Recommending Turmeric Variety for Higher Production Using Interval-Valued Fuzzy Soft Set Model and PSO

Introduction

Fuzzy set (Zadeh, 1965) is one of the most popular mathematical models for handling uncertainty and vagueness in data. Fuzzy set is used in almost all domains of computer science. Zadeh (1975) introduced interval valued fuzzy set (IVFS) and approximate reasoning. IVFS is a generalized model of fuzzy set where membership value of an element is an interval lying in [0, 1], instead of being an element in it. Atanassov (1986) introduced another generalized model of fuzzy set called as intuitionistic fuzzy set (IFS). In IFS model, non-membership value of an element in the set is not necessarily the one’s complement of its membership and can be less than that value. So, hesitation comes into picture which makes IFS more realistic than fuzzy set. If the hesitation becomes zero, the IFS reduces to fuzzy set. In Atanassov (1989), it is proved that IFS and IVFS are equipollent generalizations of the notion of fuzzy set.

The notion of soft set introduced by Molodtsov (1999) which associates each parameter to a subset of elements in the universe of discourse. Soft set gives topological flavour to classical set theory. Subsequently, many new operations are given in Maji et al (2003, 2004) and Tripathy and Arun (2015). Tripathy and Arun (2015) redefined soft set using characteristic function approach, which made the definition of soft set and operations defined over it more authentic and easier to understand. Also, the definitions became more accurate and meaningful.

It has been observed that suitable hybrid models have been found to be more efficient than their individual components. Maji et al (2002) extended the notion of soft set by introducing the notion of fuzzy soft set. Yang et al (2009) enhanced the concept and introduced Interval valued fuzzy soft set by combining IVFS and Soft set. Xu et al. (2010) extended further to introduce IFSS by fusing the notion of IFS with soft set. Using the characteristic approach Tripathy et al (2016a, 2016b, 2016c, 2016d, 2016e, 2016f, 2016g, 2016h, 2017, 2018), Tripathy and Panigrahi(2016), Sooraj and Tripathy(2018), Sooraj et al (2015, 2017,2018a, 2018b), Mohanty et al (2017), Mohanty and Tripathy (2017, 2020) have defined many other hybrid models of soft set. Applications of these models are also provided in these papers. The applications are mostly based on different kinds of decision making problems. Tripathy et al redefined fuzzy soft set (FSS) to systemize many operations as given in (Tripathy et al., 2016a). Similarly, membership function for IFSS is defined in Tripathy et al (2016b). Tripathy et al. (2016a) identified many issues in Maji et al (2002) and rectified them while introducing a new algorithm for decision making.

The number of parameters in a soft set is directly proportional to the time complexity for the decision making. So, to reduce time complexity, we need to reduce the number of parameters. The significance of parameters need to be computed to remove less significant parameters by which the final decision would not change. There are many articles in literature for soft set parameter reduction. In this paper we have followed the approach of Kong et al (2015) for parameter reduction using PSO algorithm. There are many evolutionary algorithms in the literature for optimization. Few such techniques are mentioned in (Reddy et al. 2018, 2019; Gadekallu et al. 2020)

Without doubt, it is important to choose a good variety as per the demand of the environmental circumstances to get more production. If the selected variety is better as per the environmental factors, then the quality of crop will also be improved. To decide a variety, it is necessary to think about many parameters like soil type, temperature, humidity, rain, expenses, selling price, profit etc. Selection of quality parameter is also a concern (Padma et al, 2016). Some techniques to overcome agricultural crises mentioned in (Devereux, 2002; Dercon, 2002). All the parameters to choose a better variety are uncertain in nature. So, it is important to use a suitable model which can handle uncertainty. There exist a lot of uncertainty based models to handle uncertainties. Some of the most popular uncertainty based models which are popular now are fuzzy sets, rough sets, soft sets, their generalisations and hybrid models formed from them.