An interval extension of homogeneous and pseudo-homogeneous t-norms and t-conorms

Homogeneity of Complex Fuzzy Operations

The homogeneity of binary functions on the unit interval [0, 1] is a very useful property in many real practical applications. This paper studies the homogeneity of binary functions on the unit circle of the complex plane. The homogeneity is a generalization of both rotational invariance and ratio scale invariance for complex fuzzy operations. We show that a binary function is homogeneous if and only if it is both rotationally invariant and ratio scale invariant. Moreover, we consider the simplification of the homogeneity for complex fuzzy binary operators.

Interval-Valued Pseudo Overlap Functions and Application

A class of interval-valued OWA operators can be constructed from interval-valued overlap functions with interval-valued weights, which plays an important role in solving multi-attribute decision making (MADM) problems considering interval numbers as attribute values. Among them, when the importance of multiple attributes is different, it can only be calculated by changing the interval-valued weights. In fact, we can directly abandon the commutativity and extend the interval-valued overlap functions (IO) to interval-valued pseudo overlap functions (IPO) so that function itself implies the weights of the attributes, thus there is no need to calculate the OWA operator, which is more flexible in applications. In addition, the similar generalization on interval-valued pseudo t-norms obtained from interval-valued t-norms further enhances the feasibility of our study. In this paper, we mainly present the notion of interval-valued pseudo overlap functions and a few their qualities, including migrativity and homogeneity, and give some construction theorems and specific examples. Then, we propose the definitions of residuated implications induced by interval-valued pseudo overlap functions, give their equivalent forms, and prove some properties satisfied by them. Finally, two application examples about IPO to interval-valued multi-attribute decision making (I-MADM) are described. The results show that interval-valued pseudo overlap functions can not only be used to obtain the same rankings, but also be more flexible, simple and widely used.

A study of an EOQ model where the demand depends on time and varying number of tourists using fuzzy triangular norms

The fundamental prerequisite of decision making is how to aggregate individual expert's preference information. For constructing various aggregation operators on intuitionistic fuzzy set, various kinds of t-norms and co-norms are the most significant tools. This work takes a closer look on various fuzzy triangular norms and uses them for the first time in an economic order quantity (EOQ) model. Traditional economic theory has a paradigm shift on objective factors affecting demand such as price and income. Recently, behavioural economics gives more weightage to psychological and social factors that affect our preferences and choices in markets differently. As per literature survey concern, this paper may indeed be the first to adopt the concept of the number of variations of a tourist's dependent demand in inventory management problems. Utilizing several triangular norms, we have characterized Attanassov (standard) and non-Attanassov's (non-standard) feasible region. A case study has been performed for numerical illustration and model validation. A solution algorithm, has also been developed which proves Attanassov's solution space is quite inferior to non-Attanassov's domain. Finally, sensitivity analysis and graphical illustrations are also provided to justify the model.

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