Iranian journal of fuzzy systems
Volume:19 Issue: 6, Nov-Dec 2022

This work studies Interval Initial Value Problems (IIVPs), where the derivative is given by the generalized Hukuhara derivative ($gH$-derivative) and the initial condition is given by an interval. The focus of the paper is to provide the numerical approximations for the solutions associated with the $gH$-derivative of IIVPs. This article considers the Euler numerical method, where the classical arithmetic operation is adapted for intervals. The arithmetic considered here is obtained using sup-$J$ extension principle, where $J$ is a particular family of joint possibility distributions. This family gives raise to different types of interactivity and this work shows what kind of interactivity is necessary in the numerical method, in order to approximate the solution via $gH$-derivative. To illustrate the results, the paper focuses in the decay Malthusian model.

The issue of distributivity of aggregation operators is crucial for many different areas such as the utility theory  and the integral theory. The topic of  this paper is distributivity between 2-uninorms and Mayor's aggregation operators. The presented research is an extension and upgrade ofthe previously obtained results. The full characterization of distributive pairs of operators is given.

Picture fuzzy set is characterized by neutral membership function along with the membership and non-membership functions, and is, therefore, more general than the intuitionistic fuzzy set which is only characterized by membership and non-membership functions. In this paper, first, we are going to point out a drawback and try to fix it by the existing trapezoidal picture fuzzy number. Furthermore, we define an $LR$ flat picture fuzzy number, which is a generalization of trapezoidal picture fuzzy numbers. We also discuss a linear programming model with $LR$ flat picture fuzzy numbers as parameters and variables and present a method to solve these type of problems using a generalized ranking function.

One of the main goals of network planners is the protection of important nodes in a network against natural disasters, security threats, attacks, and so on.  Given the importance of this issue,  a new model is presented in this paper for protecting an important node  in a typical network based on a defensive location problem where the two  agents threaten  this node.  The protecting facilities location problem with two agents is formulated as a three-level programming problem.   The decision maker in the upper level is a network planner agent. The planner agent wants to find the best possible location of protecting facilities  to protect the important node against threatening agents. The second and third levels problems are stated as the shortest path problems in the network in which the edges are weighted with positive values. In this work, the genetic, variable neighborhood search, simulated annealing algorithms are used to solve the problem.  The performance of the used metaheuristic algorithms on this class of problems is investigated by a test problem that is generated randomly. Then,   t-test  are used to compare the performance of these algorithms. The best results are obtained by  the variable neighborhood search algorithm.

We introduce generalized structures of L-algebras, called pseudo L-algebras, which are the multiplication reduct of pseudo hoops and are structures combining two L-algebras with one compatible order. We prove that every pseudo hoop gives rise to a pseudo L-algebra and every pseudo effect algebra gives rise to a pseudo L-algebra. The self-similarity is the most important property of an L-algebra $L$, which guarantees to induce a multiplication on $L$. We introduce a notion of self-similar pseudo L-algebras and prove that a self-similar pseudo L-algebra becomes an L-algebra if and only if the multiplication $\odot$ is commutative. We get some interesting results for self-similar pseudo L-algebras: (1) The negative cone $G^-$ of an $\ell$-group $G$ can be seen as a self-similar pseudo L-algebra. (2) Every self-similar pseudo L-algebra is a pseudo hoop. Next, we introduce the notion of self-similar closures of pseudo L-algebras and obtain a self-similar closure by a recursive method. Given a pseudo L-algebra $(L, \rightarrow, \rightsquigarrow ,1)$, we can generate a free semigroup $(A, \ast)$ by the set $L\setminus \{1\}$. Furthermore, we let $S(L)=A\cup\{1\}$ and define a binary operation $\odot$ on $S(L)$. Then we extend the operations $\rightarrow$ and $\rightsquigarrow$ from $L$ to $S(L)$, and prove that $(S(L), \rightarrow, 1)$ and $(S(L), \rightsquigarrow, 1)$ are two cycloids, respectively. Furthermore, under some conditions, $(S(L), \rightarrow, \rightsquigarrow, 1)$ becomes a self-similar pseudo L-algebra.  Finally, we introduce the notion of the structure group of pseudo L-algebras, and give an interesting example to show how to extend a pseudo L-algebra $L$ into the pseudo self-similar closure $S(L)$, and furthermore, derive it's structure group $G(L)$.

In this paper, we establish the GH-derivative of multiplication of fuzzy functions, the so-called product rule. For the first time, a product rule is constructed while both of the multiplied functions are assumed to be fuzzy without any restriction on the signs of multiplied functions. The rule is extracted based on the MCE-product and its property of distributivity. Then, we propose two important applications of the fuzzy product rule: An integration by parts formula for fuzzy functions and solving a nonlinear fuzzy differential equation. Some illustrative examples are given to verify the theoretical results.

In this paper using the connections between some subvarieties of residuatedlattices, we investigated some properties of the lattice of ideals incommutative and unitary rings. We give new characterizations for commutativerings $A$ in which $Id(A)$ is an MV-algebra, a Heyting algebra or a Booleanalgebra and we establish connections between these types of rings. We arevery interested in the finite case and we present summarizing statistics. Weshow that the lattice of ideals in a finite commutative ring is a Booleanalgebra or an MV-algebra (which is not Boolean).Using this result we generate the binary block codes associated to thelattice of ideals in finite commutative rings and we present a new way togenerate all (up to an isomorphism) finite MV-algebras using rings.

