Formal Representation of the Theory of Alternatives in Mobilization

This research article expands the formal representation of human thinking to a most generalized hybrid theory, namely, complex q‐rung orthopair fuzzy N‐soft set. It is able to capture a great deal of graded imprecision and vagueness, which so often appear together in human interpretations. This model renders a parameterized mathematical tool for the ranking‐based fuzzy modeling of two‐dimensional paradoxical data. To that purpose, the proposed theory integrates complex q‐rung orthopair fuzzy sets with the parametric structure of N‐soft sets. The framework that arises captures information beyond the confined space of complex intuitionistic fuzzy N‐soft sets and complex Pythagorean fuzzy N‐soft sets, with the assistance of a parameter q. We establish the basic set‐theoretical operations of this model and prove some of its fundamental properties. The Einstein and other elementary algebraic operations on complex q‐rung orthopair fuzzy N‐soft values shall be introduced to broaden the mathematical toolbox of this field. Its relationships with contemporary approaches shall demonstrate its outstanding flexibility. Moreover, we establish two competent multicriteria decision‐making algorithms that capture the nuances of periodical inconsistent data. Their feasibility shall be demonstrated with an explicit application to the selection of optimum aerospace technology required for the economic development of the Mexican space agency. A comparative analysis of both strategies with the prevailing techniques substantiates their rationality. In addition, we illustrate this comparative study with an explicative bar chart that shows the compatibility of their outcomes. Finally, we examine the functionality of the proposed model and compare it with alternative theories.


 
 
 Description Logics (DLs) are a family of well-known terminological knowledge representation formalisms in modern semantics-based systems. This research focuses on analysing how our developed Occurrence Logic (OccL) can conceptually and logically support the development of a description logic. OccL is integrated into the alternative theory of natural language syntax in Deviational Syntactic Structures under the label ‘EFA(X)3’ (or the third version of Epi-Formal Analysis in Syntax, EFA(X), which is a radical linguistic theory). From the logical point of view, OccL is a formal logic that mainly deals with the occurrences of symbols as well as with their priorities within linguistic descriptions, i.e. natural language syntax, semantics and phonology. In this article—based on our OccL-based definitions of the concepts of strong implication and occurrence value as well as of the logical concept Identical Occurrence Constructor (IDOC) that is the most fundamental logical concept in our formalism—we will model Occurrence Description Logic (ODL). Accordingly, we will formally-logically analyse ‘occurrence(s) of symbol(s)’ within descriptions of the world in ODL. In addition, we will analyse and assess the logical concepts of occurrence and occurrence priority in ODL. This research can make a strong logical background for our future research in the development of a Modal Occurrence Description Logic.