aggregation (2DLOWAA) operator, are developed, and then some desirable properties of the operators are studied. Subsequently, based on 2DLWAA and 2DLOWAA operators, a decision making approach is provided to solve multi-attribute group decision making (MAGDM) problem with 2DLL assessment. Finally, an illustrative example is provided to show the concrete steps of the developed decision making approach and to demonstrate the practicality and the flexibility of this proposal by comparing with existing decision making approaches.
In many application domains, there is an urgent need for data owners to mine attribute associations hidden in linguistic conceptual knowledge. Numerous linguistically valued facts from the actual ...world have been modeled using the fuzzy linguistic approach. To solve the problem of association rule mining with fuzzy linguistic information, this paper proposes an association rule mining approach based on fuzzy linguistic attribute partial ordered structure diagram (FL-APOSD). First, complex relationships between linguistic values in association rule mining are represented by fuzzy linguistic association nodes and association paths via FL-APOSD. On this basis, the maximum frequent attribute set is mined from the FL-APOSD, and then the non-redundancy association rules are extracted. Second, to show the information hidden in the rules and help users to deeply understand the mining results, a fuzzy linguistic association rule visualization approach is proposed to convert the association rules into the FL-APOSD-based knowledge representation. Finally, experimental results on real-world datasets show the proposed approach’s high efficiency, outperforming two relevant state-of-the-art approaches.
Algebraic characters of linguistic truth-valued lattice implication algebras (L-LIAs) are focused in this paper. Concretely, the concept of derivation coming from analytic theory is introduced in ...L-LIAs, and then some properties of derivations are given in L-LIAs. Subsequently, some special derivations (such as isotone deri-vation, embedding derivation, isomorphism derivation and regular derivation) are discussed in L-LIAs along with the relations among them. The relations between derivations and lattice implication homomorphisms are also investigated in L-LIAs. At the end, the derivations of some algebraic substructures are described in L-LIAs.