The conception of T-spherical fuzzy set (TSFS) is a recent phenomenon in the environment of fuzzy notions that describe opinion about some certain objects under uncertainties with the help of four types of degrees known as the degree of membership (DM), degree of abstinence (DA), degree of non-membership (DNM) and degree of refusal (DR). The focus of this manuscript, to examine the interrelationship among any numbers of T-spherical fuzzy numbers (TSFNs) by the use Maclaurin symmetric mean (MSM) operators. We investigate and develop T-spherical fuzzy (TSF) MSM (TSFMSM) operator, TSF weighted MSM (TSFWMSM) operator, TSF dual MSM (TSFDMSM) operator, TSF weighted dual MSM (TSFWDMSM) operator. By using these investigated operators, some special cases of the explored operators are also developed, and their properties are examined. In addition, an algorithm for handling multi attribute decision making (MADM) problems based MSM operators in TSF setting. An illustrative example to check the applicability of the MSM operators of TSFSs is presented where the evaluation of technology commercialization is observed. To show the superiority of the newly established MSM operators, a comprehensive comparative study is designed numerically. In view of the comparative analysis, some advantages of the new MSM operators of the TSFNs are stated.

This paper studies the quadratic programming problem subject to asystem of bipolar fuzzy relation equations with the max-productcomposition. A characterization of structure of its feasible domain is presented using the lower and upper bound vector on its solution set. A sufficient condition is proposed which under the condition, a component of one of its optimal solutions is the corresponding component of either the lower or upper bound vector. Some sufficient conditions are suggested to reveal one of its optimal solutions without resolution of the problem. Furthermore, some sufficient conditions are then given to determine some components from one of its optimal solutions. Based on these conditions, we can simplify the problem and reduce its dimensions. The simplified problem can be reformulated to an 0-1 mixed integer programming problem. Other unknown variables can be found by solving the current problem.

This article advances the idea of extended picture fuzzy set (E-PFS), which is especially an augmentation of generalised spherical fuzzy set (GSFS) by releasing the restricted selection of $p$ in the description of GSFSs.Moreover, by the use of triangular conorm term in the description of E-PFS, it indeed widens the scope of E-PFS not only compared to picture fuzzy set (PFS) and spherical fuzzy set (SFS), but also to GSFS. In the sequel, a given fundamental theorem concerning E-PFS depicts its more ability in comparison with the special types to deal with the ambiguity and uncertainty.Further, we propose a parametric E-PFS similarity measure which plays a critical role in information theory.In order for revealing the advantages and authenticity of E-PFS similarity measure, we exhibit its applicability in multiple criteria decision making entitling the recognition of building material, the recognition of patterns, and the selection process of mega project(s) in developing countries.Furthermore, through the experimental studies, we demonstrate that E-PFS is able to handle uncertain information in real-life decision procedures with no extra parameter, and it has a prominent role in decision making whenever the concepts of  PFS, SFS and GSFS do not make sense.

The aim of this paper is to introduce a new multiple attribute decision-making model named picture m-polar fuzzy soft sets, which is a combination of the soft sets and picture m-polar fuzzy set. Some operations and properties of the new model, including subset, equality, union, intersection, and complement are discussed.Further, the basic six definitions, three theorems, and six examples on picture m-polar fuzzy soft sets are explained. Lastly, we construct a new methodology to extend the TOPSIS to picture m-polar fuzzy soft sets (i.e., an application of  picture m-polar fuzzy soft sets) in which capable of different objects recognizing belonging to the same family is constructed and illustrated its applicability via a numerical example.

Hesitant fuzzy linguistic term set (HFLTS) is an approach giving ability to obtain more flexible decision-making (DM) process by integrating linguistic fuzzy modeling (LFM) with hesitative expert judgments. Although HFLTS is widely-studied in the literature and many enhancements are made on HFLTS procedure, none of these enhancements gives ability to continue with precise fuzzy modeling (PFM) in decision process. LFM has a big drawback about accuracy because of the dependency between the size of term set and the comprehensiveness of fuzzy sets (FSs). This issue creates a very critical difficulty in modeling of DM problems that need sensitive evaluations by using HFLTS. This paper aims to solve this problem by proposing a novel HFLTS methodology that is usable for DM problems that need sensitive calculations in the decision stage. The proposed methodology integrates 2-tuple LFM and linguistic fuzzy modifiers with HFLTS to overcome the accuracy problem and obtain more sensitive and flexible decision procedure. This paper also presents an envelopment transformation technique to aggregate expert assessments as a fuzzy membership function instead of membership grades. It becomes possible to keep interpretability in a certain level and achieve sensitive results at the same time with the help of these modifications. The proposed HFLTS approach is analyzed on a real case example from manufacturing industry for acceptance sampling plans (ASP) that is a DM problem requiring sensitive calculations. As another originality of the paper, the main formulations of ASP are derived based on hesitant fuzzy defectiveness information. The obtained results are also compared with some existing enhancements of the HFLTS and the success of the proposed methodology is proved in terms of sensitive calculation.