We introduce notions of soft rough m-polar fuzzy sets and m-polar fuzzy soft rough sets as novel hybrid models for soft computing, and investigate some of their fundamental properties. We discuss the relationship between m-polar fuzzy soft rough approximation operators and crisp soft rough approximation operators. We also present applications of m-polar fuzzy soft rough sets to decision-making.

Connectivity has an important role in neural networks, computer network, and clustering. In the design of a network, it is important to analyze connections by the levels. The structural properties of intuitionistic fuzzy graphs provide a tool that allows for the solution of operations research problems. In this paper, we introduce various types of intuitionistic fuzzy bridges, intuitionistic fuzzy cut vertices, intuitionistic fuzzy cycles, and intuitionistic fuzzy trees in intuitionistic fuzzy graphs and investigate some of their interesting properties. Most of these various types are defined in terms of levels. We also describe comparison of these types.

Graph theory has numerous applications in modern sciences and technology. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set. In this paper, we apply the concept of intuitionistic fuzzy sets to multigraphs, planar graphs, and dual graphs. We introduce the notions of intuitionistic fuzzy multigraphs, intuitionistic fuzzy planar graphs, and intuitionistic fuzzy dual graphs and investigate some of their interesting properties. We also study isomorphism between intuitionistic fuzzy planar graphs.

We introduce the notion of derivation for an MV‐algebra and discuss some related properties. Using the notion of an isotone derivation, we give some characterizations of a derivation of an MV‐algebra. Moreover, we define an additive derivation of an MV‐algebra and investigate some of its properties. Also, we prove that an additive derivation of a linearly ordered MV‐algebral is an isotone.

Hypergraph theory is the most developed tool for demonstrating various practical problems in different domains of science and technology. Sometimes, information in a network model is uncertain and vague in nature. In this paper, our main focus is to apply the powerful methodology of fuzziness to generalize the notion of competition hypergraphs and fuzzy competition graphs. We introduce various new concepts, including fuzzy column hypergraphs, fuzzy row hypergraphs, fuzzy competition hypergraphs, fuzzy k-competition hypergraphs and fuzzy neighbourhood hypergraphs, strong hyperedges, kth strength of competition and symmetric properties. We design certain algorithms for constructing different types of fuzzy competition hypergraphs. We also present applications of fuzzy competition hypergraphs in decision support systems, including predator–prey relations in ecological niche, social networks and business marketing.

We propose certain types of interval-valued fuzzy graphs including balanced interval-valued fuzzy graphs, neighbourly irregular interval-valued fuzzy graphs, neighbourly total irregular interval-valued fuzzy graphs, highly irregular interval-valued fuzzy graphs, and highly total irregular interval-valued fuzzy graphs. Some interesting properties associated with these new interval-valued fuzzy graphs are investigated, and necessary and sufficient conditions under which neighbourly irregular and highly irregular interval-valued fuzzy graphs are equivalent are obtained. We also describe the relationship between intuitionistic fuzzy graphs and interval-valued fuzzy graphs.