Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory More
Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a universe. There are many studies on the relations between generalized rough set approximation and rough topological space. In this paper, We are defined some properties of an n-ary relation such as reflexive, symmetry, strongly symmetry, quasi-transitive, n- transitive and n-equivalence on a set . We introduce topological method to generalized rough set and study the relationship between topological theory and rough set theory. By using an n-ary tolerance relation and quasi-transitive relation, we define a topology on nonempty set . In the end, we prove some topological properties such as quasi-discreteness, connectivity, compactness, quasi-metric able, separateness.
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Background and Objective: The Purpose of this research is evaluating the Competitive of Green Product Development Consequences in the Existence of Technology-Based Capabilities of Knowledge-Based Companies: Extended Rough Set Theory (ERST).
Material and Methodology: Th More
Background and Objective: The Purpose of this research is evaluating the Competitive of Green Product Development Consequences in the Existence of Technology-Based Capabilities of Knowledge-Based Companies: Extended Rough Set Theory (ERST).
Material and Methodology: The methodology of this research is hybrid and to perform it, hyper-combined analyzes have been used to identify the components and propositions of the research in the qualitative part and the rough set has been used to determine the most effective components and propositions in the quantitative part. The target population was qualitative, similar research and academic experts in management. However, the target population was a quantitative part number of 22 executives of knowledge-based companies in food products, which is acceptable from the statistical population due to the requirement of Rough Set Theory.
Findings: The results of the study indicated the identification of 4 components of competitive implications for green product development and 5 themes of technology-centric capabilities in the quality sector. Also, the results in the quantitative part showed that the effective management information system is considered as the most effective technology capability of knowledge-based companies as a positive stimulus in the consequences of green product development.
Discussion and Conclusion: The result shows that management information systems as one of the most important achievements of technology as the capabilities of knowledge-based companies can, in a systematic cycle to determine information from outside the company and perform processes on it to make effective decisions and staff. It is the increase of environmental productivity as a favorable consequence of green product development in these companies.
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In fuzzy set theory, the concept of a non-membership function and the hesitation margin were not considered while these two concepts have been included along with the membership function for intuitionistic fuzzy sets. It is also to be noted that the intuitionistic fuzzy More
In fuzzy set theory, the concept of a non-membership function and the hesitation margin were not considered while these two concepts have been included along with the membership function for intuitionistic fuzzy sets. It is also to be noted that the intuitionistic fuzzy set is reflected as an extension of the fuzzy set accommodating both membership and non-membership functions together with a hesitation margin. In the intuitionistic fuzzy set theory, the sum of the membership function and the non-membership function is a value between 0 and 1. In recent times, intuitionistic fuzzy rough set theory has emerged as a powerful tool for dealing with imprecision and uncertain information in relational database theory. Measures of similarity between fuzzy rough sets as well as intuitionistic fuzzy rough sets provide wide applications in real-life problems and that is why many researchers
paid more attention to this concept. Intuitionistic fuzzy rough set theory behaves like an excellent tool to tackle impreciseness or uncertainties. In this paper, we propose a new approach of similarity measure on an intuitionistic fuzzy rough set based on a set-theoretic approach. The proposed measure is able to give an exact result. In the application part, we consider a real-life problem for selecting a fair play award-winning team in a cricket tournament and describe the algorithm.
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