Fuzzy-grey system is an ambiguous system where unclear, incomplete and only small data is available. Fuzzy Grey relational maps model the causal relation between complex systems. In this fuzzy model, the nodes are fuzzy while the edges are grey and they represent the grey causal relationship between two disjoint sets of concepts. Intelligence is one of the most admired and coveted features of human mind for, human intelligence has played a greater role in placing human beings at the top of the evolutionary pyramid of creation. Intelligence is widely accepted as hereditary, but at the same time there are researches going on to prove that it is also influenced by the beliefs the individual holds. In this paper, the causal influence between intelligence and self-beliefs is studied using Fuzzy Grey relational maps.

Fuzzy Relational Map is an efficient tool in establishing the causal relationship between two disjoint sets of concepts. In situations, wherein the data available is unsupervised involving emotions and reasons described in a language that is vague or difficult to interpret, Fuzzy Relational Map is the pertinent approach of choice. Personality is a psychological construct that has different traits and these traits have some unique behavioral beliefs underneath. In this paper, an extension of a fuzzy relational map called aggregatedFuzzyRelational Map is used to study the association between the traits of personality and the behavioral beliefs that influence a certain type of personality. Further, the fixed points are analyzed with the aid of Kosko-Hamming Distance.

Fuzzy relational maps are neuro-fuzzy systems that are useful in approximate reasoning. A problem that is studied by several experts simultaneously using an FRM model choosing different sets of concepts would require an appropriate model to capture the consensus of the experts opinion pertaining to the problem under study. Special Mixed Fuzzy relational map (SMFRM) is identified as an appropriate fuzzy tool to be used in situations where different experts study a problem with different set of concepts. SMFRM is an extension of FRM which is the union of several fuzzy relational maps. In this paper, the model Special Mixed Fuzzy relational map (SMFRM) is used to study the causal relationship between human emotions and beliefs.

Achievement in mathematics is widely recognised as a sign of intelligence and cognitive development. Students’ involvement in acquiring mathematical competencies is not just automatic, but needs conscious efforts from the part of students. The intrinsic factor that motivates the students to plunge into activities that develop mathematical competencies is self-belief or belief system. The relationship between personal beliefs and competencies acquired is so important that it attracts the interest of researchers to create an ‘intellectual and competent’ community. In this paper, the causal influence of mathematics related beliefs on mathematical competencies is studied using a hybrid fuzzy model called IVIFRM-TOPSIS. This expert based method is more comprehensive in its approach as the uncertain information is modelled with interval-valued intuitionistic fuzzy sets. This study exhibits the efficiency of the fuzzy hybrid model in analysing the causal relationship and ranking the order of influence.