The fuzzy linguistic approach provides favorable outputs in several areas, whose description is relatively qualitative. The encouragement for the utilization of sentences or words instead of numbers is that linguistic characterizations or classifications are usually less absolute than algebraic or arithmetical ones. In this research article, we animate the m-polar fuzzy (mF) linguistic approach and elaborate it with real life examples and tabular representation to develop the affluence of linguistic variables based on mF approach. As an extension of the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, we develop an m-polar fuzzy linguistic TOPSIS approach for multi-criteria group decision-making (MCGDM). It is used to evaluate the best alternative, to get more authentic and comparable results and to handle the real life problems of having multi-polar information in terms of linguistic variables and values. In this approach decision-makers contribute their estimations in the form of linguistic term sets. To show the efficiency and compatibility of the proposed approach, we compare it with the m-polar fuzzy linguistic ELECTRE-I (Elimination and Choice Translating Reality) approach. Finally, we draw a flow chart of our proposed approach as an algorithm and generate a computer programming code.

In this article, we introduce the concept of graphs associated with commutative UP-algebra, which we say is a UP-graph whose vertices are the elements of commutative UP-algebra and whose edges are the association of two vertices, that is two elements from commutative UP-algebra. We also define a graph of equivalence classes of a commutative UP-algebra and prove some related results based on the algebraic properties of the graph. We show that two graphs are the same and complete bipartite if they are formed by equivalence classes of UP-algebra and the graph folding of commutative UP-algebra. An algorithm for checking whether a given set is a UP-algebra or not has also been given.

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Parameter reduction is a very important technique in many fields, including pattern recognition. Many reduction techniques have been reported for fuzzy soft sets to solve decision-making problems. However, there is almost no attention to the parameter reduction of bipolar fuzzy soft sets, which take advantage of the fact that membership and non-membership degrees play a symmetric role. This methodology is of great importance in many decision-making situations. In this paper, we provide a novel theoretical approach to solve decision-making problems based on bipolar fuzzy soft sets and study four types of parameter reductions of such sets. Parameter reduction algorithms are developed and illustrated through examples. The experimental results prove that our proposed parameter reduction techniques delete the irrelevant parameters while keeping definite decision-making choices unchanged. Moreover, the reduction algorithms are compared regarding the degree of ease of computing reduction, applicability, exact degree of reduction, applied situation, and multi-use of parameter reduction. Finally, a real application is developed to describe the validity of our proposed reduction algorithms.

We introduce a notion of oriented dialgebras and develop a cohomology theory for oriented dialgebras based on the possibility to mix the standard chain complexes computing group cohomology and associative dialgebra cohomologies. We also introduce a 1-parameter formal deformation theory for oriented dialgebras and show that cohomology of oriented dialgebras controls such deformations.

A motion of a robot in space is represented by a graph. A robot change its position from point to point and its position can be determined itself by distinct labelled landmarks points. The problem is to determine the minimum number of landmarks to find the unique position of the robot, this phenomena is known as metric dimension. Motivated by this a new modification was introduced by Kelenc. In this paper, we computed the edge metric dimension of barycentric subdivision of Cayley graphs Cay(Z α ⊕Z β), for every α ≥ 6, β ≥ 2 and an observation is made that it has constant edge metric dimension and only three carefully chosen vertices can appropriately suffice to resolve all the edges of barycentric subdivision of Cayley graphs Cay(Z α ⊕ Z β).

Coronoid systems actually arrangements of hexagons into six sides of benzenoids. By nature, it is an organic chemical structure. Hollow coronoids are primitive and catacondensed coronoids. It is also known as polycyclic conjugated hydrocarbons. The mathematical study of chemicals is of great interest to different specialties researchers. While graph theory always played a significant role to make chemical structures understandable and blessed with applications also. After transforming the chemical structure into a graph, one can implement different theoretical and implicative studies on structures. Metric dimension is considered as one of the most studied and implicative parameters of graph theory. In this concept, few suggested vertices are chosen such as the remaining vertices have unique locations or identifications. In this study, we discussed different metric-based parameters for the hollow coronoid structure. INDEX TERMS Hollow coronoid; metric dimension; resolving set; fault-tolerant metric dimension.

Geometric arrangements of hexagons into six sides of benzenoids are known as coronoid systems. They are organic chemical structures by definition. Hollow coronoids are divided into two types: primitive and catacondensed coronoids. Polycyclic conjugated hydrocarbon is another name for them. Chemical mathematics piques the curiosity of scientists from a variety of disciplines. Graph theory has always played an important role in making chemical structures intelligible and useful. After converting a chemical structure into a graph, many theoretical and investigative studies on structures can be carried out. Among the different parameters of graph theory, the dimension of edge metric is the most recent, unique, and important parameter. Few proposed vertices are picked in this notion, such as all graph edges have unique locations or identifications. Different (edge) metric-based concept for the structure of hollow coronoid were discussed in this study.