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Key research themes
1. How are neutrosophic soft set extensions applied for modeling uncertainty and decision making?
This theme explores the integration of neutrosophic sets with soft set theory, leading to neutrosophic soft sets and their generalizations (intuitionistic neutrosophic soft set, generalized neutrosophic soft set). These frameworks aim to handle imprecise, indeterminate, inconsistent, and vague data more effectively than classical fuzzy or soft sets, addressing uncertainty in complex decision making.
Key finding: The paper defines intuitionistic neutrosophic soft set (INSS) by combining intuitionistic neutrosophic sets with soft sets, introduces key operations such as equality, subset, union, and intersection, and establishes... Read more
Key finding: Introduces generalized neutrosophic soft sets (GNSS), extending generalized neutrosophic sets with soft set frameworks. Defines operations like subset, union, intersection, and applies GNSS to multi-criteria decision making,... Read more
Key finding: The paper formulates neutrosophic parameterized soft sets (NP-soft sets) as a generalization of fuzzy parameterized soft sets, introduces associated operations and aggregation operators, and presents a structured method to... Read more
Key finding: Combines neutrosophic vague sets and soft expert sets into neutrosophic vague soft expert sets (NVSES), introduces operations like complement, union, intersection, AND, OR, and studies algebraic properties. NVSES allows... Read more
2. What advances have been made in parameterization and multiparameter generalizations of soft sets?
This research area investigates the expansion of soft sets from single parameter sets to multiple or multiparameterized frameworks. It includes formalizing soft multisets, multiparameterized soft sets, and bipolar soft sets, aiming to represent complex multi-attribute decision problems and model negation and opposition in parameter sets for enhanced flexibility and expressiveness.
Key finding: Defines soft multisets as generalizations of Molodtsov’s soft sets to collections of multiple universes and parameter sets, formalizes basic operations (complement, union, intersection) for these multisets, and provides... Read more
Key finding: Introduces multiparameterized soft sets, a generalization involving multiple parameter sets for one universe, and develops operations such as complement, union, intersection, and OR. Examples illustrate the concept for... Read more
Key finding: Redefines bipolar soft sets with a more functional approach using bijective functions to represent negation systematically, defines enhanced operations including union, intersection, and complement, and applies the model to... Read more
3. How do soft set extensions relate to topological and algebraic structures to enable novel theoretical and application insights?
This theme covers the incorporation of soft sets into broader mathematical structures such as topologies (soft topology, interval-valued soft topology) and algebraic structures (soft semigroups, generalized algebraic codes). These generalizations support deeper theoretical developments and facilitate applications in decision making, data analysis, and coding theory by enriching the representation and operations on soft sets.
Key finding: Proposes weakly soft semi-open subsets as a new class of generalizations of soft open sets within soft topological spaces, characterizes their structural properties, and relates them to earlier generalizations with... Read more
Key finding: Introduces fuzzy soft semigroups as a generalization of soft semigroups with fuzzy parameterization, defines product operations and various ideal-related notions (quasi-ideals, bi-ideals), investigates algebraic properties... Read more
Key finding: Develops soft linear algebraic codes using soft set theory, defines soft canonical generator and parity check matrices and soft syndromes for encoding/decoding, and constructs error detection and correction methods.... Read more
Key finding: Defines interval-valued fuzzy topologies (cotopologies) on soft sets, establishes that such topologies form descending families of soft topologies, and investigates related structures such as interval-valued fuzzy... Read more